In this article, Sky Marketing presents a creation of the Japanese architecture studio Nendo which has created a house and warehouse out of pieces of precast concrete sewers in central Japan.
The Prefab House with Concrete Tunnels
Architecture with prefabricated elements is nothing new. In fact, the architectural future – if not already – goes through this industrialized architecture to save on costs and build better.
We have seen how they transform freight containers into houses and play with their shapes, as well as how they build prefabricated exterior walls that are placed like a Tetris game or how large concrete pipes become micro-apartments and rooms, in short, a thousand ideas!
The imagination of some architects to innovate in prefabricated houses is causing really interesting architectural projects to appear.
Nendo architecture studio – Photos Daici Ano, Takumi Ota and Toru Shiomi
The famous Japanese architecture studio Nendo also presents us with a magnificent house built with precast concrete sewer tunnels. Called the Culvert Guesthouse, a construction between warehouse and residential housing that was built from four huge precast concrete tunnels that were stacked.
The unique building is located among the dense forests on the outskirts of the city of Miyota in Japan. In a quiet environment rich in nature where streams intertwine through a thick forest of red pines.
Nendo architecture studio – Photos Daici Ano, Takumi Ota and Toru Shiomi
Its elongated concrete forms were constructed from joining pieces of precast concrete culverts, commonly used to enclose utilities such as water and electricity underground.
As they are elements destined for infrastructures and the architectural project had other needs. The study used the prestressing method to achieve a more coherent stacking and tightness between pieces.
The prestressing method is a technique used in civil engineering structures, such as bridges, in which members are aligned and then tensioned with steel wires to connect the members. In this way, a smooth and seamless surface finish is achieved, obtaining a hermetic seal and greater durability.
A total of 63 square-shaped pieces of approximately 12 tons each were used in the prefabricated house. By connecting these pieces, a slender tunnel-like space is created with an internal dimension of approximately 2 x 2.3 meters.
According to the Nendo studio… “The space is not so architectural, but a project that combines civil engineering concepts with product design details.”
On the ground floor, the main space of the warehouse is located in a 40-meter-long tunnel that has large glass windows at each end for filing furniture, products, and works of art. Parallel to this space, there is another tunnel that houses the residential area that includes a kitchen, bathroom, and toilet.
Nendo architecture studio – Photos Daici Ano, Takumi Ota, and Toru Shiomi
Nendo architecture studio – Photos Daici Ano, Takumi Ota, and Toru Shiomi
Both ground floor tunnels are located in parallel. They are joined by a flat roof creating an interior space for the dining room. This is closed with large glass windows that occupy the entire wall on both sides.
The floor of the living room is finished with gravel hardened with a resin base, which facilitates the passage and avoids the glassy surface that would result from the poured resin. The windows were made without metal frames as far as possible, and the high-transparency glass is up to 10 meters in length.
Stacked over the two tunnels, two other perpendicular caissons form the top floor of the building. They contain a bedroom and a secondary archive with a study space.
The smallest details of the house are meticulously designed, from a bathtub carved into the ground, where the water is flush with the ground, suggesting a continuous and uninterrupted surface or the design of the door handle that integrates perfectly into the narrow tunnel opening.
All the concrete elements on the outside are painted white to give the warehouse and residential area a minimalist look. In addition to offering a contrast with the exterior landscape and its vigorous green.
Nendo architecture studio – Photos Daici Ano, Takumi Ota, and Toru Shiomi
In its interior spaces, the line of white colours is followed in all the rooms and the use of wooden furniture with simple and straight lines.
In the garden, there is a fifth concrete tube next to the main warehouse building to house additional living space that will be used in the future.
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In a practical medium- to long-span structures, post-tensioned slabs are economically competitive with reinforced concrete slabs and make up a sizable share of all prestressed concrete construction. The numerous drawbacks of reinforced concrete slabs (especially for long-span structures) are eliminated by prestressing.
In post-tensioned concrete construction, fresh concrete is cast around hollow ducts that are fitted to any desired profile. Normally, the steel tendons are unstressed in the ducts during the concrete pour. Nevertheless, they can also be threaded through the ducts at a later date. The tendons are tensioned (stressed) after the concrete reaches the desired strength at a later date. Tendons can either be stressed from both ends or from one end while the other end is anchored. At each stressed end, the tendons are then anchored.
After the tendons are anchored, the prestress is maintained by bearing the end anchorage plates onto the concrete, which places the concrete in compression during the stressing operation. Every time the cable’s direction changes, the post-tensioned tendons place a transverse force on the member.
Figure 1: Construction of post-tensioned slab
Post-Tensioned Slabs
In post-tensioned slabs, deflection, which is usually the controlling design consideration for concrete floors is controlled better. With an appropriate selection of prestressing/post-tensioning solutions, a designer is able to minimize or even completely eliminate deflection. As a result, thinner slab systems are possible, which can increase headroom or decrease floor-to-floor heights.
Additionally, prestress prevents cracking and can be utilized to create flooring that is watertight and devoid of cracks. Steel reinforcement layouts and fixes for prestressed slabs are often fewer and less complicated. As a result, pouring concrete and fixing steel reinforcements are simpler and faster. Additionally, prestressing reduces formwork costs and stripping times while enhancing punching shear. Conversely, prestressing frequently results in substantial axial shortening of slabs, necessitating special attention to the details of movement joints.
Post-tensioning is usually done on prestressed slabs using draped tendons. Flat-ducted tendons with five or fewer strands in a flat sheath and fan-shaped anchorages are frequently used, as shown in Figure 2. The use of small, portable hydraulic jacks allows for the one-at-a-time stressing of individual strands. The flat ducts allow for maximal tendon eccentricity and drape while being structurally effective. In order to provide a bond between the steel and the concrete, these ducts are usually grouted after stressing.
Figure 2: Details of typical flat-ducted tendons and anchorages (Gilbert et al, 2017)
Pre-stressed concrete slabs are typically thin in proportion to their span. A concrete slab may experience a high magnitude of deflections at full load or show excessive camber after transfer if it is too thin. The serviceability criteria for the member often dictate the initial choice of slab thickness.
The decision on the thickness of a slab is usually made using prior experience or suggested maximum span-to-depth ratios. Note that the initial choice of slab thickness, while useful as a starting point for design, does not always guarantee that serviceability requirements will be met.
Unbonded tendons are frequently used in a majority of post-tensioned slabs simply because they lower the cost of construction. Post-tensioned slabs provide a number of important advantages over reinforced concrete slabs, such as:
• Longer spans with fewer columns leading to flexibility in the positioning of partitions. • Thinner slabs lead to saving in construction costs and reduced height of the building. • Especially in the case of car parks, the virtually crack-free slabs are a great advantage to limit damage due to seepage of water with de-icing salts from melting snow.
Balanced Load Stage for Two-Way Slabs
Two-way panels bend into dish-shaped surfaces when subjected to transverse loads, as depicted in Figure 3. Because the slab is curved in both major directions, bending moments exist in each of those directions. Additionally, twisting moments that develop in the slab at all points other than the lines of symmetry resist a portion of the applied load.
Figure 3: Deformation of interior two-way slab panels. (a) Edge-supported slab. (b) Flat slab. (Gilbert et al, 2017)
Each prestressing tendon resists a portion of the applied load, and they are typically arranged in two directions parallel to the panel edges. The transverse force that is applied to the slab by the tendons in one direction adds to (or deducts from) the transverse load that is applied in the opposite direction by the tendons. The amount of the load to be borne by tendons in each direction for edge-supported slabs is more or less arbitrary; the only strict condition is that statics be met.
For flat slabs, tendons must carry the entire load from column line to column line in both directions. The concept of using the transverse forces produced by the draped tendons’ curvature to balance a portion of the applied load is advantageous from the perspective of managing deflections. Load balancing not only offers the foundation for creating a proper tendon profile but also makes it possible to calculate the prestressing force necessary to achieve zero deflection in a slab panel under the chosen balanced load.
It is important to know that the slab is essentially flat (has no curvature) at the balanced load and is only affected by the prestressing forces applied at the anchorages. Only uniform compression (P/A) in the directions of the orthogonal tendons is applied to a slab of uniform thickness. When the condition of the slab under the balanced load is confidently known, any suitable method can be used to determine the deflection caused by the unbalanced portion of the load.
Since only the unbalanced portion of the total service load must be taken into account and, unlike reinforced concrete slabs, prestressed slabs frequently do not crack at service loads, the calculation of the deflection of a prestressed slab is typically more accurate than that of a conventionally reinforced slab.
The external load that needs to be balanced typically makes up a significant amount of the sustained or permanent service load in order to minimize deflection issues. The sustained concrete stress (P/A), if all the permanent loads are balanced, is constant throughout the slab depth. There is little long-term load-dependent curvature or bending due to uniform creep strain caused by uniform compressive stress distribution.
Of course, bonded reinforcement limits creep and shrinkage and, if the steel is eccentric to the slab centroid, results in a change in curvature with time. Prestressed slabs typically contain a limited amount of bonded steel, therefore the time-dependent curve this restraint produces rarely results in appreciable deflection.
Potential serviceability issues may be indicated by the average concrete compressive stress after all losses. The prestress may not be enough to avoid or control cracking brought on by shrinkage, temperature changes, and unbalanced loads if P/A is too low. The average concrete compressive stress after all losses is subject to minimum limits that are outlined in some standards of practice. Prestressing levels for a two-way slab are typically in the range P/A = 1.2 – 2.6 MPa using flat-ducted tendons with four or more strands.
Axial deformation of the slab may be significant and cause distress in the supporting structure if the average prestress is high. Regardless of the typical concrete stress, the rest of the structure must be able to withstand and accommodate the shortening of the slab, but when P/A is high, the issue is made worse (Gilbert et al, 2017). It could be essential to use movement joints to separate the slab from rigid supports.
In particular, for slabs containing less than minimum quantities of conventional tensile reinforcement (i.e. less than around 0.15% of the slab’s cross-sectional area), the spacing of tendons in at least one direction shall not exceed the smaller of eight times the slab thickness and 1.5 m.
General Approach to the Design of Post-Tensioned Slab
After making an initial selection of the slab thickness, the second step in slab design is to determine the amount and distribution of prestress.
Usually, load balancing is employed to achieve this. The transverse stresses induced on a slab by the draped tendons in each direction balance out a portion of the load. The slab stays flat (without curvature) under the balanced load and is only susceptible to the resulting longitudinal compressive P/A stresses.
The remaining imbalanced load is taken into account when calculating service load behaviour, especially when estimating load-dependent deflections and determining how much cracking has occurred and how much crack control has been applied.
The complete factored design load must be taken into account at ultimate limit state conditions, where the slab behaviour is non-linear and superposition is no longer valid. The factored design moments and shears at each critical section must be computed and compared with the design strength of the section. Slabs are typically fairly ductile, and as the slab’s collapse load approaches, moments redistribute. Secondary moments can typically be disregarded in these circumstances.
Load Balancing
Figure 4: Interior edge-supported slab panel (Gilbert et al, 2017)
Consider the interior panel of the two-way edge-supported slab shown in Figure 4. The panel has parabolic tendons in both the x and y axes and is supported by walls or beams on all sides. The upward forces per unit area that the tendons in each direction exert if the cables are uniformly spaced in each direction are;
wpx = 8Pxzd.x/lx2 ——— (1)
and
wpy = 8Pyzd.y/ly2 ——— (2)
where Px and Py are the prestressing forces in each direction per unit width, and zd.x and zd.y are the cable drapes in each direction.
The uniformly distributed downward load to be balanced per unit area wbal is calculated as:
wbal = wpx + wpy ——— (3)
In practice, perfect load balancing is not possible, since external loads are rarely perfectly uniformly distributed. However, for practical purposes, adequate load balancing can be achieved (Gilbert et al, 2017). Any combination of wpx and wpy that satisfies Equation (3) can be used to make up the balanced load. The smallest quantity of prestressing steel will result if all the loads are balanced by cables in the short-span direction, i.e. wbal = wpy.
Figure 5: Post-tensioned slab construction
However, under unbalanced loads, serviceability problems in the form of unsightly cracking may result. It is often preferable to distribute the prestress in much the same way as the load is distributed to the supports in an elastic slab, i.e. more prestress in the short-span direction than in the long-span direction. The balanced load resisted by tendons in the short direction may be estimated by:
wpy = [lx4/(δly4 + lx4)] × wbal ——— (4)
where δ depends on the support conditions and is given by:
δ = 1.0 for 4 edges continuous or discontinuous = 1.0 for 2 adjacent edges discontinuous = 2.0 for 1 long-edge discontinuous = 0.5 for 1 short edge discontinuous = 2.5 for 2 long + 1 short edge discontinuous = 0.4 for 2 short + 1 long edge discontinuous = 5.0 for 2 long edges discontinuous = 0.2 for 2 short edges discontinuous
Equation (4) is the expression obtained for that portion of any external load which is carried in the short-span direction if twisting moments are ignored and if the mid-span deflections of the two orthogonal unit-wide strips through the slab centre are equated.
With wpx and wpy selected, the prestressing force per unit width in each direction is calculated using Equations (1) and (2) as:
Px = wpxlx2/8zd.x ——– (5)
and
Py = wpyly2/8zd.y ——– (6)
Equilibrium dictates that the downward forces per unit length exerted over each edge support by the reversal of cable curvature (as shown in Figure 4) are:
wpxlx (kN/m) carried by the short-span supporting beams or walls wpyly (kN/m) carried by the long-span supporting beams or walls
The total force imposed by the slab tendons that must be carried by the edge beams is, therefore:
wpxlxly + wpylylx = wballxly ——– (7)
and this is equal to the total upward force exerted by the slab cables.
Therefore, for this two-way slab system, to carry the balanced load to the supporting columns, resistance must be provided for twice the total load to be balanced (i.e. the slab tendons must resist wballxly and the supporting beams must resist wballxly). This requirement is true for all two-way floor systems, irrespective of construction type or material.
At the balanced load condition, when the transverse forces imposed by the cables exactly balance the applied external loads, the slab is subjected only to the compressive stresses imposed by the longitudinal prestress in each direction, i.e. σx = Px/h and σy = Py/h, where h is the slab thickness.
Post-Tensioned Slab Design Example
It is required to design an exterior panel of a 175 mm thick two-way floor slab of a commercial building. The rectangular panel is supported by monolithic beams at all edges and discontinuous on two adjacent sides. It supports an additional dead load of 2.5 kN/m2 apart from its self-weight and a live load of 4 kN/m2. The slab is post-tensioned in both directions using the draped parabolic cable profiles shown below. The level of prestressing required to balance a uniformly distributed load of 4 kN/m2 is required. Relevant material properties are fck = 40 MPa, fctm = 3.5 MPa, Ecm = 35,000 MPa, fpk = 1,860 MPa and Ep = 195,000 MPa.
Self weight of the slab = 25 × 0.175 = 4.375 kN/m2 Superimposed dead load = 2.5 kN/m2 Total dead load = 6.875 kN/m2 Live load = 4 kN/m2 The total load on the slab = 6.875 + 4 = 10.875 kN/m2
Solution
Load Balancing
Load balancing: Flat-ducted tendons containing four 12.5 mm strands are to be used with a duct size of 75 mm × 19 mm.
With a 25 mm concrete cover to the duct, the maximum depth to the centre of gravity of the short-span tendons is:
dy = 175 − 25 − (19 − 7) = 138 mm (refer to the Figure above)
Eccentricity at the mid-span (short span) ex = 175/2 – 38 = 50 mm (say) Eccentricity at the mid-span (long span) ey = 175/2 – 38 – 13 = 37 mm (say)
The cable drape in the short-span direction is, therefore: zd.y = (50 + 0)/2 + 50 = 75 mm
The depth dx of the long-span tendons at mid-span is less than dy by the thickness of the duct running in the short-span direction, i.e. dx = 143 − 19 = 124 mm. The cable drape in the long-span direction is given by:
zd.x = (50 + 0)/2 + 37 = 62 mm
Self-weight of the slab = 25 × 0.175 = 4.375 kN/m2 If 40% of the live load is assumed to be sustained, then the total sustained load is: wsus = 4.375 + 2.5 + (0.4 × 4.0) = 8.475 kN/m2
In this example, the effective prestress in the tendons in both directions balances an external load consisting of the self-weight and 10% of the superimposed dead load;
wbal = 4.375 + 0.1(2.5) = 4.625 kN/m2. The transverse load exerted by the tendons in the short-span direction is determined using Equation 4:
wpy = [lx4/(δly4 + lx4)] × wbal Where δ = 1.0 for two adjacent edges discontinuous.
wpy = 94/(1.0 × 84 + 94) × 4.625 = 2.85 kN/m2
and the transverse load imposed by the tendons in the long-span direction is calculated; wpx = wbal − wpy = 4.625 − 2.85 = 1.775 kN/m2
The effective prestress in each direction is obtained from Equations (1) and (2): Pi = wpili2/8zd.i
Maximum force per tensioning = 137 kN Assuming a 25% loss over the long term, the force per strand = 0.75 × 137 = 102.75 kN For four strands = 4 × 102.75 = 411 kN
The number of strands required: x-direction: nx = 290/411 = 0.7 (say 1 duct/m; comprising of 4 strands per duct), Prestress provided = 102.75 × 4 = 411 kN/m Load balanced, qx = (8 × 411 × 0.062)/92 = 2.516 kN/m2
y-direction: ny = 304/411 = 0.73, say (say 1 duct/m; comprising of 4 strands per duct) Prestress provided = 102.75 × 4 = 411 kN/m Load balanced, qy = (8 × 411 × 0.075)/82 = 3.853 kN/m2
Both the time-dependent losses and friction losses must be estimated in order to determine the jacking forces and cable spacing in each direction. Assuming a 25% loss is used to account for all the losses;
Using four 12.5 mm strands/tendon, Ap = 372 mm2/tendon and the maximum jacking force/tendon is 137 × 4 = 548 kN, and the required tendon spacing in each direction (rounded down to the nearest 10 mm) is therefore:
sy = (1000 × 548)/405.3 = 1352 mm and sx = (1000 × 548)/386.7 = 1417 mm
However, it is recommended that the spacing of tendons should not exceed 8h in the span. Therefore, the maximum spacing of the tendons can be taken as = 8 × 175 = 1400 mm.
We will select a tendon spacing of 1000 mm in each direction. This simply means that the tendons in the y-direction will balance slightly more load than previously assumed. With one tendon in each direction per metre width, the revised prestressing forces at the jack per metre width are Py = Px = 548 kN/m and at mid-span, after all losses, are:
Under this unbalanced load, the maximum moment in the slab can be investigated;
The aspect ratio of slab = ly/lx = 9/8 = 1.125
The negative moment at the continuous edge (short span) = 0.056 × 3.306 × 82 = 11.84 kNm/m The positive moment at midspan (short span) = 0.042 × 3.306 × 82 = 8.886 kNm/m The negative moment at the continuous edge (long span) = 0.045 × 3.306 × 82 = 9.521 kNm/m The positive moment at midspan (short span) = 0.034 × 3.306 × 82 = 7.193 kNm/m
Obviously, in this case, the maximum moment is 11.84 kNm/m
Check for cracking
The concrete stresses in the top and bottom fibres caused by the maximum moment after all losses are:
where A is the area of the gross cross-section per metre width (A = bh = 175 × 103 mm2/m) and Z is the section modulus per metre width (Z = I/y = 5.104 × 106 mm3/m). Both the top and bottom stresses are relatively low. Even though the moment used in these calculations is an average and not a peak moment, if cracking does occur, it will be localised and the resulting loss of stiffness will be small. Deflection calculations may be based on the properties of the uncracked cross-section.
Maximum total deflection
The deflection at the mid-panel of the slab can be estimated using the so-called crossing beam analogy, in which the deflections of a pair of orthogonal beams (slab strips) through the centre of the panel are equated. The fraction of the unbalanced load carried by the strip in the short-span direction is given by an equation similar to Equation (4).
and with the deflection coefficient β taken as 3.5/384, the corresponding short-term deflection at mid-span of this 1 m wide slab strip in the short-span direction through the mid-panel (assuming the variable live load is removed from the adjacent slab panel) is approximated by:
The sustained portion of the unbalanced load on the slab strip is: [lx4/(δly4 + lx4)] × (wsw + wG + y2wQ – wbal) = 0.61 × [4.375 + 2.5 + (0.4 × 4.0) – 6.369] = 1.28 kPa
and the corresponding short-term deflection is:
vsus.0 = 1.28/2.035 × v0 = 3.056 mm
Assuming a final creep coefficient φ(∞,t0) = 2.5 and conservatively ignoring the restraint provided by any bonded reinforcement, the creep-induced deflection may be estimated using:
vcc = 2.5 × 3.056 = 7.64 mm
The final shrinkage strain is assumed to be εcs = 0.0005. The shrinkage curvature κcs is non-zero wherever the eccentricity of the steel area is non-zero and varies along the span as the eccentricity of the draped tendons varies.
A simple and very approximate estimate of the average final shrinkage curvature is; κcs = 0.3εcs/h = (0.3 × 0.0005)/175 = 0.857 × 10-6 mm-1
The average deflection of the slab strip due to shrinkage is given by Equation 12.8: vcs = 0.090 × 0.857 × 10-6 × 80002 = 4.936 mm
The maximum total deflection of the slab strip is therefore: vtot = v0 + vcc + vcs = 4.86 + 7.64 + 4.936 = 17.436 mm = span/456 < Span/250
Check flexural strength
It is necessary to check the design strength of the slab. As previously calculated, the dead load is 4.375 + 2.5 = 6.875 kN/m2 and the live load is 4.0 kN/m2. The factored design load is:
wEd = 1.35(6.875) + 1.5(4) = 15.28 kN/m2
The negative moment at the continuous edge (short span) = 0.056 × 15.28 × 82 = 54.763 kNm/m The positive moment at midspan (short span) = 0.042 × 15.28 × 82 = 41.07 kNm/m The negative moment at the continuous edge (long span) = 0.045 × 15.28 × 82 = 44kNm/m The positive moment at midspan (short span) = 0.034 × 15.28 × 82 = 33.25 kNm/m
A safe lower bound solution to the problem of adequate strength is obtained if the design strength of the slab at this section exceeds the design moment. The resistance per metre width of the 175 mm thick slab containing tendons at 1000 mm centres (i.e. Ap = 372 mm2/m) at an effective depth of 138 mm can be obtained by considering the figure above.
The stress in the tendon caused by the effective prestressing force Pm,t = 411 kN is:
σpm,t = Pm,t/Ap = (411 × 103)/372 = 1105 MPa
EN1992-1-1 permits the design stress in the tendon at the strength limit state to be taken as: σpud = σpm,t + 100 = 1205 MPa and therefore the tensile force in the steel is Fptd = 448.26 kN (= Fcd).
x = Fptd/ ηfcdλb = (448.26 × 103 )/(1.0 × 26.67 × 0.8 × 1000) = 21 mm
Such an analysis indicates that the cross-section is ductile, with the depth to the neutral axis of x1 = 21 mm (or 0.152d).
This shows that no additional reinforcement is required. However, 12 mm diameter non-prestressed reinforcing bars in the y-direction at 450 mm centres can be provided all over the slab.
Reference
Gilbert R.I, Mickleborough N.C. and Ranzi G. (2017): Design of Prestressed Concrete to Eurocode 2 (2nd Edition). CRC Press, Taylor and Francis,
Biocementation is an environmentally friendly, cost-effective alternative to imported granular fills, concrete, costly hauling of materials or export to a landfill. In-service performance of soils, foundations, and other earthen structures and their required maintenance is highly dependent on methods of stabilisation, ranging from expensive mechanical stabilisation to chemical processes.
As such, many alternative materials originating from bio-based sources are being explored as potential stabilising additives to improve weak subgrade soils (i.e., dispersive soils, erodible and collapsible soil, and soft or expansive clays). In order to prevent geotechnical failures induced by water infiltration and/or erosion, some relevant alternatives include the use of bio-derived enzymes, microorganisms, and polymeric additives.
Bio-based Innovations in Geotechnical Engineering
For sustainable road infrastructure development, various microorganisms and other bio-based materials, including secondary metabolites, enzymatic materials, and polymeric materials, have been studied as viable substitutes for traditional chemical stabilisers (Ikeagwuani and Nwonu, 2019). Thus, increasing the adoption of these bio-based materials and technologies in the building industry requires a deeper understanding.
The use of bacteria in bio-based admixtures produced through industrial fermentation processes is gaining popularity because of a number of positive aspects, including their quick biosynthesis rates, high yields of desired products, quick growth on cheap culture media that is readily available in large quantities, openness to genetic manipulation, and lack of pathogenic traits (Pei et al., 2015). By the outcomes of the microbial treatment of soil, at least eight different types of biotechnological processes associated with construction can be categorized as shown in Figure 1 (Ivanov et al., 2015).
Figure 1: Construction-related microbial biotechnology (Ramdas et al, 2021)
Of these, two biological processes (as far as the fundamental characteristics of research techniques) stand out;
(a)bioclogging, the production of pore-filling materials through biological means, to significantly reduce the hydraulic conductivity of soil or porous matrix and,
(b) biocementation, the generation of particle-binding materials through microbial processes in situ so that the shear strength of soil can be increased.
This is further reinforced by DeJong et al. (2010) stating that these methods allow a holistic view and meaningful characteristics in the area of soil stabilisation. The micro-organisms best suited for these techniques (i.e., soil bio-clogging, biocementation, and bio-aggregation) are facultative anaerobic and microaerophilic bacteria, although anaerobic fermenting bacteria have been suggested (Ivanov et al., 2015).
Microbial Biocementation
One of the most researched techniques is microbial-induced calcium carbonate precipitation (MICCP), also known as microbial biocement, which occurs when biological action increases the pH of soils to create supersaturated conditions (Oyediran and Ayeni, 2020).
Figure 2: The process of bio-cementation
Recently, biocementation has gained attention as a practical method for soil improvement, notably because of its superior performance and environmental sustainability. For instance, an essential approach called microbially induced calcite precipitation (MICP) uses bacteria to create calcium carbonate precipitates and introduce “biocementation” between the sand grains (Cheng et al., 2013).
For instance, the alkalophilic soil bacteria Bacillus pasteuri uses the highly active urease enzyme to consume urea and break it down into carbon dioxide (CO2) and ammonia (NH3). In the presence of water, NH3 is changed into NH4+, while CO2 equilibrates with carbonic acid, carbonate, and bicarbonate ions in a pH-dependent manner. The alkaline environment and carbonate needed for the reaction with Ca2+ and precipitation of calcite (CaCO3) are provided by the rise in pH, as schematically depicted in Fig. 2.
Figure 3. Biocementation is two-step process a: Phase I, bacteria ingest nutrients such as, sugar, nitrogen, & proteins with the growth of the bacterial population and enzymes produced from the bacterial species they hydrolyse urea components in the presence of water to form ammonium and carbonate ions which leads to b: Phase II, again the addition of nutrients such as calcium chloride, in the presence of calcium ions and nucleation sites on the soil particles, the carbonate ions react spontaneously with the calcium ions to form calcium carbonate, c-d: the calcite precipitates/the cementing agent (produced by the bacteria) used to bind the soil particles together to increase strength and stiffness of the soil
Another significant but understudied example of biocementation and bioengineered soil structures is termite mounds (anthills). Ecologists, entomologists, architects, and soil chemists are very interested in these above-ground mounds, particularly those made by the termites known as Macrotermitinae that grow fungi.
According to Kandasami et al (2016), a critical component for termite societies with millions of individual termites is the stability of termite mounds, which are bioengineered granular ensembles. Termites are skilled engineers, as shown by an experimental investigation on the mechanobiology of mounds and mound soil of the fungus-growing termite Odontotermes obesus (Rambur). The physical and mechanical characteristics of mound soil were notably different from those of the nearby or “control” soil. Yet, the clay mineralogy of the mound and surrounding soils was the same.
To build anthills, termites combine the finer soil fraction with their secretions to form boluses in the presence of water, thereby significantly altering the soil. In order to efficiently mould the soil, they control the amount of water close to the soil’s plastic limit when producing these boluses (Kandasami et al, 2016).
As a result of these processes, the strength of the soil can be increased tenfold as a result of the cementation caused by termites utilizing their excretions and/or secretions, which may not have been possible otherwise. The modification of the soil by termites reduces the likelihood of erosion and collapse of the mounds.
Figure 4: Termite mounds are a product of biocementation
Studies have also shown that termites effectively bonded foreign objects, indicating that they have a variety of cementation skills. When compared to reconstituted soil, a slope stability analysis with intact mound soil showed a much higher safety factor for the mound.
Applications of Biocementation in Soil Improvement
According to Cheng et al (2013), the MICCP method is most efficient at a particle contact right as cementation begins, and it becomes less effective as cementation spreads outward around a particle contact. Due to the increased inter-particle interactions, reallocating the CaCO3 crystals to two contact places (connection points) as opposed to one would be more beneficial. As a function of the particle radius squared, the contact stress also decreases simultaneously. As a result, smaller particles have two complementary advantages: improved MICCP and reduced particle contact stresses.
Ng et al. (2012) used the B. megaterium MICCP procedure to evaluate shear strength, and they observed that the ratio of treated to untreated shear strength rose from 1.40 to 2.64. Van Paassen et al. (2010) reported a minimum of 300 kPa compressive strength. Similar results were published by Nafisi (2019), who observed that the soil strength varies between 210 kPa and 710 kPa depending on the type of sand and carbonate mass.
Van Paassen et al. (2010) also observed a 60% reduction in the permeability of treated soils at less than 100 kg/m3 CaCO3 precipitation; however, as solution concentration increased, calcite crystal clogged pore spaces and reduced permeability between 50 and 99% using 1 M cementation solution.
In triaxial testing, Cheng et al. (2013) reported that the mechanical behaviour of the bio-cemented sand increased the effective shear strength parameters (i.e., cohesion, angle of internal friction) with an increase in CaCO3 concentration at all saturation levels. By increasing the frictional angle at a lower saturation level, the precipitated crystals improved the cohesion of coarse sand. Under the same saturation level and similar CaCO3 content as fine sand, coarse sand showed a greater friction angle than fine sand.
Here is how the researchers addressed this: The primary consequences of tiny soil particles include:
MICCP method can be improved by;
(a) adding additional inter-particle contact points and (b) lowering the stress per particle contact.
An exponential relationship between the UCS value and the CaCO3 content of the treated soils, according to van Paassen et al. (2010), demonstrates that even though the same amount of CaCO3 precipitated, the mechanical response can vary depending on the CaCO3 precipitation/crystals’ mechanism of action. Additionally, the process requires significant urease activity in the microorganisms, and the mode of action (MICCP) may be strain-dependent (van Paassen et al., 2010).
Several documented research works show several Bacillus spp. have the ability to precipitate calcium carbonate with structural properties, but a limited selection of micro-organisms highlights the triaxial and California Bearing Ratio (CBR) tests for potential road/pavement applications (Table 1).
Preferable microbes come from Bacillacae family
Key micro-organisms showing mechanical improvement of construction material
B. flexus
Laboratory strength tests showed an increase in compressive (>40%), flexural (>30%) & split tensile (>10%) strength. X-ray powder diffraction (XRD) shows ureolytic properties of the organism (Roa et al., 2015).
B. sphaericus
Experimental results indicate polyurethane immobilised bacteria-induced higher strength regain (60%) and lower water permeability coefficient (10 –11 m/s) (Wang et al., 2012, 2014)
Sporosarcina pasteurii formerly known as B. pasteurii
Biocalcification mechanism showing potential construction applications such as dust control and strengthening of brick masonry (Sarda et al., 2009; Meyer et al., 2011). Triaxial tests indicate that the treated specimens exhibit a non-collapse strain softening shear behaviour, with a higher initial shear stiffness and ultimate shear capacity than untreated specimens. Samples treated showed a great increment in unsoaked and soaked CBR gained more strength when soaked for hours compared to unsoaked (Oyediran and Ayeni 2020). CBR obtained in a study showed poorer outcome from CBR index treated (0.6) compared to untreated samples (2.5). These investigations are of interest to improve soil stability, to build roads and paths, and to restore monuments (Morales et al., 2019).
B. licheniformi
Calcium carbonate precipitation from the strain has the potential for sealing cement-based materials (Vahabi et al., 2015).
B. subtilis
Strength performance of microbial concrete mechanism on the principle of calcite mineral precipitation by alkali-resistant spore-forming bacteria. Its response showed autonomous improvement in the self-healing process due to microcrack formation (Rao et al., 2017).
Table 1:Bacillus species related to microbial bio-cement
According to Mujah et al (2016), the factors affecting the bio-cementation of soils are;
Temperature
pH level
Urease activity/bacterial concentration
Degree of saturation
The concentration of cementation solution
Limitations of MICP for soil biocementation
The fact that MICP can only be applied to particular soil sizes is one of its key disadvantages. The approach is currently only effective for treating sands with particle sizes comparable to 0.5-3 mm, according to a review by Fragaszy et al (2011). Hence, expanding the use of MICP for improving and stabilising fine-grained soils like silt and clay would be a huge challenge.
Furthermore, some researchers have conducted field trials and upscaled studies to test the viability of MICP for in-situ bio-cementation deployment in construction. For instance, van Paassen (2009) conducted an experiment to treat 1-100 m3 of sand in the lab and observed that, after MICP treatment, the strength of bio-cemented sand was greatly increased; however, distinct spatial variability was observed. The most important factor that still needs further focus is treatment homogeneity or the homogeneous distribution of CaCO3 across the treated soil matrix from top to bottom.
Conclusion
The engineering, mechanical, and physical properties of biocemented soils can potentially be enhanced by MICP treatment. The intended uses of MICP include slope stabilization, settlement reduction, erosion management, soil self-healing, and prevention of liquefaction.
The benefits of MICP for soil improvement include cheaper costs compared to chemical grouting and other man-made materials, treatment dependability, and an overarching idea that encourages sustainability in tandem with future needs. Before the MICP method is directly applied in the field, further study should be concentrated on optimizing it at both the micro and macro levels.
Investigations must be done into specific issues such as medium flow and transport via heterogeneous media, treatment durability, mixing procedure permanence, and particle-level stratigraphic mapping. Further potential directions in MICP technology include the use of seawater as a salt alternative as well as self-healing in terms of pre- and post-shearing of biotreated soils after significant earthquakes and related aftershocks.
References
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Ivanov V, Chu J, Stabnikov V. (2015): Basics of construction microbial biotechnology. In: Pacheco Torgal F, Labrincha JA, Diamanti MV, Yu CP, Lee HK, editors. Biotechnologies and biomimetics for civil engineering biotechnologies and biomimetics for civil engineering. Switzerland: Springer; 2015. p. 21–56.
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Morales L, Garzon ´ E, Romero E, Sanchez-Soto PJ. (2019): Microbiological induced carbonate (CaCO3) precipitation using clay phyllites to replace chemical stabilizers (cement or lime). Appl Clay Sci 2019;174:15–28. https://doi.org/10.1016/j.clay.2019.03.018
Mujah D., Mohamed A. Shahin M.A, and Cheng L. (2016): State-of-the-Art Review of Biocementation by Microbially Induced Calcite Precipitation (MICP) for Soil Stabilization. GEOMICROBIOLOGY JOURNAL http://dx.doi.org/10.1080/01490451.2016.1225866
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Oyediran IA, Ayeni OO. (2020): Comparative effect of microbial induced calcite precipitate, cement and rice husk ash on the geotechnical properties of soils. SN Appl Sci 2020;2: 1–12. https://doi.org/10.1007/s42452-020-2956-0
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Roa R, Kumar U, Vokunnaya S, Paul P, Orestis I. (2015): Effect of Bacillus flexus in healing concrete structures. IJIRSET 2015;4:7273–80. https://doi.org/10.15680/ IJIRSET.2015.0408106
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Lattice truss structural systems have been employed in constructing railway and highway bridges with great success for so many years. The design of truss bridges involves the analysis of the structure to obtain the internal forces due to moving traffic and permanent loads (self-weight), selection of adequate steel members, design of the connections, and check for fatigue. The availability of numerous commercial design software has made the analysis and design of 3D truss bridges easier than it was in the past.
The Warren truss, the Modified Warren truss, and the Pratt truss are the three major truss configurations in use today, and they can all be employed as an underslung truss, a semi-through truss, or a through truss bridge.
In an underslung truss, the live loading caused by the passage of automobiles or trains is carried directly by the top chord. In situations where the depth of construction or clearance under the bridge is not critical, underslung trusses can be conveniently used.
In semi-through trusses, vehicles travel on the bottom chord of the truss, but the transient live load projects above the top chord members due to the height of the vehicles relative to the top chord of the truss. As a result, the top chords in semi-through trusses cannot be braced laterally, and these chord elements must rely on U-frame action for lateral stability. However in a through truss bridge, vehicles travel through the centre of the bridge on the bottom chord, and the space between the live load and the top chords is sufficient that the top chord members can be braced laterally. Through truss bridge appears to be the most common type of truss bridge.
Figure 1: Major types of truss bridges (Parke and Harding, 2008)
Internal Forces in Truss Bridges
The members of a truss bridge will predominantly carry axial tension or axial compression stresses if the structure is designed and detailed so that live loading is effectively applied at the nodes. The global bending moment acting on the bridge may be resolved into a couple made up of the compression forces in the top chord and axial tension forces in the bottom chord. Similarly, the diagonal web elements carry the global shear force exerted on the truss bridge, either in axial tension or compression, depending on the configuration of the truss.
As an example, the diagonal web elements of a Warren truss alternately carry compression and tension over the bridge. The internal diagonal web members of a Pratt truss, on the other hand, are all loaded in tension, while the shorter vertical web members are loaded in compression.
Members of Truss Bridges
The chords and web members of truss bridges can be made out of a variety of steel sections. For the tension and compression chords as well as the web members of short-span (30–50 m) highway trusses, rolled “H” sections and square hollow sections are suitable. Larger fabricated sections, such as a “top hat” section or box section, will be needed for the chords of longer highway truss bridges or trusses bearing railway loads.
Built-up through truss bridge
Analysis of Truss Bridges
Truss bridges transmit imposed loads to the foundations through the axial tension and compression forces in the members. Therefore, these structures can be analyzed as pin-jointed members, either as a two-dimensional truss or, more preferably, as a three-dimensional space truss.
This form of analysis assumes that member connections are pinned, which means that none of the truss members may attract moment or torsion. By hand, a two-dimensional plane truss analysis can be solved by utilizing equilibrium equations to resolve the forces at each joint in turn, or by employing the method of sections to free-body segments of the bridge truss, again using equilibrium equations to derive member forces.
The stiffness method can also be used to calculate node displacements first, and then member forces. Nowadays, truss bridges do not have pinned joints; instead, the connections are welded or bolted; yet, analyzing the structure as a two- or three-dimensional pin-jointed assembly allows for an accurate assessment of member axial stresses but overpredicts truss node displacements.
However, since the joints are not pinned in real-life construction, it is necessary to analyze the truss as a three-dimensional space frame with six degrees of freedom at each node in order to obtain a more realistic prediction of node displacements as well as an assessment of the secondary bending and torsion moments, which will be small but still present.
Secondary moments and torsions acting on the structure can affect the bridge’s fatigue life, particularly if the truss is continuous and spans multiple supports. By guaranteeing that the neutral axes of all members meeting at a node intersect at a single location in three-dimensional space, secondary forces and hence stresses can be reduced.
Worked Example: Design of Truss Bridge
A 9.0m wide through-truss bridge is to be designed to carry normal traffic across a river. The total height of the bridge is 5m, and I-sections are to be utilised in the top and bottom chord members of the truss, while square hollow sections will be utilised for the web members. The vertical members of the web are spaced at 2.5m each and the total length of the bridge is 25m.
Modified Warren Truss Bridge
The deck of the bridge is composed of primary and secondary steel beam members. The floor beams consist of UB 457x191x161 members supported by the UB 610x305x179 bottom chord rail of the trusses and spaced at 2.5m intervals. The stringers are the secondary UB 305x102x28 members running parallel to the bottom chord and spaced at 1.5m. A 200mm thick reinforced concrete deck is expected to sit on the beams.
The truss bridge has been modelled on Staad Pro software as shown below. The top of the truss bridge (top chord) will be braced using UB 254x146x37 members in a K-truss arrangement (see below) to restrain the top chord from sway under wind action.
Structural Model of a Truss Bridge
Loading
In this article, the truss bridge will be analysed for the self-weight (all
dead and superimposed loads) and traffic load. All other environmental loads and indirect actions will not be considered.
Dead Load (1) Self-weight of steel members (to be calculated automatically by Staad Pro) (2) Self-weight of 200mm thick reinforced concrete deck = 0.2 × 25 = 5 kN/m2 (3) Self-weight of 75mm thick asphalt wearing course = 0.075 × 23.5 = 1.8 kN/m2
Total pressure dead load = 6.8 kN/m2
Live Load According to the requirements of Load Model 1 (LM 1), the carriageway width of 9m can be divided into three notional lanes as shown below;
In essence, the traffic on the bridge will be represented by the UDL as specified above and the tandem system. The worst effect of the wheel load on the bridge deck will be considered. However, it is important that the influence line analysis of the bridge be carried out, in order to determine the wheel load location that will produce the worst effects on the structure.
Bottom Chord Analysis Results
The result below depicts the internal stresses induced in the bottom chord at the load combination 1.35gk + 1.5qk (where qk represents the UDL component of the traffic load only).
The result below depicts the internal stresses induced on the bottom chord under the unfactored moving tandem wheel load only.
A little consideration will show that the following results are applicable for the bottom chord;
It is obvious that these maximum forces do not interact on the same point in the section. However, for the sake of simplicity, let us assume they interact at the same point in the structure. The design verifications are as follows;
Design of the Bottom Chord
Section s1 results summary
Unit
Capacity
Maximum
Utilisation
Result
Shear resistance (y-y)
kN
1441.9
339.1
0.235
PASS
Shear resistance (z-z)
kN
2047.7
3.6
0.002
PASS
Bending resistance (y-y)
kNm
1470.0
579.2
0.394
PASS
Bending resistance (z-z)
kNm
303.1
4.9
0.016
PASS
Compression resistance
kN
5598.0
914.2
0.163
PASS
Comb. bending and axial force
0.571
PASS
Section details Section type; UB 610x305x179 (BS4-1) Steel grade – EN 10025-2:2004; S275 Nominal thickness of element; tnom = max(tf, tw) = 23.6 mm Nominal yield strength; fy = 265 N/mm2 Nominal ultimate tensile strength; fu = 410 N/mm2 Modulus of elasticity; E = 210000 N/mm2
PASS – Combined bending and compression checks are satisfied.
Design of the Web Members (Verticals and Diagonals)
The result below depicts the internal stresses induced in the bottom chord at the load combination 1.35gk + 1.5qk (where qk represents the UDL component of the traffic load only).
The result below depicts the internal stresses induced on the bottom chord under the unfactored moving tandem wheel load only.
Design Axial compression : 1181.948 + 1.5(761.358) = 2324 kN Design axial tension = 928.940 + 1.5(623.655) = 1864 kN Design major bending moment: (ignored for brevity) Design minor axis bending moment = (ignored for brevity) Design Shear (major axis) = (ignored for brevity) Design Shear (minor axis) = (ignored for brevity)
Internal compression parts subject to compression – Table 5.2 (sheet 1 of 3) Width of section; c = b – 3t = 212.5 mm c / t = 17 = 18.4ε <= 33ε; Class 1
Internal compression parts subject to compression – Table 5.2 (sheet 1 of 3) Width of section; c = h – 3t = 212.5 mm c / t = 17 = 18.4ε <= 33ε; Class 1 Section is class 1
Slenderness ratio for y-y axis flexural buckling – Section 6.3.1.3 Critical buckling length; Lcr,y = Ly_s1 = 5590 mm (considering the length of the diagonal web members)
For completeness, the section should be checked for shear, torsional buckling, and axial/moment interaction.
Conclusion
The method adopted in this article is suitable for draft/preliminary designs. The approach can be extended and used to design and select all the members of the truss bridge. For instance, a little review of the design of the bottom chord shows that there is still room for reduction of the member size, while the same cannot be said for the web members.
The floor beams of the section will need to be designed as a composite beam, taking into account the interaction of the concrete deck. After all the members have been selected and checked, a detailed/final analysis and design can be carried out, to verify the suitability of the selected members.
The general theory of composite beam design calculations is well known among structural engineers, however, the execution of composite beam design in practice necessitates taking into account a number of factors in addition to structural calculations, such as fire engineering, constructability, and more. This article discusses the structural design of composite beams and some of the factors that must be taken into account while designing composite beams.
The construction industry in the United States of America now uses two basic approaches to composite beam design – The LRFD and ASD methods. The method featured in the 3rd Edition LRFD Manual of Steel Construction is both simpler in design and more cost-effective than the method described in the 9th Edition Manual of Steel Construction (ASD).
In the ASD method, the moment capacity is computed from the superposition of elastic stresses, while in the LRFD approach, the moment capacity is computed from the distribution of plastic stresses.
It is usually possible to produce an economical design with partial composite action in the beam. In many design situations, increasing the beam size can satisfy the design moment while significantly reducing the number of studs needed. The design of composite beams is almost always carried out using computer software or design tools like those found in the AISC Manual.
The deck size should, within reason, be chosen to allow for the beam spacing. For un-shored construction, the Steel Deck Institute (SDI) offers tables that show the maximum span permitted for a specific deck and slab arrangement. In general, the economy of the steel floor system is improved by maximizing the span for a given deck size, for un-shored construction. It is advised that you choose a deck assuming a 2-span un-shored condition and avoid single-span situations as much as possible.
The ponding of concrete as well as how the slab is poured must be taken into account. You might want to factor in an extra 1/2 inch of concrete to accommodate for ponding when estimating the amount of concrete needed to construct level slabs. Since the wet weight of lightweight concrete has been reported in the field to range up to 125 pcf, it is crucial to consider this.
Materials for Composite Beam Construction
All of the approved ASTM material specifications for the construction of composite floors are included in Section A3 of the AISC Specification. During the design of composite beams, it is pertinent to always specify ASTM A992 when broad flange beams are being used. However, HSS, pipes, and built-up shapes are also covered by the AISC requirements. The ASTM A108 shear stud, which has a tensile strength of 60 ksi, is frequently used in specifications. 3/4-inch diameter studs are the most typical size used in building construction.
In addition to reinforcing bars and welded wire, the composite slab may also be steel fibre reinforced in accordance with ASTM C1116 in specific circumstances. For normal-weight concrete and light-weight concrete, the minimum specified compressive strength of the concrete in the slab must be between 3 ksi and 10 ksi. Higher strengths should only be relied upon for rigidity. In order to comply with standard fire-rated assemblies, 3.5 ksi normal-weight concrete and 3 ksi light-weight concrete are typically specified.
Cambering in Composite Beams
Although there are several ways to obtain level steel-framed floors, cambering of beams is the technique of choice in the United States. Engineers in the field frequently misunderstand the purposes of proper beam cambering. Beam camber is just one component of a comprehensive floor levelness strategy that must take into account the slab pour method, building occupancy, and steel fabrication and installation procedure.
The main objective of cambering beams is to accurately predict how much the beam will actually deflect under the weight of the concrete. Correct camber is best attained between 75 and 80 percent of the estimated dead load deflection because of connection restraints and fabrication tolerances. Beams should never have excessive camber. Additionally, cambering is improper for a variety of beam types, including brace beams and very short beams.
Serviceability of Composite Beams
For composite floors, serviceability factors to be taken into account are long-term deflections from the superimposed dead load, short-term deflections from the live load, vibration control, and slab system performance. The acceptance standards relevant to the intended floor use, creep deflections under superimposed dead load, and partial composite action must all be taken into account when evaluating deflections.
Design and Detailing of Studs
The 1999 AISC Specification’s Section 15.6 addresses proper stud design and detailing. In the longitudinal and transverse directions, the minimum stud spacing is 6 times and 4 times the stud diameter, respectively. Two new factors—stud geometry and stud position inside the deck ribs—will need to be taken into account in accordance with the 2005 Specification.
Design Example of Composite Beams
Design a 25ft long secondary beam in a proposed commercial complex. The deck ribs are perpendicular to the beam, and the secondary beams are spaced at 10 ft intervals. The concrete for the steel deck has an overall depth of 6 inches with a compressive strength of 3 ksi. The following loadings are anticipated on the floor;
Weight of steel deck = 3.000 psf Additional dead load= 20.000 psf Weight of steel beam = 54.000 lb/ft Weight of construction live load = 20.000 psf Floor live load = 40.000 psf Lightweight partition load = 10.000 psf
Basic dimensions Beam span; L = 25.000 ft Beam spacing on one side; b1 = 10.000 ft Beam spacing on the other side; b2 = 10.000 ft Deck orientation; Deck ribs perpendicular to beam
Profiles are assumed to meet all dimensional criteria in AISC 360-16
Overall depth of slab; t = 6.000 in Height of ribs; hr = 1.500 in Centers of ribs; ribccs = 6.000 in Average width of rib; wr = 2.500 in
Material properties
Concrete Specified compressive strength of concrete; f’c = 3.00 ksi Wet density of concrete; wcw = 150 lb/ft3 Dry density of concrete; wcd = 130 lb/ft3 Modulus of elasticity of concrete; Ec = wcd1.5 × √(f’c × 1 ksi) /(1 lb/ft3)1.5 = 2567 ksi
Steel Specified minimum yield stress of steel; Fy = 50 ksi Modulus of elasticity of steel; ES = 29000 ksi
Loading – secondary beam
Weight of slab construction stage; wslab_constr = [t – hr × (1 – wr / ribccs)] × wcw = 64.062 psf Weight of slab composite stage; wslab_comp = [t – hr × (1 – wr / ribccs)] × wcd = 55.521 psf Weight of steel deck; wdeck = 3.000 psf Additional dead load; wd_add = 20.000 psf Weight of steel beam; wbeam_s = 54.000 lb/ft Weight of construction live load; wconstr = 20.000 psf Floor live load; wimp = 40.000 psf Lightweight partition load; wpart = 10.000 psf
Total construction stage dead load; wconstr_D = [(wslab_constr + wdeck + wd_add) × ((b1+b2)/2)] + wbeam_s = 924.625 lb/ft
Total construction stage live load; wconstr_L = wconstr × (b1 + b2) / 2 = 200.000 lb/ft
Required flexural strength; Mconstr_u = 111.684 kip_ft PASS – Beam bending at construction stage loading
Strength check at the construction stage for shear
Web area; Aw = d × tw = 3.737 in2 Web plate buckling coefficient; kv = 5.34 Depth to thickness ratio (h/tw);λw = 21.200 Web shear coefficient; Cv1 = 1.00 Resistant factor for shear; φv = 1.0 Design shear strength; Vconstr_n = φv × (0.6Fy × Aw × Cv1) = 112.110 kips Required shear strength; Vconstr_u = 17.869 kips PASS – Beam shear at construction stage loading
Design of shear connectors
Note – for non-uniform stud layouts a higher concentration of studs should be located towards the ends of the beam
Effective slab width of composite section; b = min(L/8, b1/2) + min(L/8, b2/2) = 75.000 in Effective area of concrete flange; Ac = b(t – hr) = 337.50 in2 Diameter of shear stud; dia = 0.750 in Length of shear stud after weld; Hs = 3.00 in Specified tensile strength of shear stud; Fu = 65 ksi Cross section area of one shear stud; Asc = π × dia2 / 4 = 0.442 in2 Maximum diameter permitted; diamax = 2.5 × tf = 1.537 in
PASS – Diameter of shear stud provided is OK
Point of max. B.M. from nearest support; LBM_near = 12.50 ft
No. of ribs from points of zero to max moment; ribnumbers = int(LBM_near /ribccs -1) = 24 No. of ribs with 1 stud per rib; Nr1 = 24 No. of ribs with 2 studs per rib; Nr2 = 0 No. of ribs with 3 studs per rib; Nr3 = 0
Total number of studs; Nprov = Nr1 + 2Nr2 + 3Nr3 = 24
Group effect factor for 1 stud per rib; Rg1 = 1.00 Group effect factor for 2 studs per rib; Rg2 = 0.85 Group effect factor for 3 studs per rib; Rg3 = 0.70
Value of emid-ht is less than 2 in (51 mm)
Position effect factor for deck perpendicular; Rp = 0.60
Nom. strength of one stud with 1 stud per rib; Qn1 = min(0.5 × Asc × √(f’c × Ec) , Rg1 × Rp × Asc × Fu ) = 17.230 kips
Nom. strength of one stud with 2 studs per rib; Qn2 = min(0.5 × Asc × √(f’c × Ec) , Rg2 × Rp × Asc × Fu ) = 14.645 kips
Nom. strength of one stud with 3 studs per rib; Qn3 = min(0.5 × Asc × √(f’c × Ec) , Rg3 × Rp × Asc × Fu ) = 12.061 kips
Total strength of provided shear connectors; Ssc = Nr1Qn1 + 2Nr2Qn2 + 3Nr3Qn3 = 413.51 kips
Moment of inertia of fully composite section; Il = Ix + A(d/2 + t – yl)2 + b(t – hr)3/(12nl) + b(t – hr)/nl (yl – (t – hr)/2)2 Il = 923 in4
Effective moment of inertia for partially composite; Il_eff = 0.75[Ix + √(Fshear / C)(Il – Ix)] = 563.6 in4
Proportion of live load which is long term; rL_l = 1 – rL_s = 33 %
Deflection due to long-term live load; DL_l = 5 × rL_l ´ wcomp_L × L4 / (384 × ES × Il_eff) = 0.0887 in
Dead load due to parallel wall & superimp. dead; wD_part = ww_par + (wserv(b1+ b2) / 2) = 0.0000 lb/ft
Long-term deflection due to superimposed dead load (after concrete has cured) Wall parallel to span and superimposed dead; D4 =5 × (wD_part) × L4 / (384 × ES × Il_eff) = 0.0000 in
Wall perpendicular to span; D5 =(ww_perp(b1+ b2) / 2) × L3 / (48 × ES × Il_eff) = 0.0000 in
Combined deflections Net total construction stage deflection; Dshort = Dshort_D + D2 – Dcamber = 1.125 in
Net total long-term deflection; Dlong = Dshort_D + DL_s + DL_l + D4 + D5 – Dcamber = 1.161 in
Combined short and long-term live load deflection; Dlive = DL_s + DL_l = 0.236 in
Net long-term dead and superimposed dead deflection; Ddead = Dshort_D +D4 + D5 – Dcamber = 0.925 in
Post composite deflection; Dcomp = DL_s + DL_l + D4 + D5 = 0.236 in
Household wastes are usually dumped in municipal solid waste landfills (MSWLFs). Landfills are sites that are designed for the dumping and management of municipal solid wastes. However, non-hazardous sludge, industrial solid waste, and construction and demolition waste can be dumped in landfills as well.
Modern landfills are well-engineered structures that are situated, developed, managed, and monitored to ensure they comply with the relevant environmental laws. The basic engineering design of landfills is to prevent the contamination of the ground and groundwater around the landfill. In essence, landfills for solid waste must be designed and constructed to safeguard the environment against contaminants that could be present in the waste stream.
Solid waste dump site
Many of the concerns with landfills in the past were caused by poorly managed and improperly engineered dump sites. The disposal of waste in landfills has a lot of possible environmental consequences. The potential for groundwater and surface water pollution, the unchecked movement of landfill gas, and the generation of odour, noise, and visual nuisances are just a few of the long-term problems that may arise.
The dangers to human health resulting from the disposal of waste will be prevented, or at least reduced, to the greatest extent practicable, by proper landfill site design. It is important that the designer embrace practices, standards, and operational frameworks that are based on best practices currently in use and that take into account advancements in management practices and containment standards. The design approach should take into account the need to safeguard both human health and the environment.
Designing a landfill is a collaborative process that takes into account conceptual design ideas, results of environmental assessments and environmental monitoring, risk assessment, and findings from site investigations. Sustainable development is the main goal of waste management. Therefore, it is implied that landfill development and operation, which are inextricably intertwined, should take this strategy into account.
Construction of a landfill
In addition to providing additional precautions, the landfill siting plan limits the placement of landfills in environmentally sensitive locations while on-site environmental monitoring systems look for any indication of groundwater pollution and landfill gas. Additionally, a lot of modern landfills capture potentially dangerous landfill gas emissions and turn them into electricity.
The main goal of landfill site design is to offer efficient control measures to prevent or reduce, as much as possible, adverse effects on the environment, in particular the contamination of surface water, groundwater, soil, and air, as well as the resulting risks to human health resulting from the landfilling of waste.
The soil properties, geology, and hydrogeology of the site, as well as any potential environmental effects, all affect a landfill’s architectural idea. A site-specific design should be able to be created with the help of the studies for a landfill.
Figure 1: Cross-section of a typical modern sanitary landfill (Megooda et al., 2006)
The philosophy of landfill design has changed recently from the dry storage concept to the bioreactor approach. Leachate is recirculated in the bioreactor approach to increase the moisture content of the municipal solid waste and speed up biodegradation. This is a financially viable solution because it would be costly to dispose of collected leachate securely. By recirculating leachate, one can avoid the costly treatment cost of leachate.
In addition, waste degrades quickly as a result of the high moisture content brought on by leachate recirculation. Consequently, bioreactor landfills offer a significant decrease in post-closure management time and operation expense (Reddy and Bogner 2003).
A bioreactor landfill is described by SWANA (2001) as “any permitted landfill or landfill cell, subject to new source performance standards/emissions guidelines, where liquid or air, in addition to leachate and landfill gas condensate, is injected in a controlled manner into the waste mass to accelerate or enhance bio-stabilization of the waste.”
There are three different types of bioreactor landfills:
anaerobic,
aerobic, and
hybrid.
In anaerobic bioreactor landfills, anaerobic microorganisms (those that do not need oxygen for cellular respiration) speed up biodegradation. These bacteria turn organic wastes into organic acids, which are then converted into methane and carbon dioxide (Sharma and Reddy 2004). Aerobic microorganisms, which need oxygen for biological respiration and create carbon dioxide, are used in aerobic bioreactor landfills. Hybrid bioreactor landfills combine the aforementioned two methods.
Types of Landfills
The Environment Protection Agency (EPA) reports that landfills are controlled under RCRA Subtitle D (solid waste) and Subtitle C (hazardous waste), or by the Toxic Substances Control Act (TSCA).
States and local governments are responsible for the principal planning, regulating, and implementing bodies for the management of nonhazardous solid waste, such as domestic waste and nonhazardous industrial solid waste (Subtitle D);
Subtitle D landfills include the following:
Municipal Solid Waste Landfills (MSWLFs) – Specifically designed to receive household waste, as well as other types of nonhazardous wastes.
Bioreactor Landfills – A type of MSWLF that operates to rapidly transform and degrade organic waste.
Industrial Waste Landfill – Designed to collect commercial and institutional waste (i.e. industrial waste), which is often a significant portion of solid waste, even in small cities and suburbs.
Construction and Demolition (C&D) Debris Landfill – A type of industrial waste landfill designed exclusively for construction and demolition materials, which consists of the debris generated during the construction, renovation and demolition of buildings, roads and bridges. C&D materials often contain bulky, heavy materials, such as concrete, wood, metals, glass and salvaged building components.
Coal Combustion Residual (CCR) landfills – An industrial waste landfill used to manage and dispose of coal combustion residuals (CCRs or coal ash). EPA established requirements for the disposal of CCR in landfills and published them in the Federal Register April 17, 2015.
Subtitle C establishes a federal program to manage hazardous wastes from cradle to grave. The objective of the Subtitle C program is to ensure that hazardous waste is handled in a manner that protects human health and the environment. To this end, there are Subtitle C regulations for the generation, transportation and treatment, storage or disposal of hazardous wastes. Subtitle C landfills including the following:
Hazardous Waste Landfills – Facilities used specifically for the disposal of hazardous waste. These landfills are not used for the disposal of solid waste.
Polychlorinated Biphenyl (PCB) landfills – PCBs are regulated by the Toxic Substances Control Act. While many PCB decontamination processes do not require EPA approval, some do require approval.
Typical section of a landfill
Design Considerations for Landfills
The designer should consider all environmental media that may be significantly impacted through the life of the landfill. The chosen design will have a major influence on the operation, restoration and aftercare of the facility. Aspects that must be considered in the design are briefly discussed below.
(1) Nature and quantities of waste The waste types accepted at the landfill will dictate the control measures required. The requirements at a landfill accepting inert waste will be different to those at one accepting non-hazardous biodegradable waste which in turn will be different from a facility accepting hazardous waste.
(2) Water control To reduce leachate generation, control measures may be required to minimise the quantity of precipitation, surface water and groundwater entering the landfilled waste. Contaminated water will need to be collected and treated prior to discharge.
(3) Protection of soil and water A liner must be provided for the protection of soil, groundwater and surface water. The liner system may consist of a natural or artificially established mineral layer combined with a geosynthetic liner that must meet prescribed permeability and thickness requirements.
(4) Leachate management An efficient leachate collection system may have to be provided to ensure that leachate accumulation at the base of the landfill is kept to a minimum. The leachate system may consist of a leachate collection layer with a pipe network to convey the leachate to a storage or treatment facility.
(5) Gas control The accumulation and migration of landfill gas must be controlled. Landfill gas may need to be collected with subsequent treatment and utilisation, or disposal in a safe manner through flaring or venting.
(6) Environmental nuisances Provisions should be incorporated in the design to minimise and control nuisances arising from the construction, operation, closure and aftercare phases of the landfill. Nuisances that may arise from landfilling include; noise, odours, dust, litter, birds, vermin and fires.
(7) Stability Consideration must be given to the stability of the subgrade, the basal liner system, the waste mass and the capping system. The subgrade and the basal liner should be sufficiently stable to prevent excessive settlement or slippages. The hydraulic uplift pressure on the lining system due to groundwater must be considered. The method of waste emplacement should ensure stability of the waste mass against sliding and rotational failure. The capping system should be designed to ensure stability against sliding.
(8) Visual appearance and landscape Consideration should be given to the visual appearance of the landform during operation and at termination of landfilling and its impact on the surrounding landforms.
(9) Operational and restoration requirements The designer must consider the manner of site development and the necessary site infrastructural requirements during landfill operation and restoration. Landfill sites should be developed on a phased basis. Site infrastructure should include for the provision of; site accommodation, weighbridge, waste inspection area, wheelwash, site services and security fencing.
(10) Monitoring requirements The designer should consider monitoring requirements at the design stage. These should be consistent with the requirements outlined in the Agency’s manual on ‘Landfill Monitoring’.
(11) Estimated cost of the facility The designer should estimate the cost of the total project (construction, operation, closure and aftercare) from commencement to completion. This should include the costs of planning, site preparation and development works, operational works, restoration/capping works, landfill aftercare, and monitoring. Consideration should be given to the financing of the facility at the design stage in order to ensure that sufficient funds can be generated to fund ongoing and potential liabilities.
(12) Afteruse The designer should consider the intended afteruse of the facility. It should be compatible with the material components and physical layout of the capping system, the surrounding landscape and current landuse zoning as specified in the relevant development plan.
(13) Construction Environmental effects during construction must be considered. These may include noise from machinery, dust from soil excavation and soil placement, disturbance, traffic diversion, and avoidance of pollution by construction related activities.
(14) Risk Assessment The design and engineering of a landfill should be supported by a comprehensive assessment of the risk of adverse environmental impacts or harm to human health resulting from the proposed development.
Conclusion
Modern landfills are well-engineered facilities which are situated, constructed, operated, and monitored in line with both federal and municipal laws. In the written word, there are three different kinds of landfills. Traditional dry landfills are the most popular choice. Dry landfills are being replaced by bioreactor landfills as a more environmentally friendly option. The newest entry on the list is sustainable landfills. Resources can be mined and refilled in sustainable landfills.
It is possible to think about landfills as a reliable and abundant source of materials and energy. This is widely recognized in the developing world, where waste pickers are frequently seen scouring the trash for useful stuff. Either landfilling is discouraged in underdeveloped nations or materials are recovered from landfills. In this framework, it is possible to see the idea of sustainable landfills as offering a universal remedy for waste disposal in both developed and developing countries.
Any engineering or building structure must always require some site investigation. A complete analysis of the soil and groundwater conditions to a significant depth below the surface using boreholes and in-situ and laboratory tests on the materials encountered may be required, as well as a simple inspection of the surface soils with or without a few shallow trial pits.
The objectives of a geotechnical site investigation are to ascertain the conditions and properties of the soil, rock, and groundwater in the site, and to obtain extra pertinent information about the site.
On-going site investigation
The type, size, and significance of the planned structure should be taken into account in the subsurface exploration program for a specific site. The number and depth of the necessary soil borings are determined by these criteria, which aid in the design of the site investigation program. Locating subterranean utilities should be part of the planning for a site investigation (i.e., phone, power, gas, etc.). As a result, many days before the planned site investigation, a local “call before you dig” service should be informed where available.
The significance and foundation configuration of the structure, the complexity of the soil conditions, and any knowledge that may be available regarding the behaviour of existing foundations on comparable soils all influence the scope of the investigation.
Categories of Site Investigation
Structures and earthworks are divided into three “geotechnical categories” according to Eurocode 7 (Geotechnical Design).
Geotechnical category 1 refers to light structures like single- or two-story buildings, low retaining walls, and buildings with column loads up to 250 kN or walls loaded to 100 kN/m. The qualitative investigations in this category can be restricted to verifying the design assumptions, at the latest, during the supervision of construction of the works, provided that the ground conditions and design requirements are known from prior experience and the ground is not significantly sloping. Visual inspection of the site, occasionally combined with inspection of small test pits, or sampling from auger borings are considered to be the main components of verification.
Conventional building types are included in category 2 structures on locations without anomalous dangers, unusually challenging ground conditions, or extraordinarily demanding loading conditions. This category includes conventional substructures such as retaining walls, bridge piers and abutments, excavations and excavation supports, rafts, piles, and shallow spread footings. Quantitative geotechnical data is needed, however standard testing techniques in the field and lab, as well as for analysis and design, are judged sufficient.
Structures in category 3 are those that are extremely massive, peculiar in nature, involve anomalous dangers, or have an unusually difficult ground or loading conditions. This category includes buildings that are located in seismically active regions.
The investigations essential for category 3 include any extra specialist research that may be required in addition to those thought to be sufficient for category 2. The processes and interpretations should be documented with references to the tests if specialized or unusual test procedures are necessary.
Site Investigations and Professional Practices
Buildings and engineering structures built upon deep excavations require extensive investigations. They offer vital information on the soil and groundwater conditions to contractors submitting bids for the work, in addition to information for foundation design. So, by collecting accurate and competitive bids based on an adequate understanding of the actual situation, money is saved.
If the cost of excavation work represents a sizeable portion of the overall project, a reputable contractor will not take a chance on it; instead, a comparably high sum will be added to the tender to account for the unforeseeable conditions. It follows the saying that “You pay for the borings whether you have them or not“.
An engineer doing a site investigation may hire local workers for hand auger boring or trial pit excavation, or they may hire a contractor for boring and soil samples. The boring contractor may send samples to his own lab or to a third-party testing facility if laboratory analysis is necessary.
Excavation of trenches for site investigation
After that, the geotechnical engineer analyzes the soil mechanics for foundation design. Alternatively, the entire investigation could be handled by a specialized company with comprehensive capabilities for drilling, sampling, field and laboratory testing, and soil mechanics analysis.
If preferred, in-situ testing can take the place of laboratory testing. In any case, the engineer in charge of overseeing the field and laboratory work on a daily basis should keep the site investigation’s objective in mind and continuously evaluate the data in a manner similar to that used when writing the report.
The relevance of characteristics like weak soil layers, deep rock weathering, and sub-artesian water pressure can be explored in as much detail as may be necessary while the fieldwork is still on by avoiding the omission of important information in this way.
Whatever method the engineer chooses to conduct his site investigation, it is important that the people or groups doing the task are diligent and absolutely trustworthy. The engineer has a significant obligation to his employers to select a qualified organization and to satisfy himself through the field, lab, and office work inspections that the work has been completed accurately and thoroughly.
Information Required from a Site Investigation
For geotechnical categories 2 and 3 the following information should be obtained in the course of a site investigation for foundation engineering purposes;
The general topography of the site, including surface configuration, adjacent property, the presence of watercourses, ponds, hedges, trees, rock outcrops, etc., and the accessibility for construction equipment and vehicles.
The position of underground utilities such as sewers, water mains, cable television, and telephone lines.
The overall geology of the region, with a focus on the primary geological formations that underlie the site and the potential for subsidence due to mining or other factors.
The prior usage and history of the site, including any defects or failures of current or former buildings related to foundation issues and the potential for toxic waste contamination of the site.
Any unique characteristics, such as the potential for earthquakes or environmental factors like flooding, seasonal swelling and shrinking, permafrost, or soil erosion.
The accessibility and quality of locally produced building materials, including water for construction, building and road stone, and concrete aggregates.
Information on normal spring and neap tide ranges, extreme high and low tidal ranges and river levels, seasonal river levels and discharges, tidal and river current velocities, wave action, and other hydrographic and meteorological data for marine or river structures.
A thorough record of the soil and rock strata, groundwater conditions, and any deeper strata that may have an impact on the site’s circumstances in any way within the zones affected by foundation-bearing pressures and construction activities.
The results of tests conducted in the field and laboratories on soil and rock samples relevant to the specific foundation design or construction issues.
The results of chemical investigations performed on soil, fill materials, and groundwater to identify potential negative effects on foundation structures.
The findings of chemical and bacterial investigations performed on contaminated soils, fill materials, and gas emissions to assess the potential health hazards.
Items (1) through (7) above can be obtained by a general site reconnaissance (the “walk-over” survey”) as well as through research of geological memoirs, maps, and other published records. Walking around the site area closely will often provide major clues about subsurface structures.
For instance, hidden swallow holes (sinkholes) in chalk or limestone formations are frequently revealed by sporadic depressions and noticeable irregularity in the ground surface; soil creep is shown by wrinkling of the surface on a hillside slope or leaning trees; abandoned mine workings are shown by old shafts or heaps of mineral waste; glacial deposits may be indicated by mounds or hummocks (drumlins) in a generally flat topography; and river or lake deposits by flat low-lying areas in valleys.
The existence of springs or wells and marshy terrain covered with reeds are surface indicators of groundwater (indicating the presence of a high water table with poor drainage and the possibility of peat). In the case of huge projects across wide areas, geological expertise should be sought.
Information on potential long-term changes in groundwater levels should be sought after. Pumping from deep mine shafts or ceasing groundwater extraction for industrial purposes can slowly raise groundwater levels over a large area.
Aerial photography is a useful tool for site inspections on large sites. Photographs may be taken from balloons, drones, or model aeroplanes. A great deal about a site’s topography and geomorphology can be learned through expert interpretation of aerial photos. A well-established science, geological mapping from aerial images is done by specialized companies.
Both outdated publications and old maps should be investigated because they may reveal the location’s prior uses and are especially helpful when looking into historically significant locations. Maps, memoirs, and images or photographs of a location in the past are frequently available at local libraries or museums. For information on buried services and coal mine workings in Britain, contact the Geological Survey and local authorities.
The list’s items (8), (9) (10), and (11) are obtained by boreholes or other subsurface research techniques, as well as through field and laboratory testing of soils or rocks. It is important to characterize soil types and consistency in accordance with accepted standards of practice. The British Standard Code of Practice Site Investigations, BS 5930, outlines the common descriptions and classifications of soils in Britain.
Soil boring
Subsurface Investigation Methods
Methods of determining the stratification and engineering characteristics of subsurface soils are as follows;
Detailed descriptions of the above methods as used in British practice are given in BS 5930 Site Investigations. Brief comments on the applicability of these methods to different soil and site conditions are given in the sections below.
In most cases, geotechnical category 1 investigations use trial pits. For shallow foundations, they are helpful for assessing the quality of weathered rocks. The most reliable method for determining the stage of deposition and characteristics of filled ground is to use trial pits expanded to trenches.
Trial pit
In soils that remain stable in an unlined hole, hand and mechanical auger borings are also suitable for category 1 examinations. Augering, when done properly, gives the least disturbance to the soil out of any other boring technique.
In British practice, light cable percussion borings are typically utilized. The straightforward and durable machinery is ideally suited to the vastly different soil types in Britain, including the extremely stiff or dense stone glacial soils and weathered boulders with a consistency similar to soil. For specialized testing, large-diameter undisturbed samples (up to 250 mm) can be recovered.
Typically, the United States, the Middle East, and countries in eastern Asia use rotary open-hole drilling. The rotary drills are typically skid- or tractor-mounted and can drill through rock as well as through dirt. Sample sizes are typically limited to 50 mm in diameter, and hole diameters are typically lower than percussion-drilled holes. Although drilling fluids such as bentonite slurry or water are employed, specialized foams have been created to aid in collecting nice, undisturbed samples.
Wash borings are holes with a small diameter (about 65 mm) that are bored using a water flush and chiselling. Sampling is done using 50 mm internal diameter open-drive tubes or 50–75 mm standard penetration test equipment.
Investigations into over-watered soils employ wash probings. They are used, for instance, in dredging investigations, to find rock heads or a strong layer overlain by loose or soft soils. They consist of a small-diameter pipe shot down. The soils cannot be positively identified, and sampling is frequently not feasible.
Soil Sampling
There are two main types of soil samples which can be recovered from boreholes or trial pits;
(a)Disturbed samples, as their name implies, are samples taken from the examples of the boring tools are auger parings, the contents of the split-spoon sampler in the standard penetration test, sludges from the shell or wash-water return, or hand samples dug from trial pits.
(b)Undisturbed samples, obtained by pushing or driving a thin-walled tube into the soil, represent as closely as is practicable the in-situ structure and water content of the soil.
Samples for rock quality designation (RQD)
It is important not to overdrive the sampler as this compresses the contents. It should be recognized that no sample taken by driving a tube into the soil can be truly undisturbed. Disturbance and the consequent changes in soil properties can be minimized by careful attention to maintaining a water balance in the borehole. That is, the head of water in the borehole must be maintained, while sampling, at a level corresponding to the piezometric pressure of the pore water in the soil at the level of sampling.
This may involve extending the borehole casing above ground level or using bentonite slurry instead of water to balance high piezometric pressures. The care in the sampling procedure and the elaborateness of the equipment depends on the class of work which is being undertaken, and the importance of accurate results on the design of the works.
The presence of well-developed solution channels, caves, springs, sinkholes, and extremely irregular weathered bedrock surfaces with cavities are the characteristics of a karstic topography. Sinkholes are “closed depressions” in the earth’s surface that are created when limestone and other rocks close to the surface dissolve and the material on top of them subside or collapses into subsurface solution caverns.
When infiltrating acidic water comes into prolonged contact with limestone, sinkholes often result. For obvious reasons, sinkholes are the major geologic hazard in karst terrain. They can cause structural damage and failure of buildings, cut off highways, drain ponds and lakes, and allow direct infiltration of contaminated groundwater.
Sinkholes are the result of a slow, continuous process. However, the effects of the sinkhole near the surface can occur suddenly and catastrophically. There are two types of sinkholes:
i) Collapse Sinkhole, and ii) Subsidence Sinkhole
Collapse Sinkholes Collapse sinkholes develop when the limestone’s solution forms a vertical cavern or throat below the surface of the ground. Initially, the surface soil may be strong enough to span across the cavern. The bridging soils will eventually crumble as the cavern widens over time. Most people have heard about sinkholes in the media in terms of this.
Subsidence sinkholes When the soil is relatively granular above the limestone formation, sinkholes might arise. In this situation, as the limestone erodes, the earth material on top fills the spaces left behind. This is known as ravelling, and if the earth keeps ravaging into the spaces in the limestone, the ground will eventually sink and produce a sinkhole.
The size of sinkholes can be influenced by the thickness of the overlying layer. The overlaying stratum can span a bigger cavern if it is sufficiently thick. For a collapse to occur, the cavern must enlarge. Additionally, sinkholes can grow to sizes large enough to engulf entire buildings.
Large collapse sinkhole
Site Investigation for Sinkholes
Rocks that are prone to solutioning activity are known to underlie around one-fourth of the earth’s crust (Syed, 2004). Numerous reports of issues with construction on karst sites have been made worldwide. Similarly, reports have been made on the sudden collapse of previously undetected solution cavities that have caused harm to existing structures and infrastructures.
It goes without saying that thorough subsurface investigations are required when significant structures are to be found in karstic regions. However, it is still true that it might be challenging to find possible sinkholes, caverns, or solutioning activity that have not yet affected the ground surface.
Because a borehole only examines a small region, the typical geotechnical study method of drilling holes may not be able to find them. Experience has shown that utilizing borings to locate sinkholes or cavities is only 10% to 20% accurate.
Studying the local geology and hydrogeology and mapping sinkholes that have already formed in the project area are the first steps in the investigation of sinkhole potential. Both surface geophysical approaches and boreholes will need to be used for the large-scale site investigation.
The typical approach should be to use borehole methods for detection and delineation and surface methods for early reconnaissance (anomaly detection). In other words, the zone in question should be drilled and sampled to give observations for the purpose of evaluation when aberrant responses are recorded during the surface surveys.
Various approaches to investigating Karstic features are:
• Aerial and Satellite Photography • Backhoe Trenches • Drilling boreholes • Modern Geophysical Techniques
Sinkhole problem
Aerial and Satellite Photography
Identifying probable sinkholes can be done through aerial surveys. Large-scale zones of subsidence may be visible on old aerial photographs, which may aid in locating smaller, localized sinkholes. Although they can be located on the ground, an aerial survey is more practical.
Backhoe Trenches
Backhoes can easily and quickly explore a relatively large area. Trenches done this way can expose near-surface solution voids or sinkhole throats. However, they can not completely replace information obtained from a borehole.
Drilling Boreholes
Test borings are an important part of sinkhole or cavity investigations. The holes are drilled to the bedrock even if this requires drilling to much greater depths than would be necessary, otherwise. Standard Penetration Tests (SPTs) are usually conducted as the bore advances. This helps in knowing the strengths of various sediment layers. The data is used to draw subsurface cross-sections that help in inferring the presence or absence of sinkholes or cavity-associated features.
Geophysical Surface Surveys
A number of such techniques are currently in vogue that can locate cavities and sinkholes. The idea behind such techniques is to probe the subsurface without disturbing the ground surface. This is done by generating a wave, which when propagated through the soil, reveals anomalies. This can be investigated to find if the same is the presence of cavities or not.
Sinkhole Management in Construction – Case Study of Saudi Arabia
Syed (2004) published a case study about the Prince Abdullah Military City Project Site, which is in the oasis of Al-Hassa, in the Eastern Province of the Kingdom of Saudi Arabia, some 12 km west of the city of Hofuf. The report was published and presented during the fifth International Conference on Case Histories in Geotechnical Engineering, April 2004.
According to Syed (2004), there are several bedrock cavities at the project site. Numerous Reports, including those written in 1992 by a geotechnical consultant for a small area of the subject Site and those completed by the US Army Corps of Engineers in 1978, have documented these conclusions for the subject site.
The following terms best describe the karstic features seen at the project site: collapse sinkholes, subsidence sinkholes, dropouts, and bedrock cavities. In order to find and map the bedrock cavities at the site, a rigorous soil investigation program was launched. In-situ testing and sampling of overburden soil by Standard Penetration Tests (SPTs) and coring in the bedrock strata were all parts of the detailed geotechnical investigation program that was carried out at the site for the purpose.
Additionally, Core Recovery and Rock Quality Designation (RQD) measurements were made. Testing typical samples of subsurface materials in the lab was also included. To further confirm the competency of the stratum below, a thorough “Cavity Search Probing” was also carried out under the footprints of each building. With the aid of a wagon drill and “Pneumatic Driving,” a rock probe was driven into the bedrock while being cleaned out of the hole as it went.
The “Karstic Terrain” at the project site was mapped with the aid of these investigation and probing. The information was also helpful in developing plans for the project’s remediation and later construction. Given the karstic issues at the project site, a semi-rigid raft foundation was chosen. This foundation system became the best option for the situation because it is known for being quite robust to bridge over the underlying cavities.
Sinkhole Investigation at the Site
The Project Site spans an area of around 6 square kilometers and is divided into 8 zones. An initial preliminary reconnaissance investigation was conducted at the site, followed by a detailed investigation for each of the 8 Zones. There were already two investigations conducted at the project site prior to the preliminary reconnaissance investigation (conducted in March 1998), each conducted by a different agency at a different time. The range of work for the various investigations carried out at the project site can be found in Syed (2004).
All of these tests at the project site proved that the limestone that makes up the bedrock is primarily light brown, fine-grained, strongly to moderately worn, and jointed. The underlying rock strata’s Total Core Recovery (TCR), which generally exceeds 50%, was determined to be between 27% and 100%. However, the Rock Quality Designation (RQD), which ranged from 0% to 100%, was typically lower than 20%.
The presence of several small cavities inside the underlying limestone bedrock is one of this limestone’s common characteristics that has been mentioned in all the studies. The findings advised performing a thorough Cavity Probing after excavation during the building stage at the locations of the foundations (under the footprints of the facilities). Drilling probing holes at least 1.5 times the width of the foundations deep is the best way to accomplish this.
The following methods were applied at the project site to investigate the local geology and hydrogeology as well as to find and map probable sinkholes and cavities.
• Trenches and Test Pits • Drilling Boreholes, and • Cavity Probing using pneumatic driving of Probe.
Trenches, test pits, and boreholes were used to collect a lot of information that indicated the presence of bedrock cavities beneath the surface. However, before starting to pour the foundations, a thorough cavityprobing was done beneath the footprints of each facility to determine whether or not there were any cavities. 5,610 probe holes total (in 166 facilities in 6 zones) were made. This comprised an extra 219 numbers in 18 numbers of facilities located surrounding the problematic locations.
The Cavity search program was quite thorough and detailed. The probing was done by using a wagon drill to pneumatically drive a rock probe into the rock. As time went by, compressed air was utilized to clear the hole. The probe’s time through each successive 20 cm depth was meticulously measured to determine the rock’s resistance to penetration.
Cavity Probing in progress at the Site (Syed, 2004)
The time for penetration records will be quite short if there are cavities or loose zones in the underlying strata. For a 20 cm penetration, a time of less than 10 seconds is regarded as the presence of loose zones, however in the case of a cavity, there will be no resistance to rock penetration and it happens suddenly.
In the course of this operation, the following details were meticulously recorded:
• Time taken for 20 cm penetration • Air escape in the finished boreholes • Sudden fall of drill rod • Boreholes, where time was 10 seconds or less
Any bore where the previous three observations were made were probed repeatedly until a cavity was identified or some logical explanations for the observations were found. If there were any cavities, grout was used to fill them in. To reveal the sinkholes or cavities, excavations were also carried out in the vicinity of these problem probing holes.
Treatment and Remedial Measures
The methods used to remedy Karst-related features may be as diverse as the cavities and sinkholes themselves. In order to expose the opening in the rock surface, the overburden soils must be removed if the “throat” of a sinkhole can be found.
The excavation is then backfilled once the throat has been sealed off or covered with an inverted filter. A less effective treatment is typically employed if the throat cannot be found or if the depth of the rock makes exposing the rock surface impractical.
Typical sinkhole at the site (Syed, 2004)
The excavation base could subsequently be sealed with concrete and/or the entire region could be covered with a geotextile if a throat is discernible but the depth to rock is excessive. If there is no neck visible and the rock is too deep, the only practicable remedy is to remove soft or organic materials, cover the region with a geotextile, and then re-fill the hole with clayey soils.
The project site’s sinkhole and cavity issues, however, required a variety of treatments and corrective actions due to the unique site characteristics.
This can be grouped as:
i) during leveling and grading ii) during foundation construction, and iii) during external works construction, like roads, water supply, sanitary sewer, storm water drainage, and other items related to landscaping and irrigation works.
With the exception of a few, the majority of the sinkholes and cavities discovered during foundation construction were outside the footprints of the facilities. Large open-mouthed sinkholes of about 5m × 4m x 3m deep were discovered inside the footprint of some foundation areas. These were overexcavated to reveal the size of the cavities, and then compaction grouting was used to cure them. This innovative method, which is known as “the Grout injected with a slump less than 25 mm,” was developed in the USA.
Typically, a soil-cement mixture with large amount of silt particles to give plasticity and create internal friction is utilized in this. In most cases, grout does not penetrate soil pores; instead, it stays in a homogenous mass that allows for controlled displacement. Additionally, regular grout was employed to address the issue in this facility. Some of them were also backfilled with rock using a bridging technique.
Due to the short duration observed for a 20 cm probe penetration during a cavity search probe, there was suspicion of the presence of sinkholes or cavities in some other facilities. Therefore, more investigations were conducted to confirm the suspicions. Except for two sites, the time recorded for the additional probes in most cases did not record fewer than 10 seconds.
Deep excavations have to be done for the service pits and hydraulic lift pits at some of the facilities. These extra probing were nearby and had time records of less than 10 seconds, which suggested the presence of cavities. Therefore, it was determined to over-excavate the limited area in order to explore the underground caverns.
The cavities were exposed during excavation, along with several lateral solution channels. These were completely cleaned before being treated using two different techniques:
(i) Compaction grouting of the vertical cavities, and (ii) Bridging utilizing boulders and geotextiles to seal the mouth of the lateral solution channels.
Foundation Design Considerations
Even with the best techniques and designs, construction in karst terrain is unquestionably not risk free, according to experts on the issue. However, the risk they pose justifies the search for a remedy that lowers the risks at a reasonable cost.
The solution in vogue are outlined as follows;
• Optimize the location on the site • Treat defects that are present • Use modified shallow foundations • Use deep foundations • Minimize future activation
For medium-sized buildings, the use of modified shallow foundations is a practical solution to the problems of Karstic hazards.
Utilizing such foundations involves:
(i) constructing a footing that spans or bridges over the cavity; and (ii) constructing a mat foundation that is rigid enough to minimize deflections that may occur due to Sinkhole formation beneath it.
The proposal accepted for the project site is a semi-rigid raft foundation. It has thicker borders or raft bands and resembles a mat. This was implemented in the project to get around the site’s sinkhole and cavern issues. This can span the cavities because it is sufficiently stiff. The same was analyzed and designed using PCA-MATS. A bearing capacity of 150 kN/m2 was used to design the foundations in accordance with the Geotechnical Report. Given the rock’s worn state and the karstic terrain, a relatively low figure of bearing capacity was advised.
Conclusion
Sinkholes are geologic hazards that can pose enormous risk to the safety of infrastructures. Extensive geotechnical site investigation is required when there is a possibility of the existence of sinkholes and cavities in an area. In a report presented by Syed (2004), a Karstic terrain was encountered in a project site in Al Hofuf, Saudi Arabia.
The detection, delineation, and mapping of bedrock cavities, sinkholes, dropouts, and solution channels were the subject of a thorough investigative program. Under the footprints of 166 facilities in 6 zones, 316 boreholes, 10 test pits, and 5610 cavity probe holes were drilled. By employing a Wagon Drill to pneumatically drive a rock probe, the cavity was probed. As time went by, compressed air was utilized to clear the hole.
The site’s karstic features were mapped, and remediation efforts were made. The majority of the sinkholes and voids were filled in using grout, with the use of geotextiles in other locations. A novel method of compaction grouting was used to fix some of them. Some of them were also “plugged” with rock utilizing the bridging method. By creating masonry and/or concrete structures, the voids and lateral solution channels in utility trenches were sealed. The roadways’ ditches were paved.
The Site’s treated karstic features are functioning effectively, and for the past four years or more, no problems have been reported. A hard and shallow style of foundation called a semi-rigid raft foundation was employed. Such footings are suggested by experts because of their capacity to span the cavities.
Reference Article: Syed, Ahmad Faiz, “Managing Sinkholes at Project Site, A Saudi Arabian Case History” (2004). International Conference on Case Histories in Geotechnical Engineering. 20. https://scholarsmine.mst.edu/icchge/5icchge/session06/20
Many civil engineering projects usually involve excavating into water-bearing soil formations. Before beginning such excavations, the proper system(s) for managing and controlling groundwater and surface water run-off should be planned. This can only be done in practice if you are aware of the ground and groundwater conditions you are likely to face through site investigation data.
It is necessary to take precautions to manage groundwater flows and pore water pressures in water-bearing soils in order to prevent problematic circumstances during excavation and construction. Effective management of surface water runoff is also necessary. Understanding the potential effects of an excavation can help determine which groundwater control measures are required to assure stability.
There are three groups of methods available for temporary works control of groundwater:
(a) Lowering groundwater levels in construction by means of water abstraction, in other words – groundwater lowering or dewatering. (b) Exclusion of groundwater inflow to the area of construction by some form of very low permeability cut-off wall or barrier (e.g. sheet-piling, diaphragm walls, artificial ground freezing). (c) Application of fluid pressure in confined chambers such as tunnels, shafts and caissons to counterbalance groundwater pressures (e.g. compressed air, earth pressure balance tunnel boring machines).
Groundwater Control Techniques
Techniques for the control of groundwater can be divided into two principal types:
(a) Those that exclude water from the excavation (known as exclusion techniques) (b) Those that deal with groundwater by pumping (known as dewatering techniques)
Exclusion Methods of groundwater control
The aim of groundwater control by exclusion is to prevent groundwater from entering the working area. Creating a physically impermeable cut-off wall or barrier around the perimeter of the excavation to keep groundwater out is one of the most widely used exclusion methods. The cut-off often produces a basal seal for the excavation by penetrating vertically down to a very low permeability stratum.
Exclusion method of groundwater control
The depth and make-up of any underlying permeable stratum have a significant impact on the costs and viability of constructing a physical cut-off wall. Base instability is possible when upward seepage occurs beneath the base of the cut-off wall due to the lack of or presence of a sufficient very low permeability layer. In these situations, dewatering techniques and exclusion techniques may be combined.
As an alternative, a horizontal barrier or “floor” might be formed adjacent to the cut-off structure to stop vertical seepage. Although it is not common, horizontal barriers have been built utilizing techniques such jet grouting, mix-in-place grouting, and artificial ground freezing.
A portion of the groundwater will become trapped inside the working area if a complete physical cut-off is established. In order to move further with the project, this must be removed, either by sump pumping during excavation or by pumping from wells or wellpoints beforehand.
The capacity of the exclusion technique to enable work to be carried out below the groundwater level with little impact on groundwater levels outside the site is one of its attractive features. This ensures that any groundwater-lowering problems are prevented. Exclusion techniques are frequently employed instead of dewatering techniques, especially in metropolitan areas, to reduce the danger of settlement damage brought on by reducing groundwater levels.
However, it is crucial to remember that practically all walls will leak to some degree when considering the use of the exclusion technique to prevent groundwater level from dropping in areas beyond the site. Particularly vulnerable to leakage are any joints (between columns, panels, piles, etc.) left behind from the installation process.
Several issues can arise if groundwater leaks through cut-offs into the excavation or work area:
(i) The seepages may hinder site operations during construction, necessitating the deployment of sump pumps or surface water management techniques to keep the working area dry. (ii) The risk of settlement or other negative impacts may result from the leaking into the excavation being severe enough to locally lower groundwater levels outside the site. (iii) If the cut-offs are a permanent construction, like the walls of a deep basement, even tiny seepages over time will be ugly and could interfere with any architectural finishes that have been applied to the walls.
Grouting or other treatments can frequently be used to address the major seepages that cause issues (i) and (ii). On the other hand, it might be quite challenging to stop or stop the little seepages of (iii). Costs significantly increase if a completely dry or leak-proof construction is required. If cut-off walls are going to be included in the permanent works, this is something that needs to be taken into account.
The techniques used in groundwater exclusion are listed below;
Steel Sheet Piling
In this groundwater control technique, steel sheet piles are driven into the soil to form a barrier against the intrusion of groundwater into the construction area. This is one of the most prominent techniques used in the construction of cofferdams. This technique is applicable to most open soils, however, it can be challenging when obstructions such as rock boulders are encountered.
Steel sheet pile walls may be installed to form permanent cut-off, or used as temporary cut-off with piles removed at the end of construction. They offer the advantage of rapid installation and are relatively cheap. Additionally, they can support the sides of the excavation with suitable propping.
The disadvantages are that the seal may not be perfect, especially if obstructions are encountered. Vibration and noise of driving may be unacceptable on some sites, but ‘silent’ methods are available.
Vibrated beam wall
In this method, a grout injection nozzle is driven into a specially made wide flange beam section using a vibratory driver-extractor that is attached to the beam’s base. A self-hardening slurry is injected into the ground with the designed beam while it is vibrated into the ground to act as a lubricant.
When the beam is withdrawn, the extracted beam element leaves a minimum of a 4 to 6-inch panel that is filled with the self-hardening slurry. A continuous cutoff wall is created by the consecutive beam element insertions and the overlapping of the earlier beam insertions.
Vibrated beam cut-off wall
The Vibrating Beam construction technology enables operations in small spaces with little room for above-ground mixing or staging. This method also decreases soil disposal costs, which can be expensive when dealing with hazardous locations, as less excavation is needed. Permeabilities in the range of 10-8 cm/sec are capable of allowing for depths greater than 50 ft.
This method is applicable in open excavations in silts and sand but will not support the soil.
Slurry trench cut-off wall
A slurry cut-off wall or slurry trench wall is an excavation made deep into the ground while simultaneously pumping an engineered slurry mix into the trench. A permanent low permeability barrier to groundwater and leachates is created by the slurry cut-off wall after it is completed. Slurry trench cut-off walls also have the capacity to prevent the transportation/movement of a range of heavy metals and organic contaminants including volatile organic compounds (VOCs), hydrocarbons, diesel, solvents and tar.
Slurry trench cut-off wall
The slurry trench walls create a low permeability curtain wall surrounding the excavation and it is a permanent water exclusion system. Slurry trench walls are can be quickly installed and relatively cheap, but the cost increases rapidly with depth. It is very applicable in silts, sands, and gravel up to a permeability of about 5 x 10-3 m/sec.
Structural Concrete Diaphragm wall
Diaphragm walls can be used as cut-off walls for dams or excavation pits, as foundations, or as enclosures for structures. A diaphragm wall is a structural concrete wall constructed panel by panel in a deep trench excavation using either precast or in-situ concrete pours.
Diaphragm walls can serve as retaining walls, water-cut-off structures, deep foundations, basement walls, or as separating structures for underground facilities. They are constructed as ground-level concrete or concrete reinforced with steel walls. They are thought to be almost water-impermeable and deformation-resistant.
Diaphragm wall in shaft construction
Diaphragm walls are permanent structures that support the sides of the excavation and often form the sidewalls of the finished construction. They can be keyed into rock and have the advantage of minimum noise and vibration. However, high cost may make the method uneconomical unless walls can be incorporated into a permanent structure.
It is applicable in side walls and shafts in most soils and weak rocks but the presence of boulders may cause problems.
Secant (interlocking)and contiguous bored piles
A retaining wall made of closely spaced bored piles can be used to construct a deep basement or a cut-and-cover tunnel. The piles could be constructed so that they almost touch each other (contiguous). A watertight retaining wall can be created by grouting the spaces between the piles.
Secant piles
This method of construction results in a more effective form of structure when the piles interlock. The piles will typically need propping during soil excavation before the permanent floor and/or roof structure is finished.
Jet Grouting
In jet grouting, a stabilizing fluid is injected into the subsoil (or the soil being treated) under high pressure and high velocity. The high-velocity fluid jets are used to create different geometries of cemented soil in the ground and typically form a series of overlapping columns of soil/grout mixture that can prevent the movement of groundwater.
Jet grouting can be messy and create large volumes of slurry. There is a risk of ground heave if not carried out with care. Jet grouting is Relatively expensive and applicable for open excavations in most soils and very weak rocks.
Deep soil mixing columns
In this permanent water exclusion solution, overlapping columns are formed by in-situ mixing of soil and injected grout/cement using auger-based equipment. Soil mixing can be categorised into deep soil mixing and shallow soil missing. The mixture of binding agent and natural soil produces columns with very low permeability. This approach produces little spoil, and it is less flexible than jet grouting. It is relatively expensive.
Injection grouting using cementitious grout
Injection grouting is a process by which grouts are injected under pressure into open fissures, voids, cracks, and pores in a soil/rock mass. The grout fills the pore spaces, preventing the flow of water through the soil.
Injection grouting in a tunnel
Equipment is simple and can be used in confined spaces. A comparatively thick zone needs to be treated to ensure a continuous barrier is formed. Multiple stages of treatment may be needed. The procedure is applicable to tunnels and shafts in gravels and coarse sands, and fissured rocks.
Artificial ground freezing
Ground freezing is a temporary water exclusion solution during construction. In this solution, a ‘wall’ of frozen ground (a freeze wall) is formed using brine or liquid nitrogen, which can support the side of the excavation as well as exclude groundwater.
Ground freezing in construction
This approach may not work if groundwater flow velocities are excessive (> 2 m/day for brine or 20 m/day for liquid nitrogen). Liquid nitrogen is expensive but quick; brine is cheaper but slower. Liquid nitrogen is to be preferred if groundwater velocities are relatively high. Plant costs are relatively high.
Compressed air
In this temporary groundwater control solution, increased air pressure (up to 3.5 bar) raises pore water pressure in the soil around the chamber, reducing the hydraulic gradient and limiting groundwater inflow. Potential health hazards to workers. Air losses may be significant in high-permeability soils. High running and set-up costs.
It is suitable for confined chambers such as tunnels, sealed shafts and caissons.
Axial compression loads from light gauge framed buildings must frequently be carried by light gauge steel members (cold-formed sections), such as the studs in a load-bearing wall. Similar to their hot-rolled counterparts, light gauge steel compression members’ failure is likely to be caused by buckling rather than cross-sectional yielding, yielding a member resistance that is much lower than the squash load of the section.
Since its buckling resistance must be calculated, the design process for such a member is in many ways comparable to that of hot-rolled steel columns. However, there are a number of ways in which the behaviour of light steel wall studs differs from that of hot-rolled columns, and these variations must be taken into account during the design process.
Contrary to columns, which function as separate parts inside a structural frame, load-bearing panels are created using light steel wall studs, plasterboard, and often some type of sheathing board. A certain amount of lateral constraint in the minor axis of the studs will be provided by the presence of the boards, which can be used to determine the buckling resistance. Any constraint must, however, be tested using studs of a representative slenderness range and a build-up of boards that is comparable to that used in actual practice.
Light gauge framed building
While hot-rolled steel columns typically behave according to flexural buckling, many light steel sections can also buckle in a torsional-flexural manner. This form of failure will naturally control the member’s resistance if torsional-flexural buckling occurs at a lower magnitude of load than flexural buckling.
The elastic critical buckling load utilized for design is assumed to be the least significant of the elastic critical buckling loads for flexural buckling, torsional buckling, and torsional-flexural buckling. This is reflected in the Eurocode design guidelines.
Last but not least, light steel sections are prone to local and distortional buckling, both of which can negatively affect a member’s ability to withstand compression. When estimating the compression resistance, this should be taken into account by utilizing the effective cross-sectional area rather than the area of the gross cross-section.
Design Procedure According to the Eurocodes
Clause 6.2 of BS EN 1993-1-3 outlines the design processes for compression members made of light gauge steel. But because the design of hot-rolled columns is comparable, designers are directed to Clauses 6.3 of BS EN 1993-1-1 for the majority of the details, including the buckling curves.
When a light gauge steel member is subjected to axial compression, the design buckling resistance is given by:
Nb,Rd = χAefffy/γM1
Where; χ is the reduction factor for flexural buckling Aeff is the area of the effective cross-section fy is the yield strength of the steel γM1 is the partial factor of safety for buckling
The reduction factor χ is used to quantify the reduction in resistance below the squash load of the section due to buckling. It may be obtained from BS EN 1993-1-1 using the appropriate buckling curve and the value of slenderness λ corresponding to the critical mode of failure.
BS EN 1993-1-1 offers a choice of 5 buckling curves, but this is restricted to 3 curves for light gauge steel according to Clause 6.2.2 of BS EN 1993-1-3. The appropriate choice of curve for various types of cross-section is given in Table 6.3 of BS EN 1993-1-3.
The slenderness λ is given by:
λ = √(Aefffy/Ncr)
Ncr is the elastic critical buckling load, which for flexural buckling is equal to the Euler load and is given by:
Ncr = π2EI/Lcr2
where: E is Young’s modulus for the material. I is the appropriate second moment of area (for the gross cross-section). Lcr is the effective length between points of restraint.
The reduction factor χ may be obtained directly from the buckling curves printed in BS EN 1993-1-1 or from the following equations:
α is the imperfection factor corresponding to the chosen buckling curve. Values of α are given in Table 6.1 of BS EN 1993-1-1.
Design Example of Light Gauge Steel Columns
A light gauge steel building is to be constructed using cold-formed sections. Determine the buckling strength of a steel column in the wall stud constructed using a lipped channel section (200 x 65 x 2) which is restrained at the top at 3.5 m in the y-direction, and at 1.75m in the z-direction.
Length of member between restraints: Ly = 3.50 m Lz = 1.75 m
Effective lengths (assuming that the member is pin-ended): Ly,cr = 3.00m Lz,cr = 1.50m
Section depth h = 200 mm Flange width b = 65 mm Stiffener depth c =25 mm Corner radius r =3 mm Nominal thickness tnom = 2 mm Core thickness t = 1.96 mm Design strength fy = 350 N/mm2 Young’s modulus E = 210000 N/mm2 Partial safety factor γM1 = 1.00
Gross section properties Area of gross cross-section A = 729 mm2 Second moment of area (major axis) Iy = 440.5 cm4 Second moment of area (minor axis) Iz = 44.26 cm4
Effective section properties The effective area of the cross-section in compression: Aeff = 459.1 mm2 (This effective area has already been calculated by Heywood and Way, 2012).
Along the major axis; Lcr,y = 3.5 m Ncr = π2EI/Lcr2 Ncr = (π2 × 210000 × 4405000)/35002 = 745296.1266 N λ = √(Aefffy/Ncr) = √(459.1 × 350)/745296.1266 = 0.464
Along the minor axis; Lcr,z = 1.75 m Ncr = π2EI/Lcr2 Ncr = (π2 × 210000 × 442600)/17502 = 299539.6737 N λ = √(Aefffy/Ncr) = √(459.1 × 350)/299539.6737 = 0.732
The buckling curve b is appropriate for the y-y and z-z axis. The imperfection factor for buckling curve b, α = 0.34
In this case, the lesser holds for the flexural buckling resistance.
Hence Nb,Rd = 122.92 kN
Article reference: Heywood M. and Way A. (2012): Design of light gauge steel elements. In Steel Designer’s Manual (Davison B. and Owens G. W. eds). Wiley-Blackwell,UK
