In our previous articles, we defined the failure load as the load that ultimately causes a pile to fail, or the load at which the soil’s bearing capacity is fully mobilised. However, in an engineering sense, failure might have occurred long before the structure was subjected to the maximum load because of the structure’s excessive settlement.
Engineers generally agree with Terzaghi’s assertion that, for practical purposes, the ultimate load can be defined as the load that results in a settlement of one-tenth of the pile’s diameter or width. However, the settlement at the working load may be excessive if this criterion is applied to piles with a large diameter and a nominal safety factor of 2.
The allowable load is almost always determined purely by tolerable settlement at the working load in situations when piles are serving as structural foundations. For every given type and size of pile in any soil or rock conditions, the engineer should be able to predict the load—settlement relationship up to the point of failure when calculating the allowable loads on piles.
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Failure Load and Settlement
In most cases a simple procedure is to calculate the ultimate bearing capacity of the isolated pile and to divide this value by a safety factor which experience has shown will limit the settlement at the working load to a value which is tolerable to the structural designer. But where settlements are critical it is necessary to evaluate separately the proportions of the applied load carried in shalt friction and end-bearing and then to calculate the settlement of the pile head from the interaction of the elastic compression of the pile shaft with the elasto-plastic deformation of the soil around the shaft and the compression of the soil beneath the pile base.
In all cases where piles are supported wholly by soil and are arranged in groups, the steps in calculating allowable pile loads are as follows;
Determine the base level of the piles which is required to avoid excessive settlement of the pile group. The practicability of attaining this level with the available methods of installing the piles must be kept in mind.
Calculate the required diameter or width of the piles such that settlement of the individual pile at the predetermined working load will not result in excessive settlement of the pile group.
Examine the economics of varying the numbers and diameters of the piles in the group to support the total load on the group.
The overall goal should be to adopt the highest working load on each individual pile while keeping the number of piles in each group as small as possible. As a result, pile caps will be smaller and less expensive, and the group settlement will be at a minimum. However, excessive settlement that causes intolerable differential settlements between neighbouring piles or pile groups may occur if the safety factor on the individual pile is too low.
The diameter and length of the piles in the case of isolated piles or piles arranged in very small groups will be determined only by taking into account the settlement of the isolated pile at the working load. Installation methods significantly impact the carrying capacity of piles. The interaction between the pile and the soil is influenced by a number of variables, including whether a pile is driven or cast in situ in a bored hole, whether it is straight-sided or tapered, and whether it is made of steel, concrete, or timber.
Engineers shouldn’t have very high expectations for formulas used to determine the carrying capacity of piles and shouldn’t be upset if the calculations show failure loads that are off by plus or minus 60% of the failure load determined by test loading. It should be kept in mind that a full-scale foundation is being evaluated when a pile is subjected to test loading.
It is not surprising that there could be relatively large differences in failure loads on any given site given the typical variability in ground conditions and the influence of installation techniques on ultimate resistance. If full-scale pad or strip foundations were loaded to failure, engineers would not be surprised to see such huge differences.
The alternative is to calculate allowable loads or design bearing capacities by dynamic formulae. These will give even wider variations than soil mechanics’ methods and, in any case, these dynamic formulae are largely discredited by experienced foundation engineers, unless they are used in conjunction with dynamic testing and analysis using standard equipment.
Over the past few years, the subject of digital fabrication with concrete has advanced significantly, with numerous alternative techniques having been created and numerous large-scale models having been built.
A recent assessment indicates that 3D concrete printing, the most extensively researched and commercially available of these technologies, is at a technology readiness level (TRL) of 6-7, comparable to polymer fused deposition modelling technology, putting it on the verge of becoming widely used. However, according to Flatt and Wangler (2022), the viability of such processes is still under discussion, which frequently results in divisive and pointless conversations.
Pioneers created these procedures with the goal of resolving productivity challenges in the building industry. However, in recent years, the need to expand architects’ creative areas and make it more cost-effective to build increasingly complex buildings made feasible by computer-aided design has been a major driving force behind digital fabrication in construction. With this capability, digital fabrication is being pushed more and more as a way to increase efficiency while also lowering the environmental impact of the building industry.
The fact that digitally fabricated structures would only use material where it was necessary, allowing for significant material savings, is a major defense of this claim. This reasoning encounters difficulties with concrete, too, because digitally created concrete frequently has a substantially larger environmental footprint per unit volume than regular concrete.
Additionally, the printing process itself may have some additional negative effects on the environment due to the manufacturing of the printing cell or the energy used to run it. It has been demonstrated that printing factors like printhead velocity and resolution have a significant impact on these process-related effects.
These well-known and currently investigated issues, as well as the fact that previous digital fabrication demonstrations have frequently focused more on “production prowess” than material savings, might result in dry and fruitless discussions of the technology’s sustainability.
Flatt and Wangler (2022) of the Institute for Building Materials, ETH Zurich, Zurich, Switzerland, recently published a paper in the journal, Cement and Concrete Research to highlight the real opportunities and challenges with regard to sustainability in digital fabrication with concrete, hopefully sparking fruitful discussions on the topic as the technology becomes more widely used.
Their article outlined a straightforward equation that incorporates the primary issues with regard to a structure’s environmental footprint. Three things come into play: Shape efficiency (or material utilized), Material footprint, and Service life (durability). The material itself was then further discussed in the context of concrete extrusion (3D printing), the technology that is most commonly used in many industries like cars, home improvement, computers, and PCB manufacturing. It was emphasized that in many cases, printed concrete is overdesigned and that well-chosen accelerators can address that issue quite effectively.
Main Factors of Concern
According to Flatt and Wangler (2022), three factors primarily determine a concrete structure’s environmental impact:
The total amount of materials used
The material’s embodied carbon dioxide, and
The durability.
According to the equation, it would be the product of the volume of material used and the environmental impact of that substance per unit volume, divided by the service life. It was highlighted that this first-order estimation does not account for variations in this and is only appropriate for comparing structures with equivalent load-bearing capacity. Additionally, the environmental effects of related changes in concrete production, such as formwork use or the aforementioned operating energy, are not expressly taken into account in this relationship.
Schematic illustration of the main factors affecting the environmental impact of a structural element with a given load-bearing capacity per year of service life (Flatt and Wangler, 2022).
The primary benefit of digital fabrication is that it can require less material. Although the effect on durability is still being researched, this typically accompanies an increase in the material’s environmental imprint and a potential reduction in service life.
Such conflicts mean that the results of environmental balancing will typically not be trivial and will undoubtedly depend on the circumstances. According to Flatt and Wangler (2022), this necessitates a more thorough consideration of the issue, taking into account the true potential for material savings while keeping in mind the limitations of material composition and durability.
Shape Efficiency
The cost of constructing buildings that use less material to provide a certain load-bearing capacity is one of the key defenses for digital fabrication. Thus, it could facilitate structural design methods that are very successful but are all too frequently overlooked. In this context, it is worthwhile to reflect on Pier Luigi Nervi’s ribbed floor designs.
Although labour was inexpensive at the time these constructions were made, concrete was expensive. Today, the situation is the opposite, making it less expensive to create consistent floor slabs by utilizing a lot more concrete than is actually necessary. This is a particularly instructive example because it is simple to visualize the savings since floors are a significant consumer of concrete in structures.
Ribbed floor system by Per Luigi Nervi at the Gatti Wool Factor
Material Footprint
Despite the potential for material savings, digital concrete frequently has a larger environmental impact than regular concrete, at least for the most popular kind of concrete extrusion. This can be reduced by using recycled components in place of new ones, looking into using different, lower-CO2 binders, or cutting the amount of paste in the cement (increasing aggregate content).
However, none of these approaches are specifically applicable to digital concrete and are instead investigated for concrete in general. The greater level of processing, particularly pumping, which normally increases paste volume, is principally responsible for digital concrete’s higher environmental impact.
In fact, given that mix designs often do not include coarse (>4 mm) aggregate, digital “concrete” is more appropriately referred to as digital “mortar” even though coarse aggregates are beginning to emerge in both academic and industrial settings. Whatever the case, the lower maximum aggregate size restricts the maximum packing fraction of aggregates, increasing the paste volume and, consequently, cement contents and carbon footprints that are larger.
Also keep in mind that while digital concretes have water-to-binder ratios that are more in line with infrastructure and high-performance concrete, their primary use has been in non-load bearing capacities, such as replacing concrete masonry or serving as a lost formwork for cast reinforced concrete. As a result, given their current utilization, digital concrete mixes frequently have twice as much cement content than is really required.
Durability
The durability of digital concrete is a crucial final aspect to take into account when talking about its sustainability. Concerningly, the prevalent technology of extrusion printing in this context can result in cold joints between the layers. However, in general, it depends on the material qualities, state of the extruded material and the previously deposited layer.
The formation of cold joints in 3D-printed concrete is still an active area of research. Therefore, it is influenced by the time interval (contour length and printing speed), and it also seems to be significantly influenced by the substrate’s surface drying throughout the layer time interval. If created, cold joints can weaken the bond between layers, but more significantly for durability, they open up channels for faster ingression of water and/or CO2.
Investigations are now being done to determine how digital concrete reacts to freezing and thawing cycles, although early results show that it performs poorly when compared to conventional concretes. Digital concrete faces the added challenge of curing in full exposure, thus losing the formwork as a “skin,” which increases the likelihood of shrinkage cracking and opens channels for aggressive chemicals.
Only recently have shrinkage issues specific to digital concrete been studied, but future research on these issues will undoubtedly need to be expanded. Noting that lowering the paste content is an easy technique to reduce shrinkage, raising the maximum aggregate size is beneficial for lowering the material footprint as well as boosting durability.
Similar to regular concrete, durability describes a material’s performance under particular exposure conditions and for a particular use. In this situation, it is important to distinguish between structural applications—where reinforcement is required—and other situations because the majority of—but not all—concerns regarding the influx of aggressive species are caused by the presence of reinforcement.
Another noteworthy achievement is the Pantheon, a non-reinforced concrete building whose performance is dependent on sound structural planning. Digital manufacturing can therefore help with important design-related issues of durability.
Determining the appropriate applications for digital manufacturing technologies and whether steel reinforcing is necessary is then crucial. One choice is to largely abandon structural concrete in favour of competing with masonry, or to simply use printed concrete as a substitute for lost formwork.
This eliminates the challenging task of strengthening digital concrete. The problem of reinforcing, on the other hand, must be addressed if structural applications are the focus, and this involves a significant amount of continuing research. Despite this, significant advancements are still required before the majority of reinforcement schemes can be widely accepted and approved in practice.
Conclusions
The fundamental argument made in the study by Flatt and Wangler (2022) is that, in addition to being situation-specific, the subject of the environmental impact of digital fabrication is complex and has a difficult answer. Examples that highlight potential significant material savings were given, however they are now more expensive to build than bulkier pieces with simpler designs.
In fact, the potential for material efficiency is what sets digital concrete construction apart from conventional construction in terms of sustainability, a distinction that should not be lost on those who aim to promote the technology to this end.
This is especially important because adoption of the technology based solely on cost-related factors would entail accepting a higher carbon footprint in exchange for lower labour costs. The current incentives for the implementation of digital concrete processes appear to be primarily cost-driven, related to formwork and masonry labour. These technologies may still have other social advantages (or problems), but those are outside the focus of this research, which is just looking at the environmental aspect of these technologies.
For a variety of reasons, the footprint of digital concrete is bigger than that of traditional concrete. One has to do with using a stronger paste volume, and is a problem that can be solved by increasing the maximum aggregate size through material advancements, which may also have additional advantages like reduced shrinking and greater incentive to use local materials.
The use of high clinker cements and overly strong final designs appear to be another factor contributing to the high carbon footprint. Both are the outcome of ineffectively attempting to meet the needs for gaining strength. Instead, utilizing accelerators based on aluminum can increase strength when it is needed, preventing overdesign of final strength and allowing the use of carbon-lean cements. Therefore, such compounds could be taken into account for quick vertical building rates of thin (and more shape-efficient) structures as well as a way to perhaps reduce the environmental impact of digital concrete.
However, extra caution must be used while employing such compounds because doing so could result in the formation of cold joints, which could reduce durability. In fact, the effect of digital fabrication techniques on the durability of concrete must be further examined in light of durability’s relationship to environmental impact.
References: Flatt R. J., Wangler T. (2022): On sustainability and digital fabrication with concrete. Cement and Concrete Research, Volume 158, 2022, 106837 https://doi.org/10.1016/j.cemconres.2022.106837
The contents of the cited original article published by Cement and Concrete Research (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.
Roadside drains or channels are structures that are used for conveying storm water away from roads or streets. The complete design of rectangular roadside drains involves hydraulic design, geotechnical design, and structural design.
The hydraulic design involves the proper sizing of the drain to ensure that the design flood is properly discharged, while the geotechnical design involves the verification of the capacity of the supporting soil to carry the weight of the channel and the water. It also involves the verification of the soil-structure interaction since drains are buried structures. The structural design of drains involves the selection of the proper material, thickness, and reinforcement to withstand the pressures and forces exerted by the soil and water.
Similar to the design of retaining walls, roadside drains are also subjected to active and earth pressures. In the example treated below, active and passive earth pressures, surcharge loads and water pressures are considered.
Worked Example on the Design of Rectangular Roadside Drains
The rectangular drain shown below is backfilled with a typical cohesionless granular material, having a unit weight (γ) of 18 kN/m3, zero cohesion (C), and internal angle of friction (ϕ) of 30°. The allowable bearing pressure of the soil is 150 kN/m2, the coefficient of friction (μ) is 0.5, the unit weight of reinforced concrete is 24 kN/m3, and surcharge loads of 15 and 5 kN/m2 on both sides of the drain. The drain has been designed to cater to a flow of 400mm depth and the unit weight of water (γw) should be taken as 9.8 kN/m3.
All drain dimensions in mm
Given the information above, design the drain wall and base reinforcements assuming fcu = 20 N/mm2, fy = 460 N/mm2, cover to reinforcement = 40 mm, diameter of reinforcements = 10 mm, and thickness of walls and base = 150 mm.
Geotechnical Design
Wall pressure calculations
Ka = (1 – sinϕ) / (1 + sinϕ) Ka = (1 – sin30°) / (1 + sin30°) = 0.333
Wall 1
Active pressure on drain wall
Active pressure at the top of the drain wall = qKa= 15 × 0.33 = 4.95 kN/m2 Active pressure at the base of the drain wall = qKa + KaγZ = 4.95 + (0.33 × 18 × 0.85) = 4.95 + 5.049 = 9.999 kN/m2
Passive pressure on drain wall
Passive pressure at the top of the drain wall = 0 Passive pressure at the base of the wall = γwZ = (9.8 × 0.55) = 5.39 kN/m2 Net pressure at the base of the wall = 9.999 – 5.39 = 4.609 kN/m2
Wall 2 Active pressure at the top of the drain wall = qKa = 5 × 0.33 = 1.65 kN/m2 Active pressure at the base of the drain wall = qKa + KaγZ = 1.65 + (0.33 × 18 × 0.85) = 1.65 + 5.049 = 6.699 kN/m2
Passive pressure at the top of the drain wall = 0 Passive pressure at the base of the wall = γwZ = (9.8 × 0.55) = 5.39 kN/m2 Net pressure at the base of the wall = 6.699 – 5.39 = 1.309 kN/m2
Total vertical load (N) Walls (Wws) = 2(0.15 x 0.7 x 24) = 5.04 kN/m Base (Wb) = 1.1 x 0.15 x 24 = 3.96 kN/m Water (Ww) = 0.4 x 0.8 x 9.8 = 3.136 kN/m Total vertical load Wws + Wb + Ww (N) = 5.04 + 3.96 + 3.136 = 12.136 kN/m
Horizontal forces on drain walls due to surcharge load and backfill
Net horizontal force (PA) = 4.101 – 1.258 = 2.843 kN/m
Resistance to sliding
Frictional Force (Ff) = μN = 0.5 × 12.136 = 6.068 kN/m F.O.S = Ff / PA = 6.068/2.843 = 2.134 The factor of safety 2.134 > 1.5. Therefore, the drain is very safe from sliding.
Check: D/6 = 1.1/6 = 0.183m Since e < D/6, there is no tension in the drain base.
Maximum pressure in the drain base (qmax) = P/B (1 + 6e/B) = 12.136/1.1 [1 + (6 × 0.066)/1.1] = 15.005 kN/m2 Minimum pressure in the drain base (qmin) = P/B (1 – 6e/B) = 12.136/1.1 [1 – (6 × 0.066)/1.1] = 7.061 kN/m2
Since qmin and qmax are lower than the allowable bearing pressure of the soil (150 kN/m2), bearing capacity check is satisfied.
Structural Design
Design of the Walls
Since the horizontal force due to surcharge load and backfill on Wall 1 > Wall 2, we adopt Wall 1 parameters for design. Using the centroid formula of a parallelogram for the pressure diagram of wall 1 to determine the distance (x) from the centroid to the base of the wall and distance (y) from the centroid to the top of the wall;
x = 0.85 [((4.609 + (2 x 4.95)) / (3(4.609 + 4.95))] = 0.43m
Thus, y = 0.85 – 0.43 = 0.42m Taking moment at the top of the drain wall due to the active force; M = 4.101 x 0.42 = 1.722 kNm per m
Taking moment at the base of the drain wall due to the active force; M = 4.101 x 0.43 = 1.763 kNm per m
Since the moment at the base of the drain wall is greater than that at the top, we adopt the moment at the base for design.
At ultimate limit state; M = 1.4 × 1.763 = 2.468 kNm per m
This article has discussed the geotechnical and structural design of rectangular roadside drains. However, readers must note that only one load case has been treated. Therefore, a designer must consider other load cases or load combinations to ascertain the accuracy of the design. For example, it would be appropriate to rerun the design with the drain filled and when the drain is empty to determine the most critical load case or combination.
Concrete is the building material that is most usually used for sewer systems because of its favorable structural qualities, capacity for prefabrication, and freedom from form restrictions. For a variety of reasons, such as the effects of (bio)chemical deterioration, ageing, and the loss of soil support, the structural integrity of concrete sewer pipes degrades with time.
The design life of a sewer system is several decades. Due to the capital-intensive nature of maintaining a sewer system as well as the severe societal and financial consequences of catastrophic failure, accurate condition evaluation has become increasingly important over time.
Figure 1: Installation of concrete sewer pipes
The two most frequent sources of data used to determine whether to repair or replace sewers are Closed-Circuit Television (CCTV) inspection and age. The difficulty of revealing deterioration on the outside of the sewer pipe wall, the low accuracy and reliability of visual inspection data, and the weak correlation between visual inspection data and material properties are just a few drawbacks that have recently been discovered with regard to these inspection methods.
Additionally, the majority of nations lack a database that contains precise information on the state of the subsurface infrastructure. Thus, it is obvious that clear knowledge about the real structural state of sewer systems is required in order to enhance current inspection techniques and enable adequate condition assessments.
The structural state of sewer networks has been the subject of numerous study investigations during the past few decades. Much emphasis has been paid to the biogenic sulphuric acid-induced degradation process that typically occurs in concrete sewer pipes.
Investigations into the sulphuric acid-producing bacteria and the chemical deterioration mechanisms that result at the inner surface of sewer pipes have revealed that the concrete’s calcium hydroxide and calcium silicate hydrate react with the acid to create gypsum and/or ettringite, which frequently causes an increase in porosity and, as a result, a decrease in strength and stiffness.
Figure 2: Deteriorated concrete sewer pipes
Additionally, naturally occurring carbondioxide in soil may migrate to the outside of concrete sewer pipes, where it may interact with hydrated cement in the presence of moisture. The strength, porosity, and pore size distribution of the cement paste may change as a result of this carbonation process. The assessment of the structural failure behavior of sewer pipes was the focus of additional experimental researches.
Despite the fact that the aforementioned investigations have focused on important issues and facts, a complete understanding of how (bio)chemical attack affects the mechanical performance of in-situ concrete sewer pipes is still lacking. However, this information is necessary to boost the suitable recommendations that municipalities and other stakeholders can use when making decisions about the upkeep and replacement of concrete sewer pipe systems.
Evaluation of Deterioration of old Sewer Pipes
Recently, researchers (Luimes et al, 2022) from the Department of the Built Environment, Eindhoven University of Technology, Eindhoven, The Netherlands, and Department of Hydraulic Engineering, Deltares, MH Delft, The Netherlands, studied the effects of biochemical attack on the mechanical performance of used concrete sewer pipes which they published in the journal, Construction and building materials (Elsevier).
Thirty-five used, unreinforced concrete sewer pipes provided by The Netherlands’ Municipalities of The Hague and Arnhem were used for the experimental program. The tested pipes, which range in age, size, and geometry, have been in use as combined sewer systems (i.e., the tested pipes installed in the 1920s and 1950s) or as improved separated systems (i.e., the tested pipes installed in the 1990s) up until July/August 2019 (pipes from Arnhem) and January 2020 (pipes from The Hague), respectively, without undergoing rehabilitation or protection treatments.
The test program involved concrete sewer pipes that had been in use for between 22 and 95 years. During that time, exposure to particular in-situ circumstances had resulted in some chemical attack, which may have been accompanied by mechanical damage from traffic loads and excavation. This might have reduced the concrete’s mechanical qualities, which might have affected the pipe’s ability to support structural loads. The inner and outer surfaces of the sewer pipes were first given a rigorous visual inspection during the study, and were then classified using various surface condition classes in order to explore these issues in more detail.
Figure 3: Four examples of unreinforced concrete sewer pipe specimens of different age that were considered in the experimental program (Luimes et al, 2022)
The cross-sections of the sewer pipes were also tested for residual alkalinity using a phenolphthalein method, where a pH indicator was provided by a 1 percent solution of phenolphthalein. The solution turns from pink to magenta in moderately alkaline conditions with a pH in the range of 9.2 to pH 10. The solution turns magenta in extremely alkaline surroundings with a pH > 10, but it stays colorless in somewhat alkaline and acidic conditions with a pH 9.2.
The dissolution of solid calcium-hydroxide in the pore solution causes the pH of the concrete to rise to a level above 12.5 to 13, which is shown by the magenta zones. On the other hand, the colorless zones indicate the presence of a chemical attack in the past, which may have been brought on by carbonation (8.3 < pH < 9) and biogenic suphuric acid corrosion (1< pH < 3).
X-ray diffraction (XRD) data were used by the researchers to further analyze the type of chemical attack. A total of 6 different surface condition classes were identified, and a particular place may be described by many surface conditions. The surface conditions were classified as follows in accordance with nomenclature generally used by the sewer asset management community:
Smooth – A surface that is virtually intact and aesthetically comparable to the surface of a brand-new sewer pipe
Exposed granulates – Exposed granulates and porous mortar between granulates referred to chemically harmed surfaces where the granulates are now visible and/or have fallen off due to the loss of the thin outer mortar layer. In the latter class, the mortar that once held the exposed granulates together has degraded into a porous, loose material that is simple to spall off.
The deposits class — As a result of variations in the wastewater level, dark colored bands indicate obvious color changes and adhering deposits along the inner pipe surface.
Rough – A surface with minor chemical assault symptoms, wherein a portion of the thin outer mortar layer is still covering the granulates.
Excavation damage – This refers to relatively big scraped or broken off pieces brought about by bulldozers and excavators during the mechanical removal of the sewer pipes from the soil.
Figure 4: Representations of the 6 surface condition classes: (1) Smooth, (2) Exposed granulates, (3) Porous mortar between granulates, (4) Deposits — Dark coloured bands, (5) Rough, and (6) Excavation damage, as observed on the inner and outer surfaces of the tested concrete sewer pipes (Luimes et al, 2022)
The types and degree of biochemical attack were respectively assessed by performing XRD analyses and phenolphthalein tests. The following conclusions were obtained from the findings.
The process of biogenic sulphide corrosion can be blamed for a major portion of the structural deterioration of old sewer lines. This process often results in a porous mortar layer between the granulates and a weak, corroded layer that looks like exposed granulates at the inside of the pipe.
Carbonation may have an impact on the sewer pipe’s outside, but it seems to have a very small impact on the pipe’s surface condition and is thought to be less detrimental to the structural integrity.
In contrast to the relatively new pipes from the 1990s, the old pipes from the 1920s and 1950s typically exhibit quite significant levels of chemical attack. Despite the fact that the level of chemical attack tends to increase with pipe age, an explicit relationship between pipe age and the degree of chemical attack cannot be determined from measurement data because the pipe’s specific material composition and the surrounding environment also have a significant impact on the level of chemical degradation.
According to the researchers (Luimes et al, 2022), the study’s findings can be used to develop and improve inspection and condition assessment standards. Further research has shown that biogenic sulphide corrosion can significantly contribute to the mechanical deterioration of sewer pipes, making it prudent to keep an eye on how this corrosion process is progressing inside in-situ sewer pipes.
Source: Luimes R. A., Scheperboer I.C., Suiker A.S.J., Bosco E., and Clemens F.H.L.R. (2022): Effect of biochemical attack on the mechanical performance of used concrete sewer pipes. Construction and Building Materials 346 (2022) 128390 https://doi.org/10.1016/j.conbuildmat.2022.128390
The contents of the cited original article published by Construction and Building Materials (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.
A high moisture content, good aeration, a high level of acidity, and a considerable number of soluble salts, can make a soil become corrosive. Metal alloys may undergo a dealloying process in corrosive soils as a result of the hostile surroundings there. The combination of soil corrosivity and dealloying corrosion is to blame for the spread of corrosion in buried steel structures.
Corrugated metal pipes (CMPs) and corrugated metal culverts (CMCs) are subterranean steel structures that have been utilized in traffic networks and water supply systems in North America and Europe since the 1850s . Corrugated profiles are being used in pipelines and culverts in order to help these structures interlock with the surrounding backfill soils and increase confinement properties as well as overall capacity. In cold coastal regions, salt used to melt the snow causes significant chloride deposits in the soil, which exposes buried corrugated steel structures to, resulting in the formation of thick rust layers.
Corrosion, which results from exposure to hostile conditions where chlorides attack metals with or without protective coatings, is the main reason why buried steel constructions deteriorate. Such deterioration is characterized by thickness loss and a decline in the axial and flexural stiffness of the steel. To avoid structural failure, it is necessary to reevaluate the structural capability and estimated service life. Around the years, soil corrosion has had an impact on several underground steel constructions all over the world (Ezzeldin et al., 2022).
Temperature variations, humidity, airborne sea salt, salts dissolved during snow thawing, and other chemical elements can all contribute to corrosive situations that cause steel to deteriorate over time. The risk of corrosion in buried steel structures is brought on by the very variable soil conditions in the area.
The corrosion process is accelerated by repeated daily and seasonal exposure to salt and water, particularly when there is an increase in temperature fluctuation in cold regions due to the effects of global warming. To monitor potential structural degradation and damage, regular in-service inspection of culvert performance is therefore essential.
The US Pipelines and Hazardous Material Safety Administration states that exterior corrosion is typically to blame for pipeline system ruptures brought on by corrosion. In addition to causing environmental issues, corrosion is a major element in the aging of networks and facilities, needing maintenance and rehabilitation that can put a large financial strain on the nation’s budget.
Recent Research Studyon Corrosion
Recent research from the Department of Civil and Resource Engineering and the Department of Mechanical Engineering at Dalhousie University in Nova Scotia, Canada, studied the accelerated laboratory corrosion test on corrugated mild steel structures buried in cohesionless soils. The study utilized repeated wet/dry cycles to simulate the effects of chloride deposits on the buried steel structures. The findings of the study were published in the journal, Case Studies in Construction Materials.
Corrugated steel pipe
For the purpose of simulating the effects of chloride deposits on corrugated mild steel structures buried in cohesionless soil, the researchers (Ezzeldin et al., 2022) devised an accelerated laboratory corrosion test using multiple wet/dry cycles. The test was initiated by applying a 3.5% NaCl electrolyte solution to cohesionless soil above buried corrugated steel coupons, which were then subjected to repeated wet/dry cycles.
The study also examined the structural profile geometry’s loss of thickness and the degree to which the steel’s tensile strength, ductility, and hardness had been degraded. This investigation focused on the deterioration of mild steel coupons as a result of corrosion. Both micrometer gauge measurements and the weight loss method were used to calculate the corrosion damage.
Corrugated mild carbon steel (CS) type B coupons were used for the tests. The coupons had a corrugation depth of 13 mm, a wavelength of 68 mm, and a thickness of 1.5 mm. Each coupon’s total projection dimensions were 110 mm by 110 mm in order to accommodate multiple waves, one crest and two valleys at the surface facing the dirt. The interface geometry of buried CMPs and CMCs was simulated by the corrugated specimens.
Each coupon was buried beneath a layer of finely graded, well-compacted, cohesionless dirt. The system included two timers to regulate the wetting (spraying) and drying stages, a tank of distilled deionized water, a pump to transfer water from the tank, stainless steel pipes and fittings to carry the water from the tank to an oven, a convection oven to distribute heat evenly to the coupons during the drying stages, and other components.
Two programmed timers were used to regulate the timing for each stage while the wet/dry cycles were repeated. The process of soaking (spraying) took 4 seconds. The soil above each coupon was sprayed with the distilled water as it was transferred by the pump from the tank. To provide dissolved oxygen and keep the water at normal temperature, the tank containing the distilled water was left open to the atmosphere. The heat from the oven was then used to finish the drying process. The soil temperature rose gradually during the drying stage, reaching a nearly dry state (i.e., a recorded soil temperature of about 90 ℃) in about 60 minutes.
The Experimental Setup
Each full wet/dry cycle took about 60 minutes to complete because the spraying was done right away at the start of the cycle. When the soil was sprayed during the wetting stage, the temperature abruptly dropped from around 90℃ to about 60 ℃, a drop of about 30 degrees. Prior to the start of the following wetting stage, the temperature was raised once again during the ensuing drying stage in order to evaporate the majority of the remaining water.
To keep the salt content in the soil at the same level (i.e., 3.5 percent) during subsequent wetting procedures, which were carried out using just distilled water, the electrolyte solution was added just once, using the same quantity of distilled water as utilized for each wetting stage.
Gravity caused the salts to settle onto the steel coupons as a result of the repeated wetting process used to completely saturate the soil throughout each cycle. In order to provide aeration and break up salt crusts that had collected, a spatula was used to mix only the top layer of soil and then compact it on top of each coupon after every 20 wet/dry cycles.
In order to reduce any potential impact on corrosion propagation, the soil adhering to the metal surface’s interface was kept undisturbed by the researchers. To assess the spread of corrosion caused by each set of cycles, five coupons were evaluated with varying totals of wet/dry cycles (50, 100, 200, 400, and 800 cycles).
Findings from the Study
At the end of the experiment by Ezzeldin et al (2022), the following conclusions were made;
Mild steel corrosion was accelerated by repeated wet/dry cycles in the absence of a protective layer (such as zinc coating).
In the steel coupons, where more induced stresses were created during the production of the corrugated steel sheets, the degree of corrosion was greater at the corrugation crests and valleys.
Rust layers of a similar nature and morphology developed on all of the test specimens, imitating the effect of acidic environments on buried steel structures in cold climates. This effect could be clearly observed in both valleys of the coupon treated to 800 wet/dry cycles.
While the rate of corrosion steadily decreased, the level of corrosion damage increased when the number of wet/dry cycles was increased. Mixed corrosion modes, such as deep pitting that produced cavities, were a part of the corrosion that eventually evolved.
The structural geometry, which lost thickness, and the mechanical qualities, such as tensile strength, ductility performance, and hardness, all degraded as a result of the steel coupons’ deterioration. Due to the reduced axial and flexural rigidity, subterranean steel structures like CMPs and CMCs would no longer be able to function to their full potential.
A mathematical model, requiring the measurement of four physicochemical parameters at the interface between the soil and the mild steel surface, was used by the researchers to provide an approximate prediction of the depth of corrosion damage in buried steel structures. The present study suggests employing this mathematical model to make approximate predictions of corrosion damage over time, based on the following Eqs. (1,2):
Where: νp = the average long-term corrosion rate; υ0 = the initial corrosion rate = 0.6743 C0 = constant 1, = 12.2652, q0= constant 2, = 1.7326, q1 = pH constant = 0.6623, q2 = resistivity constant, = 0.0069 Ωm, q3 = redox potential constant, i.e., 0.0027 mV/SHE, q4 = soil-structure electric potential constant, i.e., 0.981 V/Cu/CuSO4, z(t) = the maximum depth of corrosion damage at time (t).
The corrosion damage and reduction in nominal thickness (%) related to number of cycles from the accelerated wet/dry test and number of years from the mathematical model is shown in the Table below;
Reference(s) Ezzeldin I., El Naggar H., Newhook J. and Jarjoura G. (2022): Accelerated wet/dry corrosion test for buried corrugated mild steel. Case Studies in Construction Materials 17 (2022) e01152. https://doi.org/10.1016/j.cscm.2022.e01152
The contents of the cited original article published by Case Studies in Construction Materials (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.
The entire area of a project site cannot be fully explored for site investigation due to logistical and financial constraints. To provide enough information for the design and construction of the foundation of a building or highway, geotechnical engineering consultants must make good decisions about the location, number, and depth of borings for soil investigation. The zone of soil that will be affected by the structural loads should be covered by the number and depth of borings. There are no fixed guidelines to adhere to.
More often, the number and depths of borings are governed by experience based on the geological nature of the ground, the importance of the structure, the structural loads, and the availability of equipment. The minimum number and depth of borings may be specified by building regulations and regulatory authorities in the local area.
Whenever possible, boreholes should always be dug close to the intended foundation location. Where the bearing stratum’s depth is uneven, this is crucial. The boreholes should be precisely positioned in relation to the proposed structures, both in terms of level and location.
A grid of holes that are evenly spaced serves as an appropriate design of boreholes when the layout of the structures has not been established at the time the soil investigation is being conducted. It is feasible to use a grid of boreholes with in-situ probes of some kind, such as dynamic or static cone penetration tests, spaced more closely apart within the borehole grid for large areas. EC 7 recommends, for category 2 investigations, that the exploration points forming the grid should normally be at a mutual spacing of 20 — 40 m.
A challenging issue that is intimately related to the relative costs of the soil investigation and the project for which it is done is the necessary number of boreholes that must be sunk at any specific place. Normally, as more boreholes are drilled, more information about the soil conditions becomes available, allowing for more efficiency in the foundation design. Additionally, the likelihood of encountering unforeseen or challenging soil conditions, which would significantly raise the cost of the foundation work, decreases over time.
An economic limit, however, is reached when the cost of borings outweighs any savings in foundation cost and merely drives up the project’s overall cost. In order to determine the true dip of the strata, it is recommended that at least two and ideally three boreholes be drilled for all but the smallest structures. However, inaccurate assumptions about stratification can still be made.
However, it is very important that the number of boreholes be sufficient to detect any variances in the soil of the site. If the loads placements (such as column footing positions) on the structure’s footprint are known (which is frequently not the case), you should think about drilling at least one borehole where the heaviest load is.
The depth to which boreholes should be sunk is governed by the depth of soil affected by foundation-bearing pressures. The vertical stress on the soil at a depth of one and a half times the width of the loaded area is still one-fifth of the applied vertical stress at the foundation level, and the shear stress at this depth is still appreciable. Thus, borings in soil should always be taken to a depth of at least one to three times the width of the loaded area.
The borings are relatively shallow for narrow, widely spaced strip or pad foundations, but for big raft foundations, the borings must be deep unless rock is present within the required depth. When strip or pad footings are placed closely together, the pressure zones overlap, and the entire loaded region effectively becomes a raft foundation with correspondingly deep borings. To cover the zones of soil affected by loading transmitted through the piles in the case of piled foundations, the ground should be studied below the pile-point level.
EC 7 recommends a depth of five shaft diameters below the expected toe level. It is usual to assume that a large piled area in uniform soil behaves as a raft foundation with the equivalent raft at a depth of two-thirds of the length of the piles.
As a guide, a minimum of three boreholes should be drilled for a building area of about 250 m2 (2500 ft2) and about five for a building area of about 1000 m2 (10,000 ft2). Some guidelines on the minimum number of boreholes for buildings and for due diligence in subdivisions are given in Table 1.
Area (m2)
Numbers of boreholes (minimum)
< 100
2
250
3
500
4
1000
5
2000
6
5000
7
6000
8
8000
9
10000
10
Table 1: Guidelines for the Minimum Number of Boreholes for Buildings
Some general guidance on the depth of boreholes is provided in the following:
In a compressible soil such as clays, the borings should penetrate to at least between 1 and 3 times the width of the proposed foundation below the depth of embedment or until the stress increment due to the heaviest foundation load is less than 10%, whichever is greater.
In very stiff clays and dense, coarse-grained soils, borings should penetrate 5 m to 6 m to prove that the thickness of the stratum is adequate.
Borings should penetrate at least 3 m into the rock.
Borings must penetrate below any fills or very soft deposits below the proposed structure.
The minimum depth of boreholes should be 6 m unless bedrock or very dense material is encountered.
Guidelines for the Minimum Number and Depth of Borings for Common Geostructures
For foundation construction on compressible soils (clay and similar materials) with sufficient strength to initially support the structure, it is important to ensure that borings penetrate these compressible layers. Alternatively, borings should reach a depth where the additional stress placed on deeper strata is minimal, ensuring negligible consolidation that wouldn’t significantly impact the proposed structure’s settlement.
Exceptions exist for exceptionally heavy loads or situations where seepage or other factors are paramount. In such cases, borings may be terminated upon encountering bedrock or penetrating a stratum of exceptional bearing capacity and rigidity for a short distance.
However, this is only advisable if prior explorations in the vicinity or regional stratigraphic knowledge confirm that these strata possess adequate thickness or are underlain by even stronger formations. If these confirmations are lacking, a subset of the borings must be extended further to verify the thickness of the strong strata, regardless of the underlying material’s characteristics.
The recommended guidelines for the number and depth of borings for common civil engineering structures are provided below;
Shallow Foundation for Buildings
Minimum number of boreholes 1, but generally boreholes are placed at node points along grids of sizes varying from 15 x 15m to 40 x 40 m.
Minimum depth The minimum depth of soil exploration for foundations should be 5 m or 1B to 3B, where B is the width of the foundation. Additionally, the depth of exploration should extend to a depth where the increment in stress is equal to or less than 10% of the maximum foundation pressure.
Pykrete is a material used for temporary buildings in cold climates. It is made of a mixture of water and a number of additives, such as wood chips, cellulose sheets that have been dissolved, sand, gums, and combinations of any of those. It was initially created so that ships could be built in cold environments. In the past ten years, this substance has typically been used in shell buildings that have been built with ropes and inflatable fabric formwork (see Figure 1).
The usage of Pykrete in linear element constructions has recently been studied, and some low-rise structures have been constructed as a result. According to Pronk et al (2022), the year 2019 saw the construction of a tower-like Pykrete structure for the International Ice and Snow Innovation Design and Construction Competition, based on an idea from the Eindhoven University of Technology. It is the tallest pykrete structure with linear elements to date, this structure has a height of 11 m.
Figure 1: Pykrete dome (Pronk et al, 2022)
Researchers (Pronk et al, 2022) from the Department of the Built Environment, Eindhoven University of Technology, Netherlands have carried out a study on the mechanical performance of pykrete beam elements. Experimental tests from the study were compared with previously conducted studies. Furthermore, the researchers presented the optimization and numerical model of a pykrete tower’s design, followed by a description of the construction techniques. The article was published in the journal, Structures (Elsevier).
Making andDesign Concept of the Lattice Tower
In the study conducted by Pronk et al (2022), a preliminary design of the tower was developed, considering a uniform cross-section for the primary elements and secondary elements. The preliminary design of the tower was symmetrical, made up of five similar partitions.
Ten principal load-bearing parts, five of which are exterior (shown in blue in Figure 2) and five of which are internal, extend vertically from the bottom to the top (green elements in Figure 2). Self-weight and wind pressure of 0.5 kN/m2 were taken into account. Recent research literature served as the source for the material’s mechanical properties.
Figure 2. Preliminary design of the tower (Pronk et al, 2022)
Fire hoses filled with pykrete were used to create the members of the lattice tower. They transfer the wind loads in addition to the dead weight of the structure to the foundations. Compression in the inner columns is primarily produced by the structure’s self-weight. Due to the additional weight of the structural elements, these compressive forces are low at the top of the tower and increase at ground level, as typical in all structures. As a result, it is anticipated to have a larger cross section close to the foundation.
According to the research, the tower’s construction was separated into three stages:
Preparing the rope and pipes: The ropes and fire hoses are trimmed to the correct length. Pykrete is injected into the fire hoses from one side. The hoses were linked together after being frozen. The secondary components, the ropes, are tied together and attached to the fire hoses in accordance with the prescribed pattern. The anchors are made of earth connectors. The hoses are hermetically sealed below ground. To keep the shape while the pykrete is being applied, a low tension is applied to these ropes.
Pipe and rope installation without the use of Pykrete: Here, the structure is raised and positioned using a crane (see Figure 3).
Application of pykrete: As soon as the necessary sections are achieved, the pykrete will be gradually applied by spraying and extrusion on the hoses and ropes. Pykrete can be sprayed on the structure until the desired member thickness is achieved after the desired form has been achieved. The top portion, which is currently being lifted by the crane, will be sawn off once enough pykrete has been put, and the tower will then stand on its own.
Figure 3: Lifting the structure with crane
Based on the preliminary tower design, two main types of samples were evaluated. The cross-section of the first kind of sample is made up of pykrete and a fire hose. A tube with a 64 mm diameter was used as the hose. Pykrete is poured into the tube, and a 44 mm thick second layer of pykrete is applied around the tube, making the section’s overall diameter 154 mm. The mixture of additives in Pykrete contains cellulose at a concentration of 20 g/L (2%).
The second type of sample, which has a smaller cross-section was used to test for secondary elements. It was made up of a rope with a diameter of 12 mm that is encircled by a layer of pykrete measuring 15 mm. The additive concentration is 80 g/L (8%).
The greatest length that can be tested corresponds to a sample length of 450 mm for both types of samples. Testing was done using three different methods: compression, tension, and 4-point bending. For pykrete samples, there aren’t any currently available standardised tests. It is important to understand that pykrete’s mechanical characteristics vary depending on temperature.
Mechanical Performances of Pykrete in Beam Elements
In comparison to common building materials, pykrete’s mechanical characteristics are still being extensively studied. Tests have been done on a large number of samples in order to compare different pykrete compositions. The force–displacement relationship obtained by the bending and compression tests in the current study generally followed the major trends already observed in previous studies. However, some of the takeaways from the study were;
Regarding the 4-point bending tests, it appears that the fire hose behaviour during bending shows a hardening phase. The authors however recommended that further research should examine additional samples with composite sections to corroborate this.
The compression tests revealed that when using slender linear elements, which weren’t taken into account for shell structures in Pykrete, it will be required to pay attention to buckling.
The tests conducted on the fire hose sections produced an elastic modulus that is relatively low and especially much below what is described in the literature. Although the cause of this outcome is unclear, a lack of uniformity in the parts may be to blame.
The tensile tests reveal that while the rope does not increase the section’s tensile strength, it does allow for the preservation of the element’s integrity after failure, which is not possible for an element constructed simply of pykrete.
The full results of the test data are available in the publication.
Optimization and Numerical Model of the Tower
Grasshopper® software was used to optimize the tower’s design based on the results of the investigation. It is a Rhino® visual programming plugin that enables the execution of parametric designs based on scripts. A Live Physics engine called Kangaroo2®allows for interactive simulation, optimization, and form-finding within Grasshopper. Kangaroo2® uses dynamics relaxation With this approach, a nonlinear equation system’s solution is reduced to an explicit iterative calculation. Therefore, a damped dynamic process led to the proposed static solution.
Figure 4: The initial design and the optimised design
The algorithm consists of the subsequent phases. The anchor points, the self-weight, the major element stiffness, and the secondary element stiffness are first defined as the constraint conditions. Then, utilizing Newton’s second law, masses are defined at each node. The total residual forces for each node, the speed, and the position are computed at each iteration. When the geometry reaches its static state, the algorithm will terminate.
The optimum design consists of a series of curves that can be connected to form a mesh. In other words, the gradient of the energy that is in the direction of the forces (masses) defined at each node is used to move the nodes in order to minimize the elastic energy.
The next step is to assess the design’s structural performance in SCIA® under wind loads and self-weight. The elements’ cross-sections are manually modified (decreased or increased). For the primary and secondary parts, there can only be three different sections. Finally, the original design and the new cross-sections are added as a new input in Grasshopper®, and Kangaroo2® generates a new shape.
Figure 5: Final cross-sections of the tower.
Conclusion
Pykrete is a promising and environmentally friendly material for constructing buildings in cold areas. Up until now, inflatable shell structures were the only types of pykrete structures. However, this restricts the kind of constructions that can be made to the shapes of inflatables that can be built.
According to the study, producing truss structures would present new opportunities. By recommending a construction method and performing testing on the sections, the research enabled the creation of an 11 m tall tower made up of linear elements. By using form-finding, the design was optimized, and SCIA® was used to verify the structure under actual loading. The experimental testing have demonstrated that, before constructing more ambitious structures, research on the buckling of these components is required.
The contents of the cited original article published by Structures (Elsevier) is open access, under the CC BY license (http://creativecommons.org/licenses/by/4.0/) which allows you to share and adapt (remix) the article provided the appropriate credit is given, and the link to this license provided.
Cost is often a major determiner of decision-making on projects. Therefore, for all civil engineering works, it is required to know the probable construction cost before the project’s commencement. This is known as the estimated cost, which comprises the cost of labour, materials, equipment, and other general overhead costs. The construction and cost comparison of rectangular and trapezoidal drains can be an important consideration during highway design.
In a previous article, determining the best hydraulic section of roadside drains was discussed whereby a particular peak discharge was designed, resulting in rectangular and trapezoidal cross-sections. However, the cost comparison of both cross-sections will be discussed in this article to determine which cross-sections will result in greater savings on cost.
The details of both drain cross-sections are provided below. However, it must be noted that it is assumed that the construction is in-situ, and the cost comparison is based on 1m length of the drain cross-sections. Furthermore, the cost of labour is proportional to the quantity of materials.
Construction Process of Reinforced Concrete Drains
The procedures for the construction of reinforced concrete drains are stated below:
Marking of alignment: This involves a surveyor marking out the alignment for the trench to be dug. This alignment includes horizontal and vertical alignment. The projection of the drain in the horizontal plane is termed as the horizontal alignment, while the projection in the vertical plane is termed the vertical alignment. Survey instruments are used in this operation.
Excavation: After the surveyors have marked out the trench alignment, the depth is also marked out. Excavation is then carried out through the use of manual labour or mechanical means by the use of excavating machine.
Concrete blinding: This is the process of pouring a thin layer of concrete over the bed of the trench to seal in the underlying soil material and prevent dirt and mud from interfering with the drain structure. It is also done to correct any irregularities in the bed of the excavated surface, and to provide smooth, level and regular surface to receive the concrete base. The concrete blinding is a mass concreting and usually 50mm in thickness.
Construction of a rectangular concrete drain
Positioning of reinforcements: U-shape or trapezoidal-shape rebars, as the case may be, are usually placed in position on the blinded surface at the designed spacing. Furthermore, the rebars are positioned with the aid of concrete biscuit to create a concrete cover. It must be ensured that the center of the base aligns with the center alignment provided by the surveyor in order to have a uniform alignment.
Concrete base: After the positioning of rebars, the next step is to cast the concrete base. Usually, a concrete base of 150mm in thickness is cast on the blinded bed of the drain. A guiding panel or formwork is placed into position to guide in casting the concrete base to achieve a uniform alignment base edge, thickness, width, and to manage the concrete while pouring.
Concrete wall: After the casting of the base, and setting and hardening of the concrete, the formwork for the drain walls are positioned to allow for the casting of the wall. The fair-finished panels to be used as formwork should be lubricated, clipped and prepared to receive the concrete. After casting, setting and hardening of the walls, the panels are removed and the concrete is cured.
Backfilling and compaction: After the casting of the drain walls, the excavated portion left beside the drain is backfilled and compacted to avoid settlement of the backfill.
Cost Analysis of Rectangular Drain
Rectangular drain details
Excavation Volume of soil = (1.1 + 0.6) × (0.05 + 0.15 + 0.7) × 1 = 1.53 m3 Unit cost of excavation = ₦1,500 per m3 Cost of excavation = 1.53 x 1,500 = ₦2,295
Concrete in blinding Volume of concrete = 0.05 × 1.7 × 1 = 0.085 m3 Unit cost of concrete = ₦55,000 Cost of concrete material = 0.085 × 55,000 = ₦4,675
Concrete in drain Volume of concrete = [(1.1 × 0.15) + 2(0.7 × 0.15)] x 1 = 0.375 m3 Unit cost of concrete = ₦55,000 Cost of concrete material = 0.375 × 55,000 = ₦20,625
Reinforcement Bar Mark 1 = 6 × 2.6 × 0.617 = 9.626 kg Bar Mark 2 = 14 × 1 × 0.617 = 8.638 kg Total weight of rebar = 9.626 + 8.638 = 18.264 kg
Unit cost of rebar = ₦ 450 Cost of rebar = 18.264 x 450 = ₦ 8,220
Formwork Base = 2(0.15) × 1 = 0.3 m2 Walls = 2(0.7+0.7) × 1 = 2.8 m2 Total area of formwork required = 0.3 + 2.8 = 3.1m2
Unit cost of formwork = ₦5,400 (marine plywood) Total cost of formwork = 3.1 x 5,400 = ₦16,740
Rectangular drain construction
Cost Analysis of Trapezoidal Drain
Trapezoidal drain details
Excavation Volume of soil = [0.5(0.8 + 1.65) × 0.95] × 1 = 1.164m3 Unit cost of excavation = ₦1,500 Cost of excavation = 1.164 × 1,500 = ₦1,745
Concrete in blinding Volume of concrete = 0.05 × 0.8 × 1 = 0.04m3 Unit cost of concrete = ₦55,000 Cost of concrete material = 0.04 × 55,000 = ₦2,200
Concrete on drain Volume of concrete = [0.5(1.65 + 0.8) × 0.9] – [0.5(0.5 + 1.35) × 0.75] = (1.1025 – 0.69375) × 1 = 0.409m3 Unit cost of concrete = ₦55,000 Cost of concrete material = 0.409 × 55,000 = ₦22,495
Reinforcement Bar Mark 1 = 6 × 2.6 × 0.617 = 9.626 kg Bar Mark 2 = 14 × 1 × 0.617 = 8.638 kg Total weight of rebar = 9.626 + 8.638 = 18.264 kg
Unit cost of rebar = ₦450 Cost of rebar = 18.264 x 450 = ₦8,220
Formwork Walls = 2(0.865) × 1 = 1.73m2 Unit cost of formwork = ₦5,400 Total cost of formwork = 1.73 × 5,400 = ₦9,345
Trapezoidal drain construction
The table below shows the cost comparison of the rectangular and trapezoidal drains;
Cost component
Rectangular Section
Trapezoidal Section
% reduction or increment
Excavation
₦2,295
₦1,745
– 23.97%
Concrete in blinding
₦4,675
₦2,200
– 52.94%
Concrete in drain
₦20,625
₦22,495
+ 9.07%
Reinforcement
₦8,220
₦8,220
—
Formwork
₦16,740
₦9,345
– 44.18%
Total
₦52,555
₦44,005
– 16.27%
Conclusion
The article has discussed the cost comparison of rectangular and trapezoidal drain cross-sections per meter run for a particular peak discharge. From the cost analysis, it can be deduced that the cost of concrete in drain required for the trapezoidal drain is 9.07% higher than that of the rectangular drain. However, there are significant reductions of 23.97% in excavation cost, 52.94% in concrete blinding cost, and 44.18% in formwork cost for the trapezoidal drain over the rectangular cross-section.
Furthermore, there is an overall cost reduction of 16.27% if the choice of drain cross-section is trapezoidal. Similarly, suppose the labour cost is directly related to the quantity of materials. In that case, adopting the trapezoidal cross-section is expected to result in savings on the cost compared to a rectangular cross-section. This justifies that trapezoidal cross-sections are usually the most economical, provided there is a right-of-way (ROW).
The standard penetration test (SPT) is made in boreholes by means of the standard 50.8 mm outside and 33.8 mm inside diameter split spoon sampler. It is a very useful method for estimating the in-situ density of cohesionless soils, and when modified by a cone end, it can also be used to assess the relative strength or deformability of rocks.
An automatic trip device triggers repeated strikes from a 63.5 kg weight falling freely through 760 mm, driving the sampler to a penetration of 450 mm.The only blows counted as part of the conventional penetration number are those for the final 300 mm of driving (N-value). For the entire 450 mm of drive, it is standard practice to count the blows for every 75 mm of penetration.
By doing so, it is possible to determine the depth of any disturbed soil in the borehole’s bottom and the height at which any obstacles to driving, such as cobblestones, huge gravel, or cemented layers, are encountered. In the test, typically no more than 50 blows are made (including the number of blows necessary to position the sampler below the disturbed zone).
Both the depth at the start of the test and the depth at which it is concluded must be given in the borehole record if the full 300mm penetration below the initial seating drive is not achieved, i.e., when 50 blows are made before full penetration is achieved. Appropriate symbols must be used to indicate whether the test was completed within or below the initial seating drive. The tube is disassembled for analysis of the soil samples after removal from the borehole (see Figure 3).
Figure 1: Driving sequence in an SPT test
In gravelly soil and rocks the open-ended sampler is replaced by a cone end. Investigations have shown a general similarity in N-values for the two types in soils of the same density.
The standard penetration test was first developed in the USA as a simple tool to determine the density of soils. The test was adopted by various nations throughout the world, and numerous relationships between the test results and soil characteristics and analytical methods were developed.
According to published data, test methodologies vary greatly across different countries. Non-standard types of hammers and samplers were being utilised, and there were several ways to manage the hammer drop, including free-fall or rope and pulley arrangement.
Figure 2: Typical SPT hammer set up
The two most common types of SPT hammers used in the field are the safety hammer and donut hammer. They are commonly dropped by a rope with two wraps around a pulley (see Figure 2).
Correction Factors to SPT Test
There are several factors that will contribute to the variation of the standard penetration number, N, at a given depth for similar soil profiles. These factors include SPT hammer efficiency, borehole diameter, sampling method, and rod length factor.
Figure 3: Split spoon sampler for SPT
It therefore became evident that if the test data were to be used for correlation with different soil parameters, as will be explained below, corrections to N-values produced by non-standard techniques would be required. The following is a summary of the correction factors that should be applied to the measured blow-count.
The primary correction is focused on the energy that the drill rods and hammer send to the sampler. This has been normalised using a 60% of the theoretical maximum energy ratio (ERM). The term N stands for the measured blow-count , while N60stands for the hammer energy correction. A further correction is applied to allow for the energy delivered by the drill rods. The N60 value is corrected to N by multiplying N’60 by 0.75 for rod lengths of 3 m or shorter. The correction factor is unity for lengths greater than 10 m. No correction for sampler size or weight is necessary if a British Standard or ASTM standard sampler is used.
Thus;
N60 = N(ERm/60) = NCE ——– (1)
where ERm is the energy ratio and CE is the 60% rod energy ratio correction factor. Correction factors for rod lengths, sampler type, borehole diameter, and equipment (60% rod energy ratio correction) are given in Tables 1 – 4.
Figure 4: Set up of SPT in site
In the field, the magnitude of ERM can vary from 30 to 90%. The standard practice now in the U.S. is to express the N-value to an average energy ratio of 60% (≈ N60). Thus, correcting for field procedures and on the basis of field observations, it appears reasonable to standardize the field penetration number as a function of the input driving energy and its dissipation around the sampler into the surrounding soil, or;
N60 = NCHCBCSCR/60 ——– (2)
where N60 = standard penetration number corrected for field conditions N = measured penetration number CH = hammer efficiency (%) CB = correction for borehole diameter CS = sampler correction CR = correction for rod length
Country
Hammer Type
Hammer Release
CH (%)
Japan
Donut Donut
Free Fall Rope and pulley
78 67
USA
Safety Donut
Rope and pulley Rope and pulley
60 45
Argentina
Donut
Rope and pulley
45
China
Donut
Free fall Rope and pulley
60 50
Table 1: Variation of hammer efficiency with hammer type and hammer release
Diameter (mm)
Diameter (inches)
CB
60 – 120
2.4 – 4.7
1.0
150
6
1.05
200
8
1.15
Table 2: Variation of borehole correction factor with borehole diameter
Variable
CS
Standard sampler
1.00
With liner for dense sand and clay
0.80
With liner for loose sand
0.90
Table 3: Variation of sampler correction factor with sampler type
Rod length (m)
CR
> 10
1.0
6 – 10
0.95
4 – 6
0.85
0 – 4
0.75
Table 4: Variation of rod length correction factor with rod length
Worked Exampleon SPT Number Calculation
The blow counts for an SPT test at a depth of 6 m in a coarse-grained soil at every 150mm are 9, 16, and 19. A donut automatic trip hammer and a standard sampler were used in a borehole 152 mm in diameter.
(a) Determine the N value. (b) Correct the N value for rod length, sampler type, borehole size, and energy ratio to 60%. (c) Make a preliminary description of the compactness of the soil.
Strategy: The N value is the sum of the blow counts for the last 0.304 m of penetration. Just add the last two blow counts.
Solution
Step 1: Add the last two blow counts. N = 16 + 19 = 35
Step 3: Use Table 5 to describe the compactness. For N = 34, the soil is dense.
Correlations Using SPT
Although the applications of SPT results are entirely empirical, their extensive use has allowed for the accumulation of vast knowledge regarding the behaviour of foundations in sands and gravels. Relationships between N-values and properties like density and shearing resistance angle have been identified.
BS 5930 gives the following relationship between the SPT N-values and the relative density of a sand as shown in Table 5;
N’60 (blows/300 mm of penetration)
Relative Density
Dr (10%)
Below 4
Very loose
< 20
4 – 10
Loose
20 – 40
10 – 30
Medium – Dense
40 – 60
30 – 50
Dense
60 – 80
Over 50
Very dense
> 80
Table 5: Relationship between SPT number and the relative density of soil
Some correlations of the SPT with soil characteristics, in particular the susceptibility of a soil to liquefaction under earthquake conditions, require a further correction to N’60 to allow for the effective overburden pressure at the level of the test. In granular soils, the standard penetration number is highly dependent on the effective overburden pressure.
A number of empirical relationships have been proposed to convert the field standard penetration number N60 to a standard effective overburden pressure σ0‘, of 96 kN/m2 (2000 lb/ft2). The general form for standard sampler is;
N’60 = CNN60 ——– (3)
Several correlations have been developed over the years for the correction factor, CN. In standard geotechnical engineering textbooks, two of these given in Equations (4) and (5) are recommended for use (SI Units);
CN = 9.78√(1/σ0‘) ——– (4)
or
CN = 2/(1 + 0.01σ0‘) ——– (5)
Values of CN derived by Seed et al (1984) are shown in the Figure below;
Figure 5: Correction factor to N’ value to allow for overburden pressure
Correlation of SPT with Cohesive Soils(Clays)
The consistency and unconfined compressive strength (qu) of clay soils can be estimated from the standard penetration number N60. It is important to point out that the correlation between N60 and unconfined compressive strength is very approximate. The sensitivity, St, of clay soil also plays an important role in the actual N60 value obtained in the field. In any case, for clays of a given geology, a reasonable correlation between N60 and qu can be obtained as shown in Equation (6).
qu/Pa = 0.58N600.72 ——– (6)
Where Pa is the atmospheric pressure (in the same unit with qu).
Standard Penetration Number N60
Consistency
Consistency Index
Unconfined Compressive Strength kN/m2 (lb/ft2)
< 2
Very soft
< 0.5
< 25 (500)
2 – 8
Soft to medium
0.5 – 0.75
25 – 80 (500 – 1700)
8 – 15
Stiff
0.75 – 1.0
80 – 150 (1700 – 3100)
15 – 30
Very Stiff
1.0 – 1.5
150 – 400 (3100 – 8400)
> 30
Hard
> 1.5
> 400 (8400)
Table 6: Approximate Correlation between Consistency Index, N60, and qu
Stroud (1975) has established relationships between the N-value, undrained shear strength, modulus of volume compressibility, and plasticity index of clays as shown in Figure 6.
Figure 6: Relationship between SPT number, plasticity index, and undrained shear strength of clay soil
Figure 6: Relationship between SPT number, plasticity index, and compressibility of clay soil
It is not advised to use the SPT in place of the direct approach of conducting laboratory tests on undisturbed samples to determine the shear strength and compressibility of clay soils. This is due to the fact that the correlations between the SPT and the strength and deformability of clays have only been established empirically, with no consideration of time effects, anisotropy, or the composition of the soil.
Correlation of SPT with Cohesionless Soils(Sands)
The drained angle of friction of granular soils, ϕ’, also has been correlated to the standard penetration number. Peck, Hanson, and Thornburn (1974) gave a correlation between (N1)60 and ϕ’ in a graphical form, which can be approximated as;
Schmertmann (1975) also provided a correlation for N60 versus σ0‘. After Kulhawy and Mayne (1990), this correlation can be approximated as;
Where Pa is the atmospheric pressure in the same unit as σ0‘.
Terzaghi and Peck also give the following correlation between SPT value, Dr, and φ as shown in Table 7.
Condition
N
Dr (%)
ϕ’
Very loose
0 – 4
0 – 15
< 28°
Loose
4 – 10
15 – 35
28° – 30°
Medium
10 – 30
35 – 65
30° – 36°
Dense
30 – 50
65 – 85
36° – 42°
Very dense
> 50
> 85
> 42°
Table 7: Correlation between SPT value, Dr, and φ
Conclusion
The SPT can be completed quickly and easily. The equipment can penetrate dense materials and is widely available The engineering characteristics of soils such as bearing capacity and foundation settlement have all been linked to SPT results. However, the majority of these correlations are marginal.
Errors can come from a variety of sources, such as test performance and the use of non-standard equipment. The incorrect lifting and dropping of the hammer, inadequate borehole cleaning prior to the test, and failure to maintain the groundwater level, if one exists, are examples of test performance errors. These mistakes result in N values that are not typical of the soil. For coarse gravel, boulders, soft clays, silts, and mixed soils containing boulders, cobbles, clays, and silts, SPT tests are unreliable.
A digital twin is computer software that simulates how a process or product would work using data from the real world. To improve the output, these systems can use artificial intelligence, software analytics, and the internet of things. These virtual models have become a mainstay in contemporary engineering to spur innovation and boost efficiency thanks to the development of machine learning and elements like big data.
To put it briefly, developing the digital twin of a system can enable the advancement of major technological trends, prevent expensive breakdowns in physical items, and test processes and services utilizing enhanced analytical, monitoring, and predictive skills.
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Typical digital twin model [Source: Bentley Systems]
Managing a Water Supply Network that is Over a Century Old
One of the world’s oldest operational water networks, the 144-year-old Zagreb water delivery system was first built in 1878. Around 30,000 people lived in Zagreb, the capital of Croatia, at the time, with 11,150 of them having access to a water delivery system with a 4-kilometer radius and a 53.2 liters per second capacity. Since then, the population has increased, resulting in a daily water intake of 310,000 cubic meters and the need for water services for approximately 900,000 people over an area of 800 square kilometers delivered by an enlarged network extending 3,500 kilometers.
The public water supply and sewerage business in Zagreb, ViO Zagreb, appointed the company Hidroing the duty of digitizing the system to better manage the network because the water loss have increased dramatically over the previous two decades and have become significantly worse since the occurrence of the 2020 earthquakes.
Construction of a Digital Supply System
For the network’s ensuing thirty years of operation, ViO anticipated that Hidroing would provide a thorough master plan and water loss program. Hidroing was required to create a comprehensive hydraulic model for the EUR 1 million project based on an updated GIS model that allowed for full diagnostic of the supply system, district meter area (DMA) zoning, and numerous measurement locations. Hidroing, however, encountered considerable problems with data collecting and had trouble detecting flow, pressure, and chlorine levels.
They concluded they needed an integrated hydraulic modeling solution to enable intelligent water management in order to meet the owner’s expectations for digitizing the water supply network.
Hydraulic Modeling is Provided by Bentley Applications
Hidroing chose Bentley’s OpenFlows and OpenUtilities solutions for GIS (Geographic Information System) creation, 3D modeling, hydraulic modeling, on-site operations, and facility management after carefully weighing their options. A hydraulic model of the complete network was built and calibrated using 3,000 measurement locations, 144 DMA zones with unique situations, and 3,500 kilometers of pipeline.
Bentley OpenUtilities
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Smart Water Management is Powered by Digital Twin
According to Bentley Systems, Hidroing shortened the production and application of the calibrated hydraulic model for water loss reduction by 16 months by utilizing Bentley’s integrated modelling and analysis technologies. The initial timeframe for developing the GIS platform and producing and calibrating the model was 36 months. However, in under 20 months, they were able to create a finished model and digital twin that identified over 50 steps to reduce water loss utilizing OpenFlows and OpenUtilities.
