Fencing of landed properties is very common in Nigeria. For residential and commercial buildings in rural, semi-urban, and urban areas in Nigeria, it is very common to construct fences using sandcrete block walls around the perimeter of the property. Fencing is done for a lot of reasons such as security, restriction of unguided access, privacy, and protection of the property from encroachment and land grabbers.
Other materials can be used in the construction of fences such as concrete walls, sandcrete block walls, timber/wooden panels, gabion walls, steel plates, wire mesh, bricks etc. However, sandcrete blocks are the most common in Nigeria. This is mainly due to the availability of materials and labour, convenience, flexibility, different options for finishes, stability, low maintenance, and durability of sandcrete block fences.
Fence Construction in Nigeria
The materials that are commonly used for the construction of masonry wall fences are;
Sandcrete blocks
Cement
Sand
Gravel, and
Water
Other ancillary components that are usually found in fences are copings, railings, barbed fence wire, electric fence wires, etc. For beauty, other finishes such as cornices and mouldings of different types may be added. It is also important to note that fences are ultimately provided with access gates which can be constructed of wrought iron, timber, aluminium, or stainless steel.
Typical wire fence
For durability and aesthetics, it is very important that fences constructed with sandcrete masonry walls be plastered on both faces and the top of the wall protected with concrete coping. The coping may be precast or cast in-situ.
For fences that are to be constructed on sites with marginal soils or marshy soils with low bearing capacity, it is very important that reinforced concrete columns (pillars) be provided at intervals of about 3 metres. Normally also, it is not advisable to have a very long stretch of fence walls without introducing separation (open joints) or properly bound block pillars. This adds more stability and beauty to the wall, and prevents progressive failure whenever there is a lateral impact on the wall.
It is also important that the fence be chained (in a manner similar to reinforced concrete lintels) at the foundation level and/or at the mid-level. By so doing, the movements, swelling pressure, and shrinkage-induced stresses from the surrounding soil will not cause cracks or failure of the fence.
The height of the fence wall around a property can be determined by a lot of reasons such as building regulations, cost, client taste/intentions, aesthetic requirements, and security requirements. Typically, the average height of fences constructed using sandcrete blocks is around 2.25 metres (approximately 10 blocks) above the ground level. The height may however vary depending on some of the factors listed above which are explained below;
Building Regulations: In many locations or estates in Nigeria, there are laws or guidelines on how fences should be constructed. Some of these guidelines may include set-back from the road, height, design, colour, etc. The maximum height of a fence may occasionally be specified by a local government ordinance, building control or town planning agencies, etc., in which case all residents building fences in that region must abide.
Clients’ taste/intentions: Where regulations on fencing do not abide, the height and type of fence may also be influenced by individual preferences. Some people like shorter fences so they can display their homes better, while others may prefer a completely concealed compound. Sometimes also, the height of a fence may be influenced by cost, especially when the client is indifferent to security and/or privacy.
Aesthetic requirements: As was previously mentioned, the height of a fence may be influenced by the desire to display the home’s attractiveness. In this situation, people almost always choose short or average fences.
Security requirements: Many homeowners use higher fences to protect their homes from intruders, enhance privacy, and take people’s attention off their property. This is very typical in areas with volatile security issues.
TheProcess of Fencing in Nigeria
When fences are to be constructed on sites with good soil, strip foundations are typically adopted. For sloping terrain, the foundation can be stepped at intervals to prevent failure of the foundation due to scour or loss of bearing capacity due to erosion. The depth of foundation for fences is typically around 2 feet (600 mm), while the thickness of the concrete strip can be between 100 mm to 150 mm of grade 15 concrete, or according to the structural engineer (for challenging soils).
Stepped fence on a sloping terrain
Fences can be constructed using different types of sandcrete blocks such as 9 inches hollow blocks, six inches blocks (hollow or solid), five inches blocks (hollow or solid), etc. The process of constructing fences in Nigeria is therefore as follows;
(1) Excavation of the strip footing to the required level (2) Levelling and compaction of the footing base to receive concrete (3) Establishment of the block pillar or reinforced column locations and installation of appropriate bases and rebars (4) Pouring of the concrete strip footing (5) Laying of blocks and forming of the block pillars (where applicable) (6) Casting of the columns (where applicable) (7) Installation or casting of the copings (8) Installation of the gates and railings (9) Plastering and finishes (10) Installation of barbed wire or electric security wires
Cost of Fencing One Plot of Land in Nigeria
In many states in Nigeria, the size of one plot of land is 450 m2 (5000 ft2), typically comprising a parcel of land measuring 30 m x 15 m (100 feet x 50 feet). This dimension will be used in estimating the cost of fencing a plot of land in Nigeria. Furthermore, the size of the opening for gates is usually about (4 to 5 metres). For this calculation, 5 metres will be adopted.
It will be assumed that reinforced concrete columns will be provided at intervals of 3m across the fence line.
Therefore, the perimeter to be fenced = 2(30) + 2(15) – 5 = 85 m Height of fence = 2.25m (above natural ground level) + 0.5m (below ground level) = 2.75m
Cost of foundation excavation
Total number of partitions to be excavated = 24 Cost of excavation per partition = ₦1200 The total cost of excavation = ₦28,800
Cost of Concrete works (foundation and pillars)
The volume of concrete required for the foundation = 6m3 The volume of concrete required for columns = 2.8 m3 Cement required = 40 bags @ ₦4,200 = ₦168,000 Granite required = 15 tonnes = ₦135,000 (depending on location, transportation alone may double this price) Sand required = 10 tonnes = ₦40,000 Labour = ₦72,000 Total cost of concrete works = ₦415,000
Cost of Column formworks
1″x12″ planks = 28 pcs (reuse twice) @ ₦1,500 = ₦42,000 3″ inches nails (allow) = ₦4,000 Labour (allow) = ₦20,000 Total = ₦66,000
Cost of Column Rebars
Y10mm bars = 28 pcs @ ₦3,300 = ₦92,400 R6 mm stirrups = 35 pcs @ ₦1,200 = ₦42,000 Binding wire allow = 1 roll = ₦17,000 Labour allow = ₦25,000 Total = ₦176,400
On-going fence construction work
Cost of block wall
The total area of the block wall = 233.75 m2 Number of blocks required = 2340 (no allowance for wastes has been made) Unit Price of 6 inches blocks = ₦220 Total cost of blocks = ₦514,800
Cement required = 45 bags The unit price of cement = ₦4200 The total cost of cement = ₦189,000
Total cost for the fence walls = ₦514,800 + ₦189,000 +₦70,000 + ₦187,200 = ₦961,000
(Depending on the location, allowance for the cost of water should also be made) Furthermore, allowance for contingencies such as scaffolding should also be made.
The total cost of fencing one plot of land in Nigeria = ₦28,800 + ₦415,000 + ₦66,000 + ₦176,400 + ₦961,000 = ₦1,647,200
Therefore, the cost of fencing one plot of land in Nigeria is about ₦1,647,200, disregarding the contractor’s profit and overhead.
Luis Menard developed dynamic compaction (DC), also known as dynamic deep compaction, in the middle of the 1960s. However, there are claims that the technique was used more than a thousand years before. In this ground improvement technique, a heavy weight is dropped on the ground’s surface to compact soils to depths of up to 40 feet (12.5 metres).
The technique is utilised to reduce settlements in foundations, reduce seismic subsidence and liquefaction potential, permit development on fills, densify refuse dumps, enhance mining spoils, and reduce settlements in collapsible soils.
Applicable Soil Types for Dynamic Compaction
The most suitable types of soil for dynamic compaction are granular, permeable soils. In cohesive soils, the compaction energy tends to be absorbed by fine soil particles, which reduces the technique’s effectiveness. Table 1 shows the anticipated improvement for various soil types.
Soil Description
Expected Improvement
Typical Energy Required (tons ft/cf)
Gravel and sand <10% silt, no clay
Excellent
2.0 – 2.5
Sand with 10—80% silt and <20% clay, PI < 8
Moderate if dry; minimal if moist
2.5-3.5
Finer-grained soil with pI > 8
Not applicable
–
Landfill
Excellent
6-11
Table 1: Expected Improvement and Required Energy with Dynamic Compaction (Hussin, 2006)
Note that for Table 1 above, Energy = (drop height x weight x number of drops)/soil volume to be compacted; 1 ton ft/ft3 = 94.1 kJ/m3.
For the procedure to be successful, the groundwater table must be at least 6 feet (1.8 metres) below the working surface. Sand or stone columns have been built using dynamic compaction in organic soils by repeatedly filling the crater with the material and forcing the column through the organic layer.
Equipment
Although specifically designed rigs have been made, the weight is typically dropped using a cycle-duty crane. Standard cranes are often not designed to handle high-cycle dynamic loading, so in order to maintain a safe working environment, the cranes must be in good condition and constantly maintained and inspected while performing the operation.
Typical weight for dynamic compaction
The crane is often set up with enough boom to drop the weight from heights of 50 to 100 ft (15.4 to 30.8 m) and only one rope to let it almost “free fall,” maximising the force of the weight hitting the soil. The weight to be lowered must be less than the crane’s and cable’s safe single-line capability. Typically weights range from 10 to 30 tons (90 to 270 kN) and are constructed of steel to withstand the repetitive dynamic forces.
Procedure
Lifting and dropping a weight repeatedly till it hits the ground surface is the major technique for dynamic compaction. The primary drop locations are normally laid out in a grid of 10 to 20 feet (3.1 to 6.2 metres), with a secondary pass placed at each of the primary pass’s midpoints. Prior to doing subsequent drops at that place, the crater is filled with granular material once it has reached a depth of 3 to 4 ft (about 1 m).
Large soil vibrations are generated by the operation, which may negatively affect surrounding existing structures. In particular, structures within 500 feet (154 metres) of the locations of the intended drops should be examined for their vibration sensitivity and their antecedent conditions. Monitoring the vibrations when carrying out dynamic compaction is also advisable. If dynamic compaction is intended to be carried out within 200 feet (61.5 metres) of an existing structure, extreme caution and close observation should be made.
Materials
A clean, freely draining granular earth is often used to fill the craters left behind by the operation. Sandy soils can be treated by using a backfill made of sand. Finer-grained soils or landfills are frequently treated with a crushed stone backfill.
Design
An examination of the proposed construction and the current subsurface conditions will serve as the starting point for the design (bearing capacity, settlement, liquefaction, etc.). The minimal values required to deliver the required performance are then determined using the same study with the improved soil characteristics (e.g., SPT N value, etc.). The next step is to calculate the vertical and lateral extent of improved soil required to deliver the desired performance.
The square root of the energy from a single drop (weight times drop height) applied to the ground surface determines the depth of the effect. Dr. Robert Lucas created the correlation shown below using data collected in the field:
D = k(W x H)0.5
where; D is the maximum influence depth in meters beneath the ground surface, W is the weight in metric tons (9 kN) of the object being dropped, and H is the drop height in meters above the ground surface. The constant k varies with soil type and is between 0.3 and 0.7, with lower values for finer-grained soils.
Even though the largest depth of improvement predicted by this method is in the upper two-thirds, the improvement gradually decreases until it reaches zero in the bottom third. The degree of improvement attained within this zone is increased by landing strikes repeatedly at the same spot. However, when the rate of improvement falls, there comes a moment when the benefits become less valuable.
Table 1 lists the anticipated range of unit energy needed to reach this goal. Treatment of landfills is helpful in minimising voids, but it has minimal impact on the biodegradation of components in the future. As a result, treatment of landfills is normally only allowed in areas designated for planned roadways and pavement, not for structures. The soils are loose within 3 to 4 feet (1 m) of the surface once dynamic compaction is finished. A low-energy “ironing pass,” which typically entails dropping the same weight from a height of 10 to 15 feet (3.0 to 4.5 metres) over the entire surface area, is used to compact the surface soils.
Quality control and quality assurance
Penetration testing is used in the majority of applications to evaluate improvement. Penetration testing is challenging in construction waste or landfills, however large-scale load experiments using fill mounds or shear wave velocity tests can be carried out. To measure the progress made and make necessary adjustments, a test area might be treated at the start of the programme. To identify “soft” sections of the site that need more treatment, the depth of the craters can also be measured. When adequate improvement is attained, the decrease in penetration with further drops serves as a signal.
References
Hussin J. D. (2006): ‘Methods of soft ground improvement’ in ‘The Foundation Engineering Handbook’ Edited by Gunaratne M. Taylor and Francis USA.
Soil stabilisation is the alteration of one or more soil properties, by mechanical or chemical means, to create an improved soil material possessing the desired engineering properties. Stabilising soils during road construction can make the pavement more durable and resilient. Furthermore, it can stop erosion and dust production on the surface of the road.
The major objective of soil stabilisation is to develop a soil material or soil system that will endure over the design lifespan of the project under the design use conditions. In the same way that soils vary around the world, so do their engineering properties. Soil testing is therefore essential for the success of soil stabilisation. Prior to construction, ideally before selecting or buying materials, the chosen method of soil stabilisation should be tested in a lab.
The base of highway pavement is the most critical component of a road. As a result, road pavements are susceptible to the performance of the soil supporting them. Finding a method to balance road performance, constrained budgets, and tightening environmental laws is becoming a bigger challenge for road engineers. The cost-effectiveness of treatments to enhance the long-term performance of conventional pavements is declining. In comparison to the work at hand, road budgets, especially for maintenance, appear to be decreasing yearly.
Need for Soil Stabilisation of Roads
The stability of the underlying soils frequently affects the long-term performance of pavement structures. The structural integrity of each layer of pavement must meet minimal requirements in order for the engineering design of these built facilities to support and distribute the superimposed loads. These layers must withstand shear, severe deflections that can cause fatigue cracking in the layers above, and excessive permanent deformation.
In order to transform inexpensive natural earth materials into useful construction materials, it may be necessary to improve their engineering properties as they don’t always satisfy these specifications in their natural state. This is frequently achieved by stabilising or altering these problematic soils physically or chemically. The necessary strength and stability needed to ensure acceptable performance under traffic loading and environmental demands are frequently lacking in in-situ subgrades.
While stabilisation is a viable alternative for enhancing soil characteristics, the engineering properties that result from stabilisation vary greatly due to heterogeneity in soil composition, differences in the micro and macro structure of soils, heterogeneity of geologic deposits, and due to differences in the physical and chemical interactions between the soil and candidate stabilisers. The utilisation of site-specific treatment alternatives is required for stabilisation due to these variances.
On-going soil stabilisation
Advatanges of Soil Stabilisation
The basis of pavement design is the assumption that each layer of material in the pavement system will meet a minimum level of specified structural quality. Each layer must be able to withstand shearing, resist excessive deflections that could lead to fatigue cracking either inside the layer or in layers above it, and avoid excessive permanent deformation. The ability of a soil layer to disperse the load over a larger area often increases with soil quality, allowing for a reduction in the needed thickness of the soil and surface layers.
The following benefits come from stabilising soil for use in road pavements:
(a) Improved engineering characteristics Soil stabilisation improves the engineering properties of the soil, e.g., (i) strength – to increase the strength and bearing capacity, (ii) volume stability – to control the swell-shrink characteristics caused by moisture changes, and (iii) durability – to increase the resistance to erosion, weathering or traffic loading.
(b) Quality improvement The most common benefits obtained through soil stabilisation include improved soil gradation, a decrease in plasticity index or swelling potential, and gains in toughness and durability. Stabilization can also be employed in wet conditions to give construction projects a working surface. The process of improving soil quality in this way is known as soil modification.
(c) Thickness reduction Through the addition of additives, a soil layer’s strength and stiffness can be increased, allowing the stabilised material’s design thickness to be reduced in comparison to an unstabilized or unbound material. If the specific stabilised material achieves the required gradation, the design thickness strength, stability, and durability requirements of a foundation or subbase course can be decreased.
(d) Reduced maintenance requirements Soil Stabilisation can improve soil qualities, cut down on maintenance, and create an all-weather surface. Stabilization can improve the condition of the surface by reducing dust, rutting, potholes, and corrugation.
Strength parameters for mixture designs should be used to determine the ideal binder content. A pavement material should be resistant to abrasion and ravelling brought on by vehicle traffic when it is unsurfaced (i.e., no wearing course). Soil stabilisation can be utilised to lower dust, improve skid resistance, and decrease ravelling. However, regular grading and periodic reshaping cannot be used to maintain pavements that have been stabilised by a cementing operation. When maintaining the wearing surface in this way, the soil should be modified rather than stabilised.
Methods of Soil Stabilisation
Stabilization of soil may be achieved via mechanical, chemical, electrical, or thermal processes. Rarely are the last two choices chosen. The densification of soil through the use of mechanical energy is known as mechanical stabilisation, sometimes known as compaction. As air escapes from soil pores, densification happens without much change in water content. This technique works especially well in cohesionless soils where compaction energy can lead to particle interlocking and rearrangement. However, if these soils have considerable moisture variations, the approach might not work.
An increase in the fines content of the soil—that is, the proportion smaller than 75 μm—can also cause a reduction in the effectiveness of compaction. This is because particle rearrangement during compaction is hampered by cohesion and interparticle bonding. More successful than compaction for long-term stabilisation in these fine-grained soils is chemical stabilization/modification of their physio-chemical characteristics.
If a significant stabilisation response can be achieved in these soils, chemical stabilisation of non-cohesive, coarse-grained soils, soils with more than 50% by weight coarser than 75 μm, is also advantageous. When compared to the strength of the untreated material, the strength enhancement in this instance may be substantially larger—more than ten times higher. The most common methods of soil stabilization for roads include:
Mechanical stabilization.
Lime stabilization.
Cement stabilization.
Lime-Fly Ash (with or without cement) stabilization.
Bituminous stabilization.
Chemical stabilization.
Geotextiles, fibres, prefabricated materials, etc.
Selection of Stabilisers
The kind of soil to be stabilised, the intended use of the stabilised layer, the desired type of soil improvement, the required strength and durability of the stabilised layer, cost, and environmental circumstances are all important considerations when choosing a stabiliser. However, there are some broad criteria that make certain stabilisers more preferable based on soil granularity, plasticity, or texture. There may be more than one candidate stabiliser suitable for one soil type.
For instance, Portland cement can be used with a variety of soil types, but more plastic materials should be avoided since it’s crucial that the cement be thoroughly blended with the fines fraction (<0.075 mm). For Portland cement stabilisation, well-graded granular materials with enough fines to create a floating aggregate matrix (homogenous mixture) works very well.
Lime will cause soils with medium to high plasticity to become less plastic, become more workable, experience less swelling, and become stronger. Lime is used to stabilise a variety of materials by turning weak subgrade soils into a “working table” or subbase and combining them with weak granular base materials, such as clay-gravels, to create a strong, high-quality base course.
Due to the fact that fly ash is a pozzolanic substance that reacts with lime, it is virtually usually utilised in conjunction with lime in soils with little to no plastic particles. For increased strength, it has frequently been found useful to utilise a little proportion of Portland cement mixed with lime and fly ash. Lime, cement, and fly ash (LCF) have been used successfully to stabilise base courses.
Both asphalt and bituminous compounds are used to increase strength and weatherproof surfaces. Since it is desired to completely coat all of the soil particles, silty sandy and granular soils are typically good for stabilising asphalt.
Extreme weather conditions may also affect the best stabiliser choice, favouring the use of some stabilisers while discouraging the use of others, regardless of cost. Generally speaking, the hot, arid, and cold, rainy climates demand special attention.
Mechanical Stabilisation
The development of internal friction and cohesion, two naturally occurring forces inside the soil, is known as mechanical stabilisation. In some cases, compaction by itself is sufficient to stabilise the soil. The local soil can typically only be stabilised by adding a suitable quantity of soil or gravel components. When locally available soil or gravel materials with the right grading and plasticity are not available, mechanical stabilisation is used.
In order to change the particle size distribution and plasticity, mechanical stabilisation includes mixing or blending two or more chosen materials in the necessary amounts. Before final shape and compaction, mixing can be done on-site. A common application of mechanical stabilization is the blending of a granular material lacking in fines with a sand-clay. This blending of the materials has the potential to improve strength, abrasion resistance, imperviousness, and compatibility.
Lime Stabilisation
With lime stabilisation, the soil will become less plastic, more workable, less prone to swelling, and modified to give maximum strength. There is a recommended amount of lime for each type of soil, and adding more than that will have a negative impact on the mixture’s qualities. The quantity and kind of clay minerals in the soil determine how much lime is required (in percent by mass) to stabilise a material.
Lime stabilisation
Small amounts of lime (1 to 3 percent) may be used to stabilise some soils, such as clayey gravel with acceptable grading but moderately high plasticity, by lowering the plasticity index. The use of lime contents of 3 to 6 percent may result in considerable change in the material constitution.
The majority of plastic soil materials, including clayey sands (SC) and silty clays (ML), react effectively with lime in general. Materials with plasticity indices below 10% may not react quickly, nevertheless. The material’s reactivity to lime must be tested to find out. When treated with minor quantities of lime, the stabilised soil should preserve some cohesiveness of poorly graded clayey sand and gravels. They can become friable (easily crumbled or pulverised) and totally non-cohesive if too much is introduced, which will result in failures.
As a result, base material that has been treated with lime should adhere to the grading specifications that are typically given for untreated material. All lime-treated fine-grained soils generally show characteristics of reduced plasticity, enhanced workability, and reduced volume change. But not all soils have features that boost their strength. It should be underlined that there are numerous factors that affect the properties of soil-lime mixes. The most crucial factors are soil type, type of lime, quantity of lime added, and curing conditions (time, temperature, and moisture).
Cement Stabilisation
Portland cement can be used to either modify and improve the soil’s quality or to turn the soil into a mass that is cemented and has higher strength and durability. Whether the soil needs to be modified or stabilised will determine how much cement is needed. The stabilisation of soils has been accomplished with success using a variety of cement kinds.
Pavement construction has made extensive use of cement stabilisation. Cement, however, is typically not a suitable stabilising ingredient for a pavement’s wearing course. Without being covered by a wearing surface, the cementitious linkages formed cannot withstand the pressure of traffic. Additionally, unlike lime, cement cannot be reworked after initial mixing and subsequent setting. It is also not possible to rework cement using maintenance tools like graders. On the other hand, it can be utilised as a sub-base stabilising agent.
Soil stabilisation using cement
A variety of soils, from fine-grained clays and silts to sandy materials, can be stabilised using cement. When the plasticity index (PI) is low, cement is typically utilised with clays or silts for fine-grained materials. When the sulphate content of the soil is greater than 1%, cement stabilisation should be avoided.
The trial-and-error method is used to calculate the amount of cement needed to modify the soil and increase its quality. It is necessary to prepare multiple samples of soil-cement mixtures at various treatment levels in order to minimise the PI of the soil. The PI of each mixture must then be calculated. Since it was calculated using the material’s minus 40 percent, the value must be corrected in order to discover the design cement content using the entire sample weight represented in equation. The minimal cement content that provides the desired PI is selected.
A = 100BC (1) Where ; A = design cement content, percent total weight of soil B = percent passing 400 micron sieve size, expressed as a decimal C = percent cement required to obtain the desired PI of minus 400 micron material, expressed as a decimal.
Bituminous Stabilisation
When compared to cement and lime stabilisation, asphalt stabilisation of soils and aggregates is very different. A waterproofing phenomenon serves as the fundamental mechanism for the stability of fine-grained soils by asphalt. Asphalt is applied on soil particles or soil agglomerates to stop or limit water penetration, which would often result in a loss of soil strength. Asphalt stabilisation also makes the soil resistant to the negative impacts of water, such as volume, which can improve durability qualities.
There are two main mechanisms at work in non-cohesive materials like sands and gravel, crushed gravel, and crushed stone: waterproofing and adhesion. The asphalt layer on the cohesionless materials creates a membrane that stops or slows down water penetration, reducing the likelihood that the material would weaken in the presence of water.
Bituminous stabilisation
Adhesion has been named as the second mechanism. The asphalt serves as a binder or cement to hold the aggregate particles to the surface. Thus, the cementing effect boosts cohesiveness to increase shear strength. Criteria for the design of bituminous stabilized soils and aggregates are based almost entirely on stability and gradation requirements. For asphalt stabilised mixtures, the freeze-thaw and wet-dry durability tests are not relevant.
For hot, arid locations, bituminous stabilisation is more appropriate. The inclusion of bituminous binder aims to minimise water penetration through the soil and give non-plastic materials cohesiveness. Granular materials and materials that are easily granulated are the best candidates for bituminous stabilisation. There are restrictions when using bitumen-stabilised material as the wearing course for pavement. The binding action of bitumen alone won’t be adequate to stop ravelling from weathering and traffic unless significant amounts are applied. Typically, such a high bitumen content won’t be economical.
Bituminous stabilisation has been used to treat crushed rock, gravel, sandy loam, sand-clays, and other materials successfully. Bitumen can be used to stabilise fine-grained soils with increasing amounts of material passing through a 75-micron filter, however, doing so will result in increased prices and asphalt material requirements. The best candidates for this type of stabilisation are materials having a plasticity index of less than 10%.
Stabilisation with Lime-Fly Ash (LF) and Lime-Cement-Fly Ash(LCF)
Utilizing LF or LCF combinations can frequently be used to stabilise coarse-grained soils with little to no fines. During the burning of pulverised coal, a mineral byproduct known as fly ash—also known as coal ash—is produced. It contains compounds of silicon and aluminium that, when combined with lime and water, create a hardened cementitious mass with high compressive strengths.
Fly ash stabilisation in the field
Since fly ash provides an agent with which the lime can react, lime and fly ash are frequently employed together successfully to stabilise granular materials. Lime-fly ash or lime-cement-fly ash combinations can be used to stabilise any sand, gravel, or combination of sand/gravel soil. These soils shouldn’t include more than 12 percent fines, and their Plasticity Index shouldn’t be more than 25%. So stabilisation using LF or LCF is frequently acceptable for base and subbase course materials.
Stabilization using lime or cement is somewhat different from design with LF. The percentage of lime-fly ash, the moisture content, and the ratio of lime to fly ash can all be changed for a specific material combination (aggregate, fly ash, and lime) during the mix design process. It is well accepted that the quality of the matrix material directly affects engineering properties like strength and durability. The part made up of fly ash, lime, and fine aggregate particles is the matrix material. Basically, when the matrix material can “float” the coarse aggregate particles, increased strength and improved durability are possible.
The void spaces between the coarse aggregate particles are effectively filled by the fine size particles. To successfully fill the available void spaces and allow the coarse aggregate particles to “float,” a certain amount of matrix is needed for each coarse aggregate material. The optimum fines content is the amount of matrix necessary to achieve the maximum dry density of the entire combination.
It is advised that the amount of matrix in LF combinations be around 2% higher than the ideal fines content. The ratio of lime to fly ash also affects the strength development at the acceptable fines concentration. Different strength and durability values can be obtained by varying the lime-fly ash ratio.
Stabilisation with ground granulated blast furnace slag (GGBS)
Ground granulated blast furnace slag (ggbs) is a by-product from the blast-furnaces used to make iron. These run at a temperature of around 1500 °C and are fed with a precisely measured combination of limestone, coke, and iron ore. The leftover components create a slag that floats on top of the iron once the iron ore is converted to iron. This slag is regularly tapped off as a molten liquid and must be quickly cooled in a lot of water if it is to be employed in the production of ggbs.
GGBS
The quenching generates granules that resemble coarse sand and optimises the cementitious characteristics. In complex manufacturing facilities that can treat up to 500,000 tonnes of slag annually, this “granulated” slag is subsequently dried and ground to a fine powder to a precisely regulated fineness. Even though ggbs powder is a relatively slow-setting cement on its own, alkali is usually required to activate and accelerate it for practical use.
Portland cement often provides the alkalinity to activate and accelerate these capabilities because ggbs on its own only has slow cementitious properties. The alkali required for activation can alternatively be obtained from lime. Sulfides, as well as sulphates, are capable of causing disruptive expansion in stabilised soils, according to laboratory and field studies. Combinations of ggbs and lime have been demonstrated to be useful and efficient solutions for stabilising soil and to offer technical advantages. The integration of ggbs, in particular, is quite effective at preventing the expansion brought on by the presence of sulphate or sulphide in soil.
Stabilisation with geotextiles
Through their tensile strength capabilities, geotextiles can be utilised over very soft soils to help spread loads and so increase the site’s load bearing capacity. Every time any cover aggregate is to be added to a soil containing more than 10% fines, a geotextile is required as a separation layer. Geotextiles can also act as a separator to prevent excess fines from penetrating a granular material placed over it or as a water barrier to prevent moisture from entering the pavement. To manage and remove excess moisture, geotextiles can be utilised as filter media to build different drainage layers inside and next to the pavement.
The movement of traffic over low bearing capacity soils will be made easier by the use of geotextiles, particularly for expedient applications. The need for more traditional stabilisation materials may be diminished or eliminated by the use of geotextiles. The geotextile should meet the drainage or filtration requirements for the specific soil conditions when used for separation. To stop soil particle migration, the geotextile openings should be sized properly. The geotextile needs to be strong enough to adhere to survivability standards for subgrade situations and covering arterials.
There are design guidelines for situations when the geotextile is to be utilised as a reinforcement material or a water barrier. The geotextile often needs to be coated with a bitumen substance in order to function as a water barrier. While seams between geotextile sheets can be field seamed together using a variety of techniques, in the field they are typically only overlapped by a certain amount to avoid fastening issues.
Stabilisation using Fibres and prefabricated materials
Utilizing a pulverizer mixer, hair-like fibres are mixed into the moist soil to stabilise it. Sands and silty sands that are categorised as SW, SP, SM, and some SM-SC types of soils are the best materials for fibre stabilisation. Since the use of fibres in high-plasticity soils has produced erratic results, their application should typically be restricted to the aforementioned coarse-grained soil types. Uni-Mat, Hex-Mats, and any other fabricated material that can be utilised as a trafficked surface to sustain loads on a soft soil are examples of the fabricated materials mentioned for soil stabilisation.
Stabilisation with rice husk ash and lime sludge
Numerous industries across the world produce significant volumes of waste as a byproduct, including rice husk ash and lime sludge. These contaminants provide a serious disposal challenge and have dangerous consequences on the environment and nearby regions. The issue of their disposal can be greatly reduced by using this waste material in road construction. Studies on the use rice husk ash in stabilising soil masses have been carried out by a lot of researcher, and the findings showed that its application had a significant impact on the enhancement of soil qualities. According to some studies, it is particularly helpful for stabilising clayey soils.
The results of some studies are given below:
lt increases the liquid limit and plastic limit thereby decreasing the PI value of soil
It increases the unconfined compressive strength of soil.
It increases the soaked CBR of the soil.
The optimum proportioning of lime sludge and rice husk ash for maximum unconfined compressive strength and lowest plasticity index is 16% and 10% respectively.
The soaked CBR however kept on increasing at 15% and 20% rice husk ash.
Conclusion
Alteration of one or more soil properties mechanically or chemically to produce an improved soil material with the appropriate engineering properties is known as soil stabilisation. Stabilizing soils can make them stronger and more resilient, or it might stop erosion and dust production. No of the reason for stabilisation, the goal is to create a soil material or soil system that will endure over the design lifespan of the project under the design use conditions.
Engineers are in charge of deciding on or defining the appropriate stabilising strategy, methodology, and material requirements. The engineering qualities of soils vary from region to region throughout the world, as do the soils themselves. Soil testing is essential for the success of soil stabilisation. Prior to construction, ideally before selecting or buying materials, the chosen method of soil stabilisation should be tested in a lab.
Have you ever pondered the detrimental effect of water seepage on road pavements? It is common knowledge among engineers that frequent water seepage can result in road defects such as swelling of the subgrade layer and the formation of potholes and stains on roads. Perhaps you find yourself on a road construction project with water seeping out of the ground. What solution would you proffer?
This article will discuss the use of filter media in road construction as an alternative solution to water susceptibility of road pavements from groundwater absorbed into the pavement structure by capillary action. Thus, by controlling water seepage into pavement structures, we can reduce the formation of road defects and increase the lifespan of road pavements.
Detrimental effects of water seepage
Water is vital to human existence. However, given enough time, water can destroy even the best infrastructures. Therefore, water seepage and other water-related problems pose significant threats to road pavements. For instance, water action from groundwater or high hydrostatic pressure from surrounding water features leading to frequent water seepage can erode and damage road pavements. For example, look at the adverse effect of water seepage on a road near Guam Reef Hotel in Tumon, Guam, USA.
Road defect: Pothole
Water seepage is a prevalent issue that occurs after heavy rainfall. For instance, additional water is in the underlying road pavement layers when groundwater rises. This extra water then creates hydrostatic pressure against the road pavement resulting in soaked road layers, which reduces the bonding strength and load-bearing capacity of the premixed road materials.
Furthermore, the prolonged seepage of water into a road pavement in conjunction with traffic loads results in several pavement defects and problems, such as the formation of road stains and potholes, settlement, rutting, cracking, stripping, ravelling, and swelling of the subgrade layer. Therefore, it becomes necessary to give maximum consideration to water-related problems and how to reduce their damaging effects during the design and construction of road pavements.
Filter media in road construction
The granular layer serves as a filter media to prevent water seepage (Photo credit: cementconcrete.org)
A filter media is generally used in earthworks and other civil engineering structures, such as roads, dams, retaining walls, and embankments. For example, a subsurface filter media is essential in road projects because they help to prevent the decrease in the strength of the underlying layers of road pavement caused by increased water or moisture content.
Similarly, a layer of filter media is necessary when the surface of a road has its highest water table sufficiently below the crust of the road, and there is a likelihood of water rising to the subgrade or road surface through capillary action.
When filtering is targeted at preventing water seepage into a road pavement, a filter media is a layer of free-draining granular materials or clasts (e.g. cobblestones) underneath a road’s sub-base layer. The layer of granular materials or cobblestones of suitable thickness is usually provided to cut off capillary action between a road’s subgrade and its highest water table. Thus, granular materials or cobblestones prevent the build-up of hydrostatic or water pressure on the road pavement layer.
Cobblestones
Filtering in road construction significantly reduces road defects and failures resulting from water seepage. When filter materials are provided, the water that is supposed to rise into the underlying road layers will drain away into roadside drains. Furthermore, filtering with cobblestones is a suitable solution to controlling the capillary rise in waterlogged terrains where the subgrade is usually subjected to extreme soaking conditions due to high ground water table levels.
Selection criteria for granular materials and cobblestones as filter media
The filter media for roadbed drainage to remove seepage water and prevent damage to road pavements from uplift pressure may consist of either a single layer or several layers, each with different grading. The essential criteria are the grading and permeability of the granular materials and cobblestones. However, any filter material used as a filter media must be clean, hard, durable, dimensionally stable, and corrosion, dissolution, and frost-resistant.
Furthermore, the filter material must be free from deleterious materials that can adversely affect the efficiency and longevity of the material. These deleterious materials include clayey, elongated, flaky particles, chemically unsound or readily soluble materials, and excessively porous or laminated materials. Thus, the choice of filter material requires accessing a wide range of chemical and physical properties and sometimes depends on the judgment and experience of a designer.
The minimum acceptance criteria for granular materials and cobblestones as filter media are listed below.
Oven-dried relative density not less than 2.5
Maximum flakiness and elongation indices not greater than 30
Water absorption not greater than 3% by weight
Aggregate impact value, not more than 30
Aggregate crushing value, not more than 30
10% fines value not less than 100 kN
Los Angeles abrasion value not greater than 40
Aggregate abrasion value not greater than 20
Magnesium sulfate soundness value not more than 12% loss
Road construction procedures with cobblestones as filter media
A layer of cobblestones at a road section with prevalent water seepage action
The construction procedures follow the standard methods for constructing asphalt concrete roads, except for introducing cobblestones as a filter layer. The procedures are briefly discussed below;
Planning
Marking out of road alignment and dimensions
Earthworks, including excavation, grading and compaction of road subgrade
Placement of precast or casting of in-situ roadside flood drains
Laying of a suitable filter layer (cobblestones) with appropriate thickness where required along the stretch of the road
Laying, grading and compaction of sub-base and base courses
Laying and compaction of binder and surface or wearing asphalt courses
Lastly, it is essential to note that quality control is compulsory at every construction stage.
Alternative materials for filter media
Bituminous material
Bituminous layer serving as a filter media to prevent water seepage (Photo credit: cementconcrete.org)
An impermeable or bituminous layer covering a road section to seal water underneath the road’s sub-base can also serve as a filter media. Bitumen, made up of organic liquids that are highly viscous, sticky, and waterproof, is insoluble in water and water-resistant, thus, making it a viable alternative as an effective sealant and filter media. In addition, a filter media of bituminous material has significant advantages of availability and affordability and can be used over long stretches of a roadway.
Geosynthetics
Geonets
These materials can be used as filters in addition to or in place of traditional granular materials in road construction. Furthermore, geosynthetics are easy to install, have low permeability, and are often cost-effective, especially when granular materials are scarce and expensive or when the available ones do not meet project specifications.
Common geosynthetics used as filter media are geomembranes, geotextiles, and geonets. Also, it can be a combination of geotextiles and geonets to form a drainage geocomposite, whereby the geotextile act as a filter while the geonet serves as a drain. For example, geonets are designed in such a way that they can convey maximum anticipated seepage within their channels during their design life. Similarly, geotextiles are designed to dissipate pore water pressure at the base of roadway structures.
Conclusion
Capillary water that seeps into a road pavement attacks the bond between the asphalt binder and aggregates in the pavement. It is important however to note that keeping road pavements from coming in contact with water can be almost impossible. However, if you ignore and refuse to treat water seepage right away as a design or construction engineer, you put the road or a stretch of the road at risk of defects andfailure.
Therefore, a road or highway engineer needs to be aware of the potential sources of water on a road project and make provisions for them. For instance, providing a filter layer becomes necessary to prevent long-term damage or collapse if the water source is groundwater seepage. Lastly, it is vital to design and construct roads such that their water susceptibility is minimized and their service life is improved.
References
[1] Gourc, J. P. (2006), “Training Course on Geosynthetics: Geosynthetics in Drainage and Filtration”, International Geosynthetics Society (8IGG), Yokohama, Japan, September, available at: https://www.geosyntheticssociety.org/wp-content/uploads/2014/10/TrainingCourse_GeosyntheticsinDrainageandFiltration.pdf
[2] Engineering Geology Special Publications (2007), Aggregates for use in filter media, Geological Society, London, Vol. 17, No. 1, pp. 291-298, available at: https://doi.org/10.1144/GSL.ENG.2001.017.01.13 or https://www.scribd.com/document/400882158/Aggregates-for-Use-in-Filter-Media
To create hardened solid materials (also known as enhanced geomaterials), which have increased strength and stiffness, chemical agents (also known as binders) can be introduced into the ground and mixed with already-existing geomaterials such as soils and rocks. Lime, cement, silicate-based gel, and chemical solutions are examples of conventional binders.
Mixing and grouting are the two common techniques for introducing and mixing binders with soils. While the grouting method uses pipelines with high-pressure grouts, the mixing approach uses mechanical mixers or augers. Mixing can take place at depths (to form columns or walls) or at the surface (mostly for improving subgrade and base course). Deep soil mixing is the term used to describe the process of mixing binders (hardening agents) with soils at depths.
Basic Concepts of Deep Soil Mixing
The deep soil mixing (DSM) technique uses augers to mix in situ soil at depths with a binder (cement, lime, slag, or other binders). Either a wet method or a dry method can be used for deep soil mixing. Figure (a) below shows a wet method that utilises the binder as a slurry, whereas Figure (b) depicts a dry method that uses the binder as a powder.
One to eight rotary hollow shafts with cutting and mixing blades above the tip may be present in the equipment for the wet method. Each hollow shaft allows the introduction of the binder slurry into the ground, which flows from the nozzle as the shaft either sinks into the soil or is removed. To increase the consistency of the soil-binder combination, some equipment features mixing blades that rotate in opposite directions.
Single or dual rotary shafts with cutting and mixing blades above the tip may be used in the dry method equipment. By using air pressure, the nozzle and each hollow shaft, the binder powder is delivered into the soil.
Rigid inclusions (such as concrete piles or spun piles) can be used to stiffen deep mixed columns in order to increase their stiffness and vertical and horizontal load capabilities. A composite column is another name for this kind of column. Some reseachers have demonstrated that after the installation of the column, the strength of the nearby sensitive clay generally recovered or even surpassed its pre-column strength. This has been attributed the long-term property changes to thixotropic hardening, consolidation, and diffusion of ions from the hardening agent (binder), and the short-term changes to soil disturbance and fracture.
Suitability of soils for Deep Mixing
Deep soil mixing has typically been utilized to strengthen soft cohesive soils, while it has also occasionally been used to reduce permeability and prevent the liquefaction of cohesionless soils. The ideal soil characteristics for deep mixing are shown in the Table below.
Property
Favorable Soil Chemistry
pH
Should be greater than 5
Natural water content
Should be less than 200% (dry method) and less than 60% (wet method)
Organic content
Should be less than 6% (wet method)
Loss on ignition
Should be less than 10%
Humus content
Should be less than 1.0%
Electrical conductivity
Should be greater than 0.04 mS/mm
If the soil is very hard, very dense, and has rocks or other obstructions, deep soil mixing becomes challenging. Due to the massive machinery utilised in most projects, deep mixing typically requires open site access and overhead clearance. In maritime operations, deep mixing can go as deep as 70 metres, while on land it can go as deep as 30 metres.
Applications of Deep Soil Mixing
Columns from deep soil mixing have been used for many applications in soft soils:
support of superstructures, including buildings, walls, embankments, and the likes
waterfront and marine applications including quay walls, wharf structures, and breakwaters
stabilization of slopes
lateral support
containment of water and pollutant,
liquefaction mitigation, and,
vibration reduction.
Generally, deep soil mixing columns are utilised in various applications to reduce vibration, contain water and pollutant flow, improve slope stability, reduce settlement, increase bearing capacity, and provide lateral support.
As seen in the Figure below, there are commonly four distinct arrangements for DM columns. When an area replacement ratio is relatively low, such as less than 50%, individual columns are used. The main uses of individual columns have been to improve bearing capacity and reduce settlement. When a high area replacement ratio, such as more than 50%, is required, block patterns are employed to bear substantial vertical and/or horizontal loads. Large marine structures have mostly benefited from the usage of block patterns to increase stability. This design pattern has also been applied to waste containment to stop dangerous substances from leaching.
Figure 8.3 Patterns of columns: (a) individual column, (b) block, (c) wall, and (d) grid.
For retaining walls to provide lateral support, seepage walls to stop seepage, curtain walls to hold waste, and walls perpendicular to the centerline of embankments to promote stability, panel or wall patterns have been widely utilised. Between the wall pattern and the block pattern is the grid pattern. It can be utilised in applications that call for block and wall layouts. The grid layout has a special use in preventing sandy soil liquefaction. The cells of grids are where the liquefiable soils are contained.
In recent years, embankments over weak foundations have primarily been supported by columns. One of the most significant applications of column technologies is thought to be this one. Deep mixed columns have also been progressively combined with other technologies, including rigid piles, PVDs, and geosynthetic reinforcement.
The geosynthetic reinforcement placed on top of the columns serves as a bridge layer to distribute the embankment load to the columns and lessen the variance in column settlement. Geosynthetic-reinforced column-supported embankments are frequently used for the following purposes:
(1) bridge approach (2) roadway widening (3) subgrade improvement, and (4) support of storage tanks
Advantages and Limitations of deep soil mixing
The deep mixing method has the following advantages:
Applicable for most soil types
Installed at great depths
Relatively fast installation
Low noise and vibration level
Formation of a DSM wall for earth retaining and water barrier at the same location and time
Less spoil soil, especially for the dry method
However, the deep soil mixing method may have the following limitations:
To transfer structural load to a capable bearing strata, micropiles, often referred to as minipiles, needle piles, or pin piles, are employed in practically any type of ground. Micropiles are slender columns of deep foundations with relatively small diameter and low load bearing capacity that are installed relatively close to each other. They are constructed using high strength steel casing or threaded pipes, and may be filled with concrete grouts and steel reinforcement. Sometimes, micropiles are also constructed using concrete or timber.
Micropiles were initially low-capacity, small-diameter piles (2 to 4 in., or 5 to 10 cm). However, improvements in drilling technology have led to design load capacities and diameters exceeding 300 tonnes and 250 mm respectively. In sites with low headroom and restricted access, micropiles are frequently used.
Although there are many uses for micropiles, they are most frequently utilised to support new or existing foundations in places with little headroom and difficult access. Other uses of micropiles are to provide structural support, underpin foundations to eliminate settlement, improve soil and slope stability, and transfer loads to a stable soil strata.
Applicable soil types
Micropiles can be employed in almost any subsurface soil or rock since they can be inserted using drilling equipment and combined with various grouting procedures to form the bearing element. The bearing soil or rock will determine their load carrying capacity. The absence of necessary overhead or lateral site constraints that would prevent installations requiring considerably larger equipment is one of the major benefits of using micropiles.
Micropiles can offer large compressional capacity as well as good tensile capacity. According to the industry (www.rembco.com), micropiles have a working capacity of up to 2200 kN (250 tonnes). According to (www.keller.com), capacities of about 500 tonnes have also been achieved. When micropiles are pressure-grouted in place for higher capacity, the relative density and lateral pressure of the surrounding soil (if compressible) is increased, thereby leading to considerably higher shaft resistance.
Traditionally, micropiles are installed in predrilled holes that are filled with concrete.
Equipment
Typically, the micropile shaft is bored or hammered into position. A drill rig or small pile driving hammer mounted on a base unit is therefore necessary. It is necessary to have the proper grout mixing and pumping equipment since the pipe is filled with cement grout. The proper grouting equipment is also necessary if compaction grout or jet grout will be used to produce the bearing element.
Micropiles typically require compact small-sized equipment that can be used in confined spaces with limited access. The application of micropiles has a very broad range; it can be carried out in spaces with little vertical clearance, such as basements and under bridge structures. The interiors of commercial structures, tiny tunnels, mountain paths, rice fields, mountainous forested areas, steep slopes, and other places are some other examples of important sites where the micropiles can be installed. Additionally, micropiles can be inserted through existing foundations and used to support buildings as well as fix broken foundations.
Procedures for construction
Typically, the micropile shaft is either driven or drilled into position. Some sort of bearing element must be created if the specified pile capacity cannot be reached in end bearing and side friction along the pipe. This could entail drilling a rock socket, filling it with grout, and installing a full length, high-strength threaded bar if the tip is covered in rock. Compaction grouting or jet grouting can be carried out below the bottom of the pipe if it is surrounded or covered by soil. Additionally, the pipe can be partially withdrawn while being filled with grout that is pressured to produce a bond zone.
The figure above shows the micropile installation procedure. A drilling technique that is appropriate for the soil/site conditions is used to drill boreholes with casings. Following removal of the drilling rod and tools, reinforcement bars—typically corrosion-resistant steel bars—are next placed into the boreholes. Next, grouting is carried out sequentially under pressure as the casing is gradually removed.
Materials for construction of micropiles
A steel rod or pipe often makes up the micropile. The bond zone and pipe fill are frequently created using grout made of Portland cement. Another typical item is a full-length steel threaded bar made of grade 40 (275 N/mm2) to 150 ksi (1035 N/mm2) steel. The micropile may occasionally be nothing more than a reinforced concrete grout column.
Design of micropiles
Three components make up the design of micropiles;
the connection to the current or proposed structure,
the pile shaft that transmits the load to the bearing zone, and
the bearing element that sends the load to the layer of soil or rock that is carrying the load.
The piling section is designed using a typical structural analysis. In the event that a grouted friction socket is intended, the Table below can be used to determine the diameter and length of the socket. Bond lengths more than 30 feet (9.2 metres) do not improve the capacity of the piles.
Soil/Rock Description
SPT N value (blows/ft)
Grout Bond with Soil/Rock (ksf)
Nonpressure grouted
Silty clay
3—6
0.5—1.0
Sandy clay
3—6
0.7—1.0
Medium clay
4-8
0.75—1.25
Firm clay or stiffer
>8
1.0—1.5
Sands Soft shales
10-30
2—4 5—15
Slate and hard shales
15—28
Sandstones
15—35
Soft limestone
15—33
Hard limestone
20—35
Pressure grouted
Medium dense sand
3.5 – 6.5
Dense sand
5.5 – 8.5
Very dense sand
8-12
1 ft = 0.308m; 1 ksf = 47.9 kPa
Micropiles can be divided into two categories based on design uses. The first category consists of micropiles that are loaded laterally or axially. This collection of micropiles distributes structural loads to the competent strata beneath the foundation (for example, through the underpinning of structures), or they can be utilised to stop the movement of failure planes (i.e. stabilisation of slopes).
The second category consists of micropiles that are utilised to create a reinforced soil composite, which strengthens the soil mass. However, based on the grouting techniques, micropiles can also be divided into four groups (Groups A, B, C, and D).
The grouting for the group A micropiles is set under gravity. In group B, grout is injected under pressure into the hole, but the pressure is constrained to prevent hydrofracturing of the nearby soil. Group C micropiles are installed in two steps: first, a primary grout is pressure-applied to hydrofracture the surrounding ground, and then, just before the main grout sets, a secondary grout is injected through a manchette tube. The primary grout is injected after the primary grout has hardened in group “D” micropiles, which are similar to group “C” micropiles.
Quality control and assurance
During the construction of the micropile, the drilling penetration rate can be monitored as an indication of the stratum being drilled. Grout should be sampled for subsequent compressive strength testing. The piles verticality and length should also be monitored and documented. A test pile is constructed at the beginning of the work and load tested to 200% of the design load in accordance with the standard specification ASTM D 1143.
Columns are the most noticeable feature of a structure and are often used to support gravity loads transmitted from the floors or roofs of buildings. Strength, economy, adaptability, good fire resistance, and robustness are all advantages of in-situ reinforced concrete columns. During the design of columns, sound engineering judgement is often needed to balance their location, size, and shape with horizontal element spans and economy.
Circular columns are often designed for the ultimate axial load, NEd, ultimate design moment, MEd, and ultimate shear force VEd. For internal columns, moments may generally be assumed to be nominal when compared with external columns.
Due to their uniform strength in all directions, circular concrete columns are frequently employed in the design of pilings and bridge piers, and are very convenient for seismically active areas. Furthermore, it is much easier to confine the concrete using special reinforcement in circular columns than in other shapes.
Theoretical Background
When the neutral axis remains within a section, the basic equations for a section’s equilibrium under combined bending and axial load are as follows:
In Equation (2), moments have been taken about the concrete section’s centroid. The summation signs represent a summation of all layers of reinforcement in the section. Tensile stresses must be considered negative when summing them up. di is the distance between the section’s compressive face and the ith layer of reinforcement.
We can substitute 0.459fck for fav and 0.416 for β by assuming that the partial safety factors for the steel and concrete are 1.15 and 1.5, respectively, and that αcc is 0.85. For cases in which the neutral axis remains within the section, the resulting equations are rigorous. More complex expressions must be resolved when the entire section is in compression for the following situations;
(1) the portion of the parabolic curve cut off by the bottom of the section and (2) the reduction in the ultimate strain at the compressive face
Additionally, for situations when the concrete strength is greater than 50 N/mm2, more complicated equations are required. Because of how complex the resulting equations are, it is inappropriate to present them here. Using design charts is an easier method.
Some design charts for circular columns are given below. Since six reinforcing bars are the minimum that can be employed in a circular section, this is the assumption made while drawing the charts. It is discovered that no specific arrangement of reinforcement in relation to the axis of bending will always result in minimal strength. As a result, the charts are produced to provide a lower bound envelope to the interaction diagrams for different bar arrangements.
Design Example of RC Circular Columns
Verify the resistance of 6H25 bars to withstand the loads in a column of a high-rise building in accordance with EN1992-1-1 incorporating Corrigendum January 2008 and the UK national annex. The design information is as follows;
Height of column = 5m fck = C25/30 fyk = 500 MPa Diameter of column = 400 mm
Design axial load; NEd = 1500.0 kN Moment about y-axis at top; Mtopy = 66.0 kNm Moment about y-axis at bottom; Mbtmy = 32.0 kNm Moment about z-axis at top; Mtopz = 25.0 kNm Moment about z-axis at bottom; Mbtmz = 5.5 kNm
Column geometry Overall diameter; h = 400 mm Clear height between restraints about y-axis; ly = 5000 mm Clear height between restraints about z-axis; lz = 5000 mm
Stability in the z direction; Braced Stability in the y direction; Braced
Concrete details Concrete strength class; C25/30 Partial safety factor for concrete (2.4.2.4(1)); γC = 1.50 Coefficient αcc (3.1.6(1)); αcc = 0.85 Maximum aggregate size; dg = 20 mm
Reinforcement details Nominal cover to links; cnom = 35 mm Longitudinal bar diameter; φ= 25 mm Link diameter; φv = 8 mm Total number of longitudinal bars; N = 6
Area of longitudinal reinforcement; As = N × (π × φ2 / 4) = 2945 mm2 Characteristic yield strength; fyk = 500 N/mm2 Partial safety factor for reinft (2.4.2.4(1)); γS = 1.15 Modulus of elasticity of reinft (3.2.7(4)); Es = 200 kN/mm2
Fire resistance details Fire resistance period; R = 60 min Exposure to fire; Exposed on more than one side Ratio of fire design axial load to design resistance; mfi = 0.70
Axial load and bending moments from frame analysis Design axial load; NEd = 1500.0 kN Moment about y axis at top; Mtopy = 66.0 kNm Moment about y axis at bottom; Mbtmy = 32.0 kNm Moment about z axis at top; Mtopz = 25.0 kNm Moment about z axis at bottom; Mbtmz = 5.5 kNm
Beam/slab concrete strength class; C25/30
Beams/slabs providing rotational restraint about y axis Depth on side A; hA1y = 500 mm Width on side A; bA1y = 300 mm Length on side A; lA1y = 4500 mm
Depth on side B; hB1y = 500 mm Width on side B; bB1y = 300 mm Length on side B; lB1y = 6000 mm
Beams providing rotational restraint about z axis Depth on side A; hA1z = 500 mm Width on side A; bA1z = 300 mm Length on side A; lA1z = 3500 mm
Depth on side B; hB1z = 500 mm Width on side B; bB1z = 300 mm Length on side B; lB1z = 3500 mm
Relative flexibility end 2 for buckling about y axis; k2y = 1000.000 Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
Check nominal cover for fire and bond requirements Min. cover reqd for bond (to links) (4.4.1.2(3)); cmin,b = max(φv, φ – φv) = 17 mm Min axis distance for fire (EN1992-1-2 T 5.2a); afi = 40 mm Allowance for deviations from min cover (4.4.1.3); Dcdev = 10 mm Min allowable nominal cover; cnom_min = max(afi – φ/2 – φv, cmin,b + Dcdev) = 27.0 mm
PASS – the nominal cover is greater than the minimum required
Effective depth and inertia of bars for bending about y axis For the purposes of determining the bending capacity and interaction diagrams in this calculation, bending about the y axis is taken to be when there are two furthest equidistant bars on each side of the column centreline. Bending about the z axis is taken to be when there is one furthest bar on each side of the column centreline.
Area per bar; Abar = π × φ2 / 4 = 491 mm2 Radial dist from column centre to longitudinal bar; rl = h/2 – cnom – φv – φ/2 = 144.5 mm Subtended angle between adjacent bars; α = (360 deg) / N = 60.0 deg
Layer 1; dy1 = h/2 + rl × cos(α/2) = 325.1 mm 2nd moment of area of reinft about y axis; Iy1 = 2 × Abar × (dy1 – h/2)2 = 1537 cm4
Layer 2; dy2 = h / 2 + rl × cos[(2 – 1) × a + a/2] = 200.0 mm 2nd moment of area of reinft about y axis; Iy2 = 2 × Abar × (dy2 – h/2)2 = 0 cm4
Layer 3; dy3 = h / 2 + rl × cos[(3 – 1) × a + a/2] = 74.9 mm 2nd moment of area of reinft about y axis; Iy3 = 2 × Abar × (dy3 – h/2)2 = 1537 cm4
Total 2nd moment of area of reinft about y axis; Isy = 3075 cm4
Radius of gyration of reinft about y axis; isy = √(Isy / As) = 102 mm Effective depth about y axis (5.8.8.3(2)); dy = h / 2 + isy = 302 mm
Effective depth of bars for bending about z axis Layer 1 (tension face); dz1 = h / 2 + rl = 344.5 mm 2nd moment of area of reinft about z axis; Iz1 = Abar × (dz1 – h / 2)2 = 1025 cm4
Layer 2; dz2 = h / 2 + rl × cos[(2 – 1) × a] = 272.3 mm 2nd moment of area of reinft about z axis; Iz2 = 2 × Abar × (dz2 – h/2)2 = 512 cm4
Layer 3; dz3 = h / 2 + rl × cos[(3 – 1) × a] = 127.8 mm 2nd moment of area of reinft about z axis; Iz3 = 2 × Abar × (dz3 – h/2)2 = 512 cm4
Layer 4; dz4 = h / 2 + rl × cos[(4 – 1) × a] = 55.5 mm 2nd moment of area of reinft about z axis; Iz4 = 1 × Abar × (dz4 – h/2)2 = 1025 cm4
Total 2nd moment of area of reinft about z axis; Isz = 3075 cm4
Radius of gyration of reinforcement about z axis; isz = √(Isz / As) = 102 mm Effective depth about z axis (5.8.8.3(2)); dz = b / 2 + isz = 302 mm
Relative flexibility at end 1 for buckling about y axis Second moment of area of column; Iy = π × h4 / 64 = 125664 cm4 Second moment of area of beam on side A; IA1y = bA1y × hA1y3 / 12 = 312500 cm4 Second moment of area of beam on side B; IB1y = bB1y × hB1y3 / 12 = 312500 cm4 Relative flexibility (PD6687 cl. 2.10); k1y = max(0.1, (Ecm × Iy / ly) / [2 × Ecm_b × (IA1y/lA1y + IB1y/lB1y)]) = 0.103 Relative flexibility end 2 for buckling about y axis; k2y = 1000.000
Relative flexibility at end 1 for buckling about z axis Second moment of area of column; Iz = π × h4 / 64 = 125664 cm4 Second moment of area of beam on side A; IA1z = bA1z × hA1z3 / 12 = 312500 cm4 Second moment of area of beam on side B; IB1z = bB1z × hB1z3 / 12 = 312500 cm4 Relative flexibility (PD6687 cl. 2.10); k1z = max(0.1, (Ecm × Iz / lz) / [2 × Ecm_b × (IA1z/lA1z + IB1z/lB1z)]) = 0.100 Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
Calculated effective length (cl. 5.8.3.2)
Eff. length about y axis (braced) (5.8.3.2(3)); l0y = 0.5 × ly × [(1 + k1y/(0.45+k1y)) × (1 + k2y/(0.45+k2y))]0.5 = 3851 mm
Eff. length about z axis (braced) (5.8.3.2(3)); l0z = 0.5 × lz × [(1 + k1z/(0.45+k1z)) × (1 + k2z/(0.45+k2z))]0.5 = 3843 mm
Column slenderness about y axis Radius of gyration; iy = h / 4 = 10.0 cm Slenderness ratio (5.8.3.2(1)); ly = l0y / iy = 38.5
Column slenderness about z axis Radius of gyration; iz = h / 4 = 10.0 cm Slenderness ratio (5.8.3.2(1)); lz = l0z / iz = 38.4
Design bending moments Frame analysis moments about y axis combined with moments due to imperfections (cl. 5.2 & 6.1(4)) Ecc. due to geometric imperfections (y axis); eiy = l0y /400 = 9.6 mm Min end moment about y axis; M01y = min(abs(Mtopy), abs(Mbtmy)) + eiy × NEd = 46.4 kNm Max end moment about y axis; M02y = max(abs(Mtopy), abs(Mbtmy)) + eiy × NEd = 80.4 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1) Factor A; A = 0.7 Mechanical reinforcement ratio; w = As × fyd / (Ac × fcd) = 0.719 Factor B; B = √(1 + 2 × w) = 1.562 Moment ratio; rmy = M01y / M02y = 0.577 Factor C; Cy = 1.7 – rmy = 1.123 Relative normal force; n = NEd / (Ac × fcd) = 0.843 Slenderness limit; llimy = 20 × A × B × Cy / √(n) = 26.7
ly > llimy – Therefore, second order effects must be considered
Frame analysis moments about z axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))
Ecc. due to geometric imperfections (z axis); eiz = l0z /400 = 9.6 mm
Min end moment about z axis; M01z = min(abs(Mtopz), abs(Mbtmz)) + eiz × NEd = 19.9 kNm
Max end moment about z axis; M02z = max(abs(Mtopz), abs(Mbtmz)) + eiz × NEd = 39.4 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1) Factor A; A = 0.7 Mechanical reinforcement ratio; w = As × fyd / (Ac × fcd) = 0.719 Factor B; B = √(1 + 2 × w) = 1.562 Moment ratio; rmz = M01z / M02z = 0.505 Factor C; Cz = 1.7 – rmz = 1.195 Relative normal force; n = NEd / (Ac × fcd) = 0.843 Slenderness limit; llimz = 20 × A × B × Cz / √(n) = 28.5 lz > llimz – Second order effects must be considered
Local second order bending moment about y axis (cl. 5.8.8.2 & 5.8.8.3)
Relative humidity of ambient environment; RH = 50 % Column perimeter in contact with atmosphere; u = 1257 mm Age of concrete at loading; t0 = 28 day Parameter nu; nu = 1 + w = 1.719 Approx value of n at max moment of resistance; nbal = 0.4 Axial load correction factor; Kr = min(1.0 , (nu – n) / (nu – nbal)) = 0.665 Reinforcement design strain; eyd = fyd / Es = 0.00217
Resultant design bending moment for a circular column Resultant design moment; MEd = √(MEdy2 + MEdz2) = 121.0 kNm
Moment capacity about y axis with axial load NEd
Moment of resistance of concrete By iteration:- Position of neutral axis; y = 289.8 mm Depth of stress block; dsby = min(lsb × y , h) = 231.8 mm Area of concrete in compression; Asby = 75498 mm2 Concrete compression force (3.1.7(3));Fyc = h × fcd × Asby = 962.6 kN Centroid of concrete compression from column cl; ysby = 68.0 mm Moment of resistance; MRdyc = Fyc × ysby = 65.4 kNm
Moment of resistance of reinforcement Strain in layer 1; εy1 = εcu3 × (1 – dy1 / y) = -0.00043 Stress in layer 1; σy1 = max(-1×fyd, Es × εy1) = -85.5 N/mm2 Force in layer 1;Fy1 = 2 × Abar × sy1 = -83.9 kN MRdy1 = Fy1 × (h / 2 – dy1) = 10.5 kNm
Strain in layer 2; εy2 = εcu3 × (1 – dy2 / y) = 0.00108 Stress in layer 2; σy2 = min(fyd, Es × εy2) – h × fcd = 204.1 N/mm2 Force in layer 2; Fy2 = 2 × Abar × sy2 = 200.4 kN Moment of resistance of layer 2; MRdy2 = Fy2 × (h/2 – dy2) = 0.0 kNm
Strain in layer 3; εy3 = εcu3 × (1 – dy3 / y) = 0.00260 Stress in layer 3; σy3 = min(fyd, Es × εy3) – h × fcd = 422.0 N/mm2 Force in layer 3; Fy3 = 2 × Abar × sy3 = 414.3 kN Moment of resistance of layer 3; MRdy3 = Fy3 × (h/2 – dy3) = 51.8 kNm
Resultant concrete/steel force; Fy = 1493.3 kN
PASS – This is within half of one percent of the applied axial load
Combined moment of resistance Moment of resistance about y axis; MRdy = 127.8 kNm
Moment capacity about z axis with axial load NEd Moment of resistance of concrete By iteration:- Position of neutral axis; z = 287.0 mm Depth of stress block; dsbz = min(lsb × z , h) = 229.6 mm Area of concrete in compression; Asbz = 74628 mm2 Concrete compression force (3.1.7(3)); Fzc = h × fcd × Asbz = 951.5 kN Centroid of concrete compression from column cl; ysbz = 69.1 mm Moment of resistance; MRdzc = Fzc × ysbz = 65.8 kNm
Moment of resistance of reinforcement Strain in layer 1; εz1 = εcu3 × (1 – dz1 / z) = -0.00070 Stress in layer 1; σz1 = max(-1×fyd, Es × εz1) = -140.2 N/mm2 Force in layer 1; Fz1 = 1 × Abar × sz1 = -68.8 kN Moment of resistance of layer 1; MRdz1 = Fz1 × (h / 2 – dz1) = 9.9 kNm
Strain in layer 2; εz2 = εcu3 × (1 – dz2 / z) = 0.00018 Stress in layer 2; σz2 = min(fyd, Es × εz2) = 36.0 N/mm2 Force in layer 2; Fz2 = 2 × Abar × sz2 = 35.3 kN Moment of resistance of layer 2; MRdz2 = Fz2 × (h / 2 – dz2) = -2.6 kNm
Strain in layer 3; εz3 = εcu3 × (1 – dz3 / z) = 0.00194 Stress in layer 3; σz3 = min(fyd, Es × εz3) – h × fcd = 375.7 N/mm2 Force in layer 3; Fz3 = 2 × Abar × sz3 = 368.8 kN Moment of resistance of layer 3; MRdz3 = Fz3 × (h/2 – dz3) = 26.6 kNm
Strain in layer 4; εz4 = εcu3 × (1 – dz4/z) = 0.00282 Stress in layer 4; σz4 = min(fyd, Es × εz4) – h × fcd = 422.0 N/mm2 Force in layer 4; Fz4 = 1 × Abar × sz4 = 207.2 kN Moment of resistance of layer 4; MRdz4 = Fz4 × (h/2 – dz4) = 29.9 kNm Resultant concrete/steel force; Fz = 1494.0 kN
PASS – This is within half of one percent of the applied axial load
Combined moment of resistance Moment of resistance about z axis; MRdz = 129.8 kNm
Minimum moment capacity with axial load NEd Minimum moment capacity; MRd = min(MRdz, MRdy) = 127.8 kNm
PASS – The moment capacity exceeds the resultant design bending moment
In civil engineering design and construction works, professional engineers (fully registered/chartered engineers) are often asked to review the work or documents prepared by another professional engineer. In all professional engineering bodies, there are existing policies or guidelines on how engineers should professionally relate with fellow engineers. The aim of this article is to highlight some well established and globally accepted guidelines for reviewing the work of a fellow professional engineer.
The guidelines in this article provide professional engineers performing reviews of work created by other practitioners with guidance on how to complete such tasks in a way acceptable to the profession. The suggestions in this article are thought to be in line with all of the practitioners’ professional obligations, and are adapted from the guidelines of the Professional Engineers Ontario (PEO).
In so many professional engineering bodies’ ethics and code of conducts (professional engineering acts), it is clearly stated that engineers should not agree to review another practitioner’s work for the same employer unless you have the other practitioner’s consent or the other practitioner’s connection to the work has been terminated.
Why should my work be reviewed?
Although fairly specific, the prohibition on reviewing another engineer’s work by several engineering acts is constrained by some factors. Professional engineers shouldn’t, however, object to having their work or that of a colleague, reviewed. It is reasonable and, in the event of legally mandated requirements, a necessary practice for another engineer to review the work of a practitioner. It is in accordance with a practitioner’s ethical requirements, the association’s duty to uphold high professional standards, and the requirement to preserve the public’s confidence in the profession as long as the practice is carried out impartially and fairly.
Giving feedback on the work of another professional engineer has wider ramifications that should be understood by all practitioners. The fact that a practitioner’s work was reviewed may occasionally have a detrimental effect on the engineer’s reputation. A negative review can permanently damage the relationship between a practitioner and a client or employer, even if the outcome is not generally publicised. Reviewing engineers must be familiar with the methods for assuring the fairness, impartiality, and thoroughness of the review process if they are to ensure reviews achieve the justifiable aims in the most professional manner.
An impartial evaluation may reveal errors or issues with the examined work that need to be disclosed. Different projects will differ in what needs to be reported and to whom, so the reviewing engineer should be given some leeway. The reviewer must understand the difference between legitimate flaws in the work and professional differences of opinion in order to correctly convey what is required. Practitioners conducting reviews must be aware of these problems and take all necessary precautions to handle them properly.
Reasons and Types of Professional Review
A practitioner’s work may be reviewed for a variety of reasons and in a variety of contexts. Colleagues inside an organisation, staff members of regulatory agencies, employees of client companies or other organisations utilising the engineer’s work, or outside engineers hired by a client to provide an unbiased evaluation of the work are all examples of reviewers. A request for a review may result from a variety of situations, including corporate quality assurance and legal action against a practitioner.
However, the Professional Engineers Ontario identified two general types of review;
Practice review, and
Technical review
In the wider context, the main objective of a practice review is to evaluate the job performed by an engineer or the service they supplied. In this case, the assessment of the practitioner’s performance is made.
Conversely, a technical review evaluates whether the information in a document or design produced by an engineer is accurate, complete, or acceptable. Technical reviews produce opinions about the output quality of the job, not the engineering process itself. In other words, a technical review evaluates a design, analysis, calculation, instruction, or opinion, but a practice review evaluates the practice of a professional engineer.
Technical Reviews
Technical reviews are conducted to evaluate a design, technical report, or other engineering service output’s acceptability and see if it complies with project criteria. Typically, these evaluations only involve randomly checking engineering documents for technical errors.
Technical reviews, however, can involve in-depth analyses of the methodology, design criteria, and calculations employed by the authoring engineer as well as the accuracy, suitability, economic viability, or other characteristics of the design decisions or study recommendations, depending on the needs of the client.
The reviewer will confirm the accuracy of computations in addition to making sure the right approach was used. Technical reviewers should also make sure that the standards, codes, and other design criteria utilised in the project under consideration are acceptable for it and that they were implemented correctly. According to the Professional Engineers Ontario, technical reviews generally aim to evaluate the following things:
whether the completed work has met the objectives;
whether the objectives set out for the work were reasonable;
whether there were other options that should have been considered by the authoring engineer;
whether the evaluation of options is comprehensive, unbiased and rigorous;
validity of any assumptions made by the authoring engineer;
validity of the conclusions or calculations;
validity of recommendations; and
fitness of the design or recommendations to the requirements.
The reviewer is free to offer feedback on whether the design is suitable for the intended use, including assessments of its effectiveness and economics. In the case of a technical report, the reviewer should state whether the analysis or facts in the report support the recommendations.
The review engineer may comment on the inventive, efficient, cost-effective, and other noteworthy parts of the design or report in addition to pointing out flaws, abuse, or lack of application of recognised industry standards, regulations, or design criteria.
A technical review wouldn’t often be as thorough as an original design or analysis. In most circumstances, random checks of the work rather than a thorough examination of every part of the writing engineer’s work would be carried out. The extent of the review, however, must be left to the reviewers’ judgement, based on what they think is required to fully complete the assignment and satisfy themselves that they have enough data to draw reliable conclusions.
The reviewing engineer may suggest to the client or employer that a more thorough examination is required if such a recommendation is justified in light of the issues found during the assessment.
Regulatory Review
Municipal building departments, building control agencies, provincial ministries and their agencies, federal government agencies, and town planning agencies are examples of regulatory authorities that carry out different types of reviews. Employees of the regulatory body in these situations examine the practitioners’ work that has been submitted for approval in order to verify that it complies with prescriptive legislation like building codes and municipal bye laws.
A professional engineer is not required to analyse regulatory compliance, with the exception of what is detailed below, as it is a legal rather than an engineering matter. In most cases, it is unlawful for those performing regulatory compliance checks to provide engineering opinions.
Only the information in the engineering papers or drawings must be compared to standards, codes, or legal requirements during the compliance check. For instance, whether the design is economical or not should not be their concern, rather it should bother on whether it meets the regulatory requirements.
A regulatory body should only notify the practitioner when performing compliance checks to identify non-compliance issues. The authoring engineer must be trusted to make the final call on how to modify the document to address non-compliant concerns.
Regulating authorities do, however, occasionally conduct more thorough evaluations to ascertain whether designs are technically adequate, to ascertain whether they fulfil performance standards, or to evaluate designs that are not subject to prescriptive rules.
For the municipality’s own due diligence, the building department, for instance, might carefully examine a proposed structural design to ensure that it is secure. A professional engineer must conduct this kind of evaluation, and it must be conducted in accordance with the guidelines for a technical review outlined in this policy.
In-house Design Review in Organisations
For a variety of reasons, professional engineers working for engineering firms or other organisations may be asked to examine their coworkers’ work. Such internal evaluations could be technical reviews for quality control or practise reviews to see if the authoring engineer is competent of completing the task at hand or for personnel performance evaluation objectives.
Because the firm will ultimately be responsible for the outcome of the engineering service, it is expected that the relationship between the practitioners will be very cooperative when reviews are conducted by a colleague within an engineering firm. The reviewer may act as a problem-solving consultant in these situations. For this reason, a practitioner with greater authority inside the company may override the authoring engineer’s judgement.
Written corporate policy notifying all practitioners that their work will be examined is sufficient notice in organisations where all drawings and documentation are scrutinised for quality before issuance or approval. Only regular reviews—including those conducted as part of employee performance audits—are subject to this regulation. The practitioner must be informed prior to the assessment of the work in situations where the review deviates from customary quality assurance because there are doubts about a person’s capacity to do the responsibilities given to them.
Pre-Construction Reviews
A professional engineer working for a contractor, fabricator, manufacturer, or other party that will use the authoring engineer’s design to build or create a product for which the reviewing engineer’s employer will then be liable is also able to examine the authoring engineer’s work. In these situations, the individual or group employing the design may be inspecting the engineering documents as part of its due diligence evaluation.
Since a company creating a product or executing a project must be able to rely on the correctness and thoroughness of the engineering work, it is reasonable for them to review the design to make sure it is error-free. In this scenario, a review is being requested by a party other than the writing engineer’s client or employer, and the review’s goal is to safeguard the general public or the design’s user rather than to evaluate the professional engineer.
Clause 77.7.ii of O. Reg. 941 (PEO) does not apply because the review was started by someone other than the authoring engineer’s employer or customer. The authoring engineer need not be made aware that a review is being conducted by the reviewing engineer.
Review or Second Opinion?
Reviewing engineers should always make it clear if the client or employer is asking for a second opinion or a review of a practitioner’s work. A second opinion is an assessment of the problem that is offered to the client in order to provide the client with more information before making a choice. An engineer offering a second opinion examines the identical problem that the first engineer was given, and without taking into account the first engineer’s work, they provide a solution, develop a concept, or offer suggestions.
For instance, a client who wishes to construct a medium rise building can contact an engineer who suggests an expensive piled-raft foundation. Due to the high cost of the suggested work, the homeowner may opt against moving forward right away in favour of seeking a second opinion. It is obvious that what is required in this case is not a review of the work of the first engineer, but rather a unique study and recommendation, which can be made without taking the work of the first engineer into account.
General Principles for carrying out a review
(1) The extent of the the review must be project-specific and as thorough as called for by the scope and kind of review. The extent of checking is always up to the reviewer’s reasonable discretion and judgements of the most effective approaches to complete the task. The reviewer must always be certain that the conclusions—whether favourable or unfavorable—regarding the documents’ quality or the writing engineer’s service are founded on accurate evaluations of the subjects under consideration.
(2) A review must be thorough enough to give the client or employer adequate information to answer all of their questions and to support the reviewer’s assessments of the work’s quality. This must be however done in accordance with the principle of fairness. If a review is not thorough enough, the reviewer may overlook problems that the client or employer should be made aware of. The reviewer’s service would be inadequate in this case.
(3) On the other side, a review shouldn’t go so far as to criticise unimportant, trivial issues. A reviewer shouldn’t point out spelling mistakes, poor grammar, poor drafting, or other features of a document’s form unless these issues make the document unclear, hard to understand, or provide others depending on it the chance to apply it incorrectly.
(4) Both verbally and in writing, it is important that the reviewer’s mandate be phrased neutrally and without making any assumptions about the desired outcome. The reviewing engineer should remind the client or employer that the reviewer is professionally required to stay independent and exhibit no bias in performing this service if the client or employer declares or implies that a practitioner should skew the evaluation in any way.
(5) Reviewing engineers should create a plan for conducting their technical reviews that outlines the documents to be examined, resources available to the reviewer, the methodology of the review, the format of the review report, the protocol of communications between the reviewer and other parties, considerations for confidentiality, a schedule for the review, and other pertinent factors. Such a plan, provided to the client before starting a review, will demonstrate the reviewing engineer’s independence and reduce the possibility of any conflicts of interest or misconceptions.
Basis for Review and Criticisms in Reporting
Reviewing engineers must identify both the positive and negative elements of the engineering work and draw attention to anything that is inaccurate, ambiguous, unsupported, or problematic in the original document as a standard part of the process. It is part of the reviewer’s job description to occasionally reflect negatively on elements of the work completed by another professional engineer. Reviewing engineers may, however, feel that they are also expected to be critical and to uncover things that, while not always wrong or harmful, can nonetheless be seen negatively.
Reviewers must make sure that their reporting of negative evaluations adheres to the provisions in the Code of Ethics that outline practitioners’ obligations to other professional engineers. According to article 77.7 of O. Reg. 941 (PEO), it stipulates the following:
“A practitioner shall, i. act towards other practitioners with courtesy and good faith, … iii. not maliciously injure the reputation or business of another practitioner”.
This approach should be carried out objectively and consistently performed in order to be fair to an authoring engineer. For this reason, while determining what is incorrect with an engineering job, reviewers should follow the procedure below.
Identifying the applicable assessment criteria is the first step in every review. It is obvious that in order to be objective, a practitioner’s work must be compared to the standard procedure for professional engineers performing identical work in order to assess both the technical and professional components of their job. Professional engineers are required to abide by all laws establishing standards and codes, however not all laws establishing best practices are adopted by practitioners experienced in a given industry.
The comparison of the work with instances of good engineering practice is another crucial factor for forming judgements in a review. Good engineering practice consists of widely accepted, well known, and generally acceptable standards that has been used or accepted by the majority of professionals that routinely work in that field.
Reviewing engineers shouldn’t inquire about an authoring engineer’s qualifications. Only when they are qualified to do so, licensed practitioners are expected to accept and complete engineering tasks. The authoring engineer makes this evaluation of skill. It shouldn’t be expected of reviewing engineers to assess the expertise of authoring engineers or to express an opinion on their suitability for the tasks described in the documents.
A reviewing engineer should not ask a client or an authoring engineer to disclose the fee or salary paid to the authoring engineer for the work under review. Practitioners must constantly devote enough time and effort to carrying out their tasks in a way that adheres to the standards of the engineering profession. Professionalism standards are unaffected by payment or income and are not negotiable with clients or employers.
Ethical obligations of a reviewing engineer
The obligations of a reviewing engineers are therefore as follows;
(1) Notification A practitioner should only take on the assignment with the knowledge of the other practitioner if a client or employer requests that they review the work of another engineer who is still working on a project under the terms of an employment contract or a contract for professional services. However, it is the review engineer’s duty to make sure that the client is aware of the obligation for notification and complies with it. This notification should be made by the client or employer.
Article 77.7.ii of PEO specifically indicates that it only applies when the engineer is asked by the same employer to examine the work of another practitioner. The relationship between the practitioner and the employer/client is, without a doubt, the crucial issue in this area. Only while that professional relationship is active does the responsibility apply.
(2) Confidentiality Practitioners need to always consider their interactions with clients and employers as professional ones. A professional relationship is based on trust, thus practitioners must conduct in a way that fosters both acquiring and preserving that trust. A reviewer shouldn’t speak to an authoring engineer or anybody else about the review without first asking and receiving authorization from the client or employer.
(3) Good faith Being driven by a conviction for the validity of one’s beliefs or the morality of one’s deeds is referred to as acting in good faith. The rightness of a course of action is determined by adherence to the Code of Ethics for a practitioner offering professional engineering services. Evaluations of whether one’s opinions are true or false are subjective judgments based on a person’s character. Every practitioner must be realistic about their own assessments and assured that using their knowledge and abilities consistently produces trustworthy results while accounting for human imperfection.
(4) Fairness Any person who has discretion over how to distribute burdens and advantages among group members must adhere to the idea of fairness. Practitioners are free to express their opinions about the work in a review. Depending on the nature of the opinions and the effects they have, they may help or hurt the customer, authoring engineer, or other stakeholders in different ways.
The reputation, standing in the engineering community, or financial interests of an authoring engineer should not be thought to be harmed by statements made by a reviewing engineer or the release of all or any portion of a review report. If the client or employer asks the reviewing engineer to take part in any such activity, they shall refuse unless the publishing of the report is mandated by the freedom of information act or another law.
However, a professional engineer is not prohibited by the duty of impartiality from stating facts or offering an honest opinion that could be detrimental to another professional or the client.
(5) Conflict of interest A relationship between a practitioner and one or more parties that could be seen as a conflict of interest is another issue that could occur when offering professional services. A conflict between two or more conflicting interests and a duty of the practitioner is the primary characteristic of a conflict of interest. A conflict of interest occurs when a practitioner finds it difficult to fulfil their obligations to someone whose interests may be impacted by their decisions.
Conflict arises when the practitioner or a third party both have interests that must be ignored or put aside in order for the practitioner to pursue their own. It would be against the practitioner’s obligation to disregard or put that person’s interests second. In general, the responsibility that needs to be upheld is one that the practitioner has to the client or employer; nevertheless, there are numerous additional obligations that practitioners have, including obligations to fellow practitioners, which may also be jeopardised by competing interests.
When settlements of foundation could be an issue, such as when a site has erratic deposits or lenses of compressible materials, suspended boulders, etc., mat foundations are frequently used. Settlement of mat foundations has been observed to be lower compared to spread footing.
It is impossible to completely eliminate the settlement of shallow foundations founded on natural soils. At least, the immediate (elastic) must occur, before the consolidation settlement will begin, if the foundation is founded on clay. The following methods are frequently used to control the settlement of foundations during the design of foundations:
Making use of a larger foundation to reduce soil contact stresses
Displaced volume of soil (flotation effect); in theory, the system “floats” in the soil mass and no settlement takes place if the weight of the excavation is equal to the total weight of the structure and mat (see design of bouyancy raft foundation).
Bridging effects attributable to mat rigidity and contribution of superstructure rigidity to the mat.
Allowing bigger settlements that are 50 mm instead of 25 mm larger.
Even in cases where consolidation is a challenge or piles are employed, the flotation effect through the use of buoyancy raft (or compensated foundation) ought to be able to keep most mat settlements to a maximum of 50 to 80 mm. For all types of foundations and structures, differential settlement is a problem that deserves more serious attention. However, the use of mat foundation tends to reduce this problem.
From our previous articles, we have seen that the bending moments (6EI∆/L2) and shear forces (12EI∆/L3) in frames are dependent on the relative movement ∆ between the beam ends.
In comparison to a spread footing (pad foundation), mat foundation due to its continuity produces somewhat reduced anticipated value of differential settlement compared to the total settlement.
Foundation Type
Expected Maximum Settlement (mm)
Expected Differential Settlement (mm)
Pad foundation
25
20
Mat foundation
50
20
The settlement of mat foundation depends on the rigidity of the mat, type of mat, the type of soil, the homogeneity of the soil, groundwater condition, and construction method.
To estimate both total and differential settlements, one can use computer approaches that take into account frame-foundation interaction. However, if any other than a strip from the mat is employed in a beam-on-elastic foundation type of analysis, the computing work is significant and the overall settlements will only be as accurate as the soil data.
The differential settlement of mat foundation may be arbitrarily taken as 20 mm (0.75 inches) if the total expected settlement ∆H is not more than 50 mm. Alternatively, it may be approximated using a rigidity factor Kr [see ACI Committee 336 (1988)] defined as;
Kr = EIb/EsB3
where: EIb = flexural rigidity of the superstructure and mat Es = modulus of elasticity of soil B = base width of foundation perpendicular to direction of interest
ACI Committee 336 suggests that mat differential settlements are related to both the total estimated foundation settlement ∆H and the structure rigidity factor Kr about as follows:
Kr
Differential Settlement Expected
0
0.5 x ∆H (for long base) 0.35 x ∆H (for square base)
0.5
0.1 x ∆H
> 0.5
Rigid Mat (no differential settlement)
However, where the net increase in pressure exceeds the current in situ pressure p’o, full settlement analyses will need to be done. Depending on the underlying soil stratification, these settlements may be immediate or consolidation settlements adjusted for OCR.
The proper design of a raft foundation should therefore strike a balance between the requirement to prevent the raft’s structure from becoming excessively rigid, and the need to limit the differential settlement of the raft and, by extension, the superstructure. Flexibility in a raft results in minimal bending moments, which saves money in the substructure.
However, this flexibility comes at the expense of relatively large differential settlement and higher costs to accommodate these movements in the superstructure, such as through joints or a flexible cladding. A raft’s stiffness reduces differential settlement but increases bending moments, which raises the cost of the raft by redistributing load.
The stiffness of the structure relative to the raft can be expressed by the following equation;
Kr = [4Ec(1 – µs2)/3Es(1 – µc2)] x (t/B)3
Where; Kr = relative stiffness Ec = Modulus of elasticity of concrete Es = Modulus of elasticity of soil µs = Poisson ratio of soil µs = Poisson ration of concrete t = Thickness of raft B = Width of raft
Heave in Mat Foundation
Expansion and/or lateral flow into the excavation base, which causes the base elevation to rise, is a significant issue, especially for deep excavations in clay. Heave is the word for this occurrence, and values between 25 and 50 mm are very typical. In literature however, values up to 200 mm (or 8 inches) have been reported. When heave has occurred, settlement calculations are challenging. Theoretically, if we restore a mat pressure q0 equal to that which was previously extant, all the heave should be recovered.
In reality, this recovery doesn’t happen, or it doesn’t happen as quickly as the heave occurs. It should be anticipated that it will be extremely difficult to forecast either the overall amount of heave or how much of this will be recovered by elastic recompression if some of the heave results from a deep-seated lateral flow.
Since there are currently no valid theories for the issue of heave, estimation of the expected soil response generally requires extensive knowledge and engineering judgement where heave is encountered. A finite element of the elastic continuum computation is said to be able to solve the problem, however this claim is speculative and based on the expectation that calculations and measurements would turn out well.
The explanation is that the accuracy of a finite-element computation depends on the input parameters soil modulus of elasticity and Poisson ratio. Even if we were able to obtain a reliable initial value Es, it would still decrease during and after excavation because of the heave that is caused by the loss of confining pressure (p’o) and expansion.
Methods of Estimating the Settlement of Mat Foundation
The method of summation of partial settlements or the method of an elastic layer of finite thickness can be used to determine the settlement of raft foundations. When using the method of summation of partial settlements, the settlement is determined at a single location without taking the stiffness of the foundation into consideration.
However, in cases involving large-scale foundations, the average settlement of the foundation must be taken into account by computing the settlement at various foundation positions. The thickness of the compressed zone, which can be influenced by the size of the foundation, the applied load of higher buildings, and the soil condition, determines the settlement results of the foundation for the method of elastic layer of finite thickness.
The settlement of mat footings can be estimated using the methods developed from the theory of elasticity, assuming that they impart stresses on the ground in a manner similar to that of spread footings. The following expression (Timoshenko and Goodier, 1951) based on the theory of elasticity can be used to estimate the corner settlement of a rectangular footing with dimensions of L′ and B′;
where q is the contact stress, B′ is the least dimension of the footing, νs is the Poisson ratio of the soil, and Es is the elastic modulus of the soil. Factors I1, I2, and IF are influence factors that can be obtained from so many geotechnical engineering textbooks, in terms of the ratios N = H/B′ (H = layer thickness), M = L′/B′ (L′ = other dimension of the footing), and D/B (the foundation depth ratio).
The same expression above can be used to estimate the settlement of the footing at any point other than the corner by approximate partitioning of the footing. It must be noted that even if the footing is considered as a combination of several partitions (B′ and L′), in determining the settlement of an intermediate (non-corner) location, the depth factor, IF, is applied for the entire footing based on the ratio D/B.
Gazetas et al. (1985) considered an arbitrarily shaped rigid footing embedded in a deep homogeneous soil and proposed the following equation for the elastic settlement:
Si = (P/EuL) × (1 – vu2) × µsµembµwall
where P is total vertical load, Eu is the undrained elastic modulus of the soil, L is one-half the length of a circumscribed rectangle, vu is Poisson’s ratio for the undrained condition, and µs, µemb, and µwallare shape, embedment (trench), and side wall factors given as;
Ab is the actual area of the base of the foundation and Aw is the actual area of the wall in contact with the embedded portion of the footing. The length and width of the circumscribed rectangle are 2L and 2B, respectively. The dimensionless shape parameter, Ab/4L2, has the values for common footing geometry shown in the Table below;
Footing Shape
Ab/4L2
Square
1
Rectangle
B/L
Circular
0.785
Strip
0
The equations proposed by Gazetas et al. (1985) apply to a foundation of arbitrary shape on a deep homogeneous soil. What is meant by “deep” is not clearly defined. When the thickness of the soil layer is such that 90% of the applied stresses are distributed within it, the author advises using the equations of Gazetas et al. The soil layer should be at least 2Br thick for a rectangle with actual width Br.
The accuracy of the elastic modulus is very important for any elastic equation for soils. It is standard laboratory procedure to calculate a secant Eu from unconfined compression tests or undrained triaxial tests with a deviatoric stress equal to 50% of the highest shear strength. However, it is preferable to determine Eu over the range of deviatoric stress relevant to the problem for better solution. One possible solution is to divide the soil into sublayers and use a weighted harmonic mean value of Eu.
Worked Example1
Determine the immediate settlement of the foundation shown below. The undrained elastic modulus varies with depth, as shown in the figure, and vu = 0.35.
Approach You have to determine the length (2L) and width (2B) of a circumscribed rectangle. The undrained elastic modulus varies with depth, so you need to consider the average value of Eu for each of the layers and then find the harmonic mean. You also need to find the shape parameter Ab/4L2.
Step 1: Determine the length and width of the circumscribed rectangle. 2L = 8 + 7 = 15 m; L = 7.5 m 2B = 6 + 4 + 10 m; B = 5 m
Step 5: Calculate the settlement Si = (P/EuL) × (1 – vu2) × µsµembµwall = (6500/17311 × 7.5) × (1 – 0.352) × 0.5678 × 0.972 × 0.856 = 0.02075 m = 20.754 mm
Worked Example 2
A medium dense sandy soil foundation layer is found under the mat shown below, which is underlain by a weathered bedrock at a depth of 6.0 m below the surface, estimate the average immediate settlement and the maximum differential settlement of the mat footing. Let us assume that in this case the sand is normally consolidated with SPT value of 15.
Depth of foundation = 1.0 m
Then, for an average SPT value of 15, Es is approximately given by 500(N + 15) = 15000 kPa or 15 MPa. A Poisson’s ratio of 0.30 can also be assumed in normally consolidated sand.
The footing has been arranged such that a uniform pressure will be obtained at the base.
P = 350 + 800 + 350 + 800 + 1200 + 800 + 350 + 800 + 350 = 5800 kN Area of base = 10 × 10 = 100 m2
Then the uniformly distributed contact stress = 5800/100 = 58 kPa D/B for the entire footing = 1/10 = 0.1 From the chart below, for L/B = 1 and D/B = 0.1, IF = 0.85.
Therefore, the immediate settlement expression can be simplified to:
For the corner settlement M = L/B = 1.0, N = H/B = 5/10 = 0.50 From Table above, I1 = 0.049, I2 = 0.074 Si = 0.00299B'(I1 × 0.571I2) si = 0.00299 × 10 × [0.049 + 0.571(0.074)] = 0.0027284 m = 2.72 mm
For the center settlement M = L/B = 5/5 = 1.0, N = H/B = 5/5 = 1.0 From Table above, I1 = 0.142, I2 = 0.083 si = {0.00299 × 5 × [0.142 + 0.571(0.083)]} × 4 = 0.01132 m = 11.325 mm
The number “4” indicates the four equal partitions required to model the center by superposition of four corners of the partitions.
Differential Settlement Differential settlement = 11.325 – 2.712mm = 8.613 mm Maximum angular distortion within the footing = (23.0 – 5.471)/5000 = 0.0017226 < 1/3000 Therefore, the foundation is safe from any architectural/structural damage.
Finite Element Modelling
The foundation was modelled on Staad Pro software. The soil was modelled with solid elements with the following properties;
Es = 15000 kPa Poisson’s ratio = 0.3
The raft slab was modelled as a thin flexible plate with a full pressure of 58 kPa applied in the global vertical direction. A fixed support was applied at the base of the ground model to represent the bedrock. It should be noted that the thickness of the selected plate affects the settlement values.
The vertical pressure distribution as a result of the loading is shown below;
The observed settlements are shown below;
The observed corner displacements was 3.914 mm and the centre displacement was 15.546 mm.
Deflection is the movement of a point on a structure or structural element, usually measured as a linear displacement or succession displacements transverse to a reference line or axis. Thus, deflection can be said to be a deformation that occurs over time on a structure or structural element under a load. The primary material parameters influencing concrete deflection are temperature, modulus of elasticity, shrinkage, modulus of rupture, and creep.
Deflection is a vital serviceability limit state criterion in the design of reinforced concrete structures. Therefore, structural designers must always consider deflection and ensure compliance with acceptance criteria for deflection as stated in RC design codes such as BS 8110, EC 2 and IS 456.
This article will discuss the theory of deflection of slabs and thin plates, the effects of deflection on the performance and functionality of RC buildings, factors affecting the deflection of RC slabs, methods of assessing the deflection of slabs, how to control deflection during design, and how to remedy a building failing in deflection.
Beam theory of slab deflection
Slabs are common structural elements of RC building structures, taking up nearly 50% of the total weight of buildings. Slabs are usually analyzed under transverse loading, and the slab thickness governs the serviceability requirement for deflection. Therefore, structural designers need to properly analyze slabs to choose the minimum slab thickness satisfying the deflection criterion and minimizing the building’s weight.
The deflection theory of slabs is similar to that of beams. However, it is more complex. Consequently, we will adopt a simplified approach for one-way and two-way spanning slabs.
One-way slabs
(a) One-way slab (b) Two-way slab
Given the figures above, the slabs are analyzed as a beam with the bending moments per unit strip. As shown in (a), one-way slabs are supported on two opposite sides. The load transfer and structural action are usually in one direction along the slab’s shorter span (la) or perpendicular to the supporting beams. Thus, we can say that the slab consists of a single parallel strip.
To derive the deflection equation, we assume the strip acts like a simply supported beam uniformly loaded across its length (l). Thus, the general slope and deflection equations can be derived using the double integration method, as shown below.
General slope equation:dy(EI/dx) = wlx2/4 – wx3/6 – wl3/24 General deflection equation:yEI = wlx3/12 – wx4/24 – wl3x/24
Since maximum deflection occurs at the mid-span of the strip, that is, where x = l/2
Then, substituting x = l/2 into the deflection equation gives the resulting equation below.
Maximum deflection at mid-span:y = 5wl4/384EI
Two-way slabs
Similarly, the two-way slab in (b) is essentially supported on all four sides, and the load transfer and structural action are in two directions resulting in biaxial bending moments. Thus, we can say that the slab consists of a parallel strip in each direction (la and lb), and they intersect each other. Consequently, the load supported by the slab is shared between the two strips though dominant in the direction of the shorter span (la).
Furthermore, it is proper to assume that the mid-span deflections in the two-way slab at the point of intersection are equal since the strips are part of the same slab. Therefore, under a uniformly distributed load (w) per square metre, each strip takes its share of w as wa and wb, and the deflection equations are given below.
5wala4/384EI in the shorter direction 5wblb4/384EI in the longer direction
It must be noted that the maximum deflection equations above hold for simply supported end conditions. Thus, the maximum mid-span deflection is wl4/192EI for hinged-fixed end conditions and wl4/384EI for fixed-fixed end conditions.
Deflection of thin plates
Plates are defined as plane structural elements with a small thickness compared to other dimensions of the plate. As a result, plates resist applied loads employing bending in two directions and twisting moment. Thus, the plate theory takes advantage of the disparity in length scale to reduce the entire 3-D solid mechanics problem to a 2-D problem.
Furthermore, plates are categorized into thick, thin, and membranes depending on thickness to width ratio. For example, if a plate’s thickness to width ratio is less than 0.1 and the maximum deflection is less than one-tenth of the thickness, then the plate is classified as a thin plate structure.
Several plate theories are associated with geometric assumptions, such as the Kirchhoff plate theory, the Reissner-Mindlin plate theory, the von Karman plate theory, and the Timoshenko plate theory. Below, the Timoshenko plate theory is briefly discussed.
One-way slabs
Timoshenko’s plate theory for cylindrical bending of uniformly loaded rectangular plates with simply supported edges can be used for one-way slabs because the bending nature of such slabs can be simulated as thin plates with small deflections. Thus, the governing differential equation for the deflection curve is given below:
–M = D(d2w/dx2) and, D = Eh3/12(1-v2)
Where D is the Flexural rigidity of the plate, E is the modulus of elasticity of the plate material, v is the Poison’s ratio, h is the thickness of the plate, and the variable quantity ‘w’ is the transverse deflection of the middle plane of the plate.
Thus, the maximum deflection for simply supported conditions is at the center, and it is given by: w = 5ql4/348D
Where q is the UDL loading intensity on the plate and l is the length of the plate along supported edges.
Two-way slabs
For a two-way, rectangular plate with sides a and b, as shown above, the derivation of the maximum deflection at the center of the plate involves rigorous analysis. Thus, it would not be considered in this article. However, if we assume that the plate is instead square such that sides a and b are equal, then the maximum central deflection is given below.
w(max) = 4qa4/π6D = 0.00416qa4/D
Effects of deflection on building performance and functionality
It is true that buildings move and experience vibrations. However, designing a building aims to achieve a state of static equilibrium. The state of equilibrium is to be among the parts of the constructed building and the forces acting on it. Therefore, deflection is one of the movements in buildings affecting performance and functionality.
Excessive deflection of flexural members above those the structural designer allows can result in several difficulties for building occupants. These difficulties include cracking of wall, floor and ceiling finishes, unsightly and unacceptable appearance or visual effects, impaired functionality, alarm and discomfort to building occupants, and damaged roof membranes and supported partitions.
Deflection of cantilever slab leading to cracking to masonry walls
Additional potential problems associated with slab deflection include jamming doors and windows, gaps between partitions and floors and between columns and floors, and visual perception of sagging floors and ceilings. Furthermore, deflection can worsen over time and lead to additional maintenance costs and structural problems.
Moreover, a suspended floor slab must be serviceable during the life of a building. Therefore, it is expected that the top profile of a slab does not show any sign of deflection. However, occupants of a building can decide to change the use of a building or space if they perceive any deflection on a floor slab surface under sustained loading. For example, an occupant can convert a building or space from an office, institutional, educational or industrial use to general domestic use.
Factors affecting the deflection of RC slabs
Several factors affect the deflection of RC slabs, and a holistic and accurate assessment of slab deflections can only be achieved if consideration is given to these factors. Furthermore, the factors affecting slab deflections vary intrinsically and may change with time. For example, factors such as elastic modulus, creep coefficient, and tensile strength of concrete significantly influence the final slab deflections.
Furthermore, some factors are influenced by others. Consequently, deflection calculations remain an estimate because of the variability of several factors. Therefore, the technical report (TR58) of a joint project of the British Cement Association, The Concrete Centre, and The Concrete Society advises that actual deflection may vary from calculated deflections in a range of -30% to +15%. The report also discusses the rigorous method of estimating slab deflections and the factors influencing deflection.
Some of the factors affecting slab deflections are discussed below.
Boundary Conditions
The boundary conditions of a slab have a profound effect on the deflection behaviour of the slab. Fully fixed supports will have less deflection compared to simple supports. Monolithic and/or continuous supports also have a more positive effect on deflection compared to corners that are free to lift.
Concrete Tensile Strength
Generally, slab designs are closer to the cracking load, and small property or loading variation can cause a slab to crack and thus deflect more. Therefore, the tensile strength of concrete is an essential property because a slab will crack once the tensile stress in the extreme fibre is exceeded. To reduce slab deflection, then tensile strength must be increased. This can be achieved by increasing concrete compressive strength because tensile strength is proportional to the square root of compressive strength.
Aggregate properties
Fine and coarse aggregates comprise about 70% of a typical volume of concrete. Thus, aggregates significantly influence the elastic modulus of concrete. Therefore, slab deflection will increase substantially if poor-quality aggregates are used.
Material properties have a profound effect on the deflection of slabs
Relative humidity (RH)
According to TR58, it is reported that predicted deflection will decrease with increasing RH. For example, an RC slab in an outdoor environment with RH between 80 – 85% is likely to have deflections about 20% lower than another slab in an indoor environment with RH between 45 – 50%.
Ambient Temperature
The hydration of cement is usually slower at a lower temperature. Therefore, a concrete slab cast under low ambient temperature will experience low strength gain and, consequently, more likely to deflect even under its self-weight.
Time of loading
The effect of early-age loading or overloading of slabs has pronounced effects on deflection, especially when the age of the slab is less than 5 days. However, the further difference in deflection is minimal.
BS 8110 methods of assessing slab deflections
Two methods can check the deflection of slabs according to BS 8110. It is important to know that in the design of RC slabs, deflections are checked in the shorter span, which is more critically loaded. The two methods of checking the deflection of slabs are discussed below.
The first method is guided by the maximum limits of deflections based on slab spans given by the code. For example, BS 8110-2:1985 states that the sag in a concrete member will become visible once deflection exceeds span/250. Therefore, if a structural designer knows the maximum slab deflection for the relevant load case, he can check whether it is within the limit given in Section 3 of BS 8120-2:1985.
Conversely, the second method limits the basic span–effective depth ratio to specific values given in Table 3.9 of BS 8110-1:1997 depending on the slab boundary condition type.
Support Condition
Rectangular Section
Flanged beam with bw/b ≤ 0.3
Cantilever
7
5.6
Simply supported
20
16.0
Continuous
26
20.8
Table 3.9 of BS 8110-1:1997: Basic span/effective depth ratio for rectangular or flanged beams
Furthermore, structural designers should modify the values given in Table 3.9 by multiplying them with the factors for tension and compression reinforcements given in Tables 3.10 and 3.11, respectively.
Eurocode 2 (EN 1992-1-1) Methods of Assessing Deflection
In Eurocode 2, the deflection of a structure may be assessed using the span-to-effective depth ratio approach, which is the widely used method. It is also allowed to carry out rigorous calculations in order to determine the deflection of a reinforced concrete structure, which is then compared with a limiting value.
According to clause 7.4.1(4) of EN 1992-1-1:2004, the appearance of a structure (beam, slab, or cantilever) may be impaired when the calculated sag exceeds span/250 under quasi-permanent loads. However, span/500 is considered an appropriate limit for good performance.
Using the span-to-effective depth approach, the deflection of a structure must satisfy the requirement below;
Allowable l/d = N × K × F1 × F2 × F3 ≥ Actual l/d
Where; N is the basic span-to-effective depth ratio which depends on the reinforcement ratio, characteristic strength of the concrete, and the type of structural system. The expressions for calculating the limiting value of l/d are found in exp(7.16) of EN 1992-1-1:2004. The expressions are given as follows;
Where: l/d is the limit span/depth ratio K is the factor to take into account the different structural systems ρ0 is the reference reinforcement ratio = √fck /1000 ρ is the required tension reinforcement ratio at midspan to resist the moment due to the design loads (at supports for cantilevers) ρ’ is the required compression reinforcement ratio at midspan to resist the moment due to the design loads (at supports for cantilevers) fck is the characteristic compressive strength of the concrete in N/mm2
The values of K for different structural systems are given in the Table below;
Structural System
K
Simply supported beam, one or two way spanning simply supported slab
1.0
End span of continuous beam or one-way continuous slab or two-way spanning slab continuous over one long side
1.3
Interior span of beam or one way or two-way spanning slab
1.5
Slab supported on columns without beams (flat slab)
1.2
Cantilever
0.4
F1 = factor to account for flanged sections (not applicable to slabs) = 1.0
F2 = factor to account for brittle partition in long spans. In flat slab where the longer span is greater than 8.5m, F2 = 8.5/leff In beams and slabs with span in excess of 7.0m, F2 = 7.0/leff
F3 = factor to account for service stress in tensile reinforcement = 310/σs ≤ 1.5 Conservatively, if a service stress of 310 MPa is assumed for the designed reinforcement As,req, then F3 = As,prov/As,req ≤ 1.5
More accurately, the serviceability stress in the reinforcement may be estimated as follows;
σs = σsu[As,req/As,prov]((1/δ)
Where; σsu is the unmodified SLS steel stress taking account γM for reinforcement and of going from ultimate actions to serviceability actions. σsu = fyk/γs(Gk + ψ2Qk)/(1.25Gk + 1.5Qk) As,req/As,prov = Area of steel required divided by the area of steel provided.
How to control slab deflection during design
Deflection control is a vital serviceability requirement in the design of RC building structures because slabs will crack due to excessive deflections if deflection control is not adequately considered. Although providing an adequate safety level against collapse is the primary design consideration, structural designers must consider the possible adverse effects of excessive deflections on the performance and functionality of a structure at service load levels.
Furthermore, design codes guide how to control slab deflection, which will be perfectly adequate and provide economical solutions for most building designs. However, such methods are semi-empirical, and while approximate deflection estimates may be made, they are not intended to predict how much a member will deflect over time.
Deflection in reinforced concrete slabs can be reduced or controlled by increasing the thickness of slab, increasing the area of steel provided, modifying the structural scheme by reducing the span, or reducing the dead load on the slab. Sometimes, two or more of these solutions are required in order to keep the deflection of slab to a minimum.
Increase slab depth
Stiffness plays an essential role in the design of RC slabs because it indicates the ability of the slab to return to its original shape or form after an applied load is removed. Thus, stiffness directly influences slab deflection. Consequently, if stiffness increases, the less the slab deflects under a load because stiffness is inversely related to deflection.
For example, stiffness is EI/L, and the moment of inertia (I) is bh3/12 for a regular, uncracked rectangular section. Therefore, increasing the dimension b or h of a slab would result in a reduced value for the deflection. However, it must be noted that the effect of increasing depth (h) is much more dominant than that of increasing width (b), especially in slabs.
Increase the area of steel provided
By increasing the area of steel, the service stress in the reinforcement reduces, and increases the modification factor for deflection control. However, there is a limit to which increment of area of steel can go.
Reduce slab span
Reducing a slab’s shorter span helps reduce deflection since deflection is also a function of the basic span–effective depth ratio (lx/d). Thus, if lx is reduced, then deflection reduces, and vice-versa. However, it is essential to note that reducing slab spans may not be possible in all cases as it involves introducing new columns and beams and depends on floor layout and architectural requirements for spaces.
Reduce additional dead loads
Additional dead loads on slabs include loads from partition walls and floor finishes. Therefore, alternative, lightweight materials for partition walls and floor finishes will help reduce long-term dead load application on slabs.
Remediation of deflected slabs
The overlay method of fixing a deflected slab
Since deflection control is a serviceability consideration, thus, small slab deflections may necessarily not lead to collapse. However, large deflections may lead to slab collapse if necessary actions are not taken to remedy the slab. Let’s look at the overlay method of fixing an existing deflected slab.
The overlay method seems to be the most practical way of remedying a slab after deflection. It involves increasing the stiffness of the slab while reducing deflection. However, the process must be carried out by experts. The steps of the overlay method are listed below.
1. Design and install lifting system. 2. Start lifting of slab from the soffit according to the recommended force. 3. Inject the cracks formed at the top of the slab due to adverse lifting force. 4. Lightly chip the surfaces of the slab and supporting columns. 5. Drill holes in the slab and supporting columns to receive new dowels. 6. Clean the drilled holes with pressurized air. 7. Fill the holes with epoxy materials to aid bonding between steel dowel bars and anchors with the concrete. 8. Insert anchors and main steel in the drilled holes. 9. Apply bonding materials on the anchor and main steel bars. 10. Cast the new concrete material on the existing slab. 11. Allow curing for at least 14 days. 12. Remove lifting system.
Perhaps you are interested in a visual aid for the overlay method; then you can click this link.
Worked Exampleon Deflection of Slab(BS 8110)
Conduct the deflection check for a continuous slab with the data given below.
Effective depth (d) = 124 mm Area of steel required = 681.48 mm2 per m run Area of steel provided = 754 mm2 per m run
Slab span = 3900 mm Steel strength (fy) = 380 N/mm2 Allowable span/depth ratio = 26
Bending moment (M) = 27.15 kNm
Solution
Service stress (fs) = (2fyAs req)/(3As prov) × (1/δb), Where δb = 1
fs = (2 x 380 x 681.48) / (3 x 754) x (1/1) = 229 N/mm2
Taking the distance between supports as the effective span, L = 3625 mm The allowable span/depth ratio = βs × 30.838 = 2.0 × 190.327 = 280.645 Actual deflection L/d = 3625/119 = 30.462 Since 280.645< 30.462 Therefore, deflection is ok.
Conclusion
Structural designers and building contractors continue to employ reinforced concrete for suspended floor slabs in building structures because of its durability and economic benefits. However, short and long-term deflection remains a concern. Therefore, structural engineers and other professionals in the building construction industry must understand the implications of slab deflection and make adequate design allowances to accommodate it.
References
[1] TR58 (2005), Technical Report No. 58: Deflections in Concrete Slabs and Beams, The Concrete Society, Camberley, UK.
[2] BS 8110 (1997), Structural Use of Concrete – Part 1: Code of Practice for Design and Construction, British Standards Institution, London.
[3] BS 8110 (1985), Structural Use of Concrete – Part 2: Code of Practice for Special Circumstances, British Standards Institution, London.
[4] Priyanka, M. D. and Ramesh, V (2022), Comparative Study on Slab Deflections, IOP Conference Series: Earth and Environmental Science, Vol. 982, available at: https://iopscience.iop.org/article/10.1088/1755-1315/982/1/012081
[5] RC Design II: One-way and Two-way slabs, University of Asia Pacific, Dhaka, Bangladesh, available at: https://www.uap-bd.edu/ce/anam/Anam_files/RC%20Design%20II.pdf
