Why are some manhole covers made of cast iron while some are made of ductile iron?
Answer: Traditionally, manholes covers are made of cast iron. However, in the viewpoint of pipe maintenance, frequent opening of manhole covers has to be carried out. Therefore, it poses potential safety hazard to the workers during the lifting-up process of manhole covers because cast iron manhole covers are very heavy to normal workers. Consequently, research has been conducted and ductile iron is considered as a better choice than cast iron because it can resist the same traffic loads with lower self-weight. Moreover, as ductile iron is less brittle than cast iron, the traditional cast iron manhole covers are more susceptible to damage and thus require higher maintenance cost.
However, ductile iron manhole covers do suffer from some demerits. For instance, owing to their relative low self-weight, vehicles passing over these manhole covers would lead to the movement of covers and generate unpleasant noises. To solve this problem, instead of increasing the self-weight of ductile iron manhole covers which similarly causes safety problems to workers during regular maintenance, the covers can be designed to be attached to the manhole frames which hold them in firm position.
Question No. 277
Under what situation shall engineers use jacking at one end only and from both ends in pre-stressing work?
Answer: During pre-stressing operation at one end, frictional losses will occur and the pre-stressing force decreases along the length of tendon until reaching the other end. These frictional losses include the friction induced due to a change of curvature of tendon duct and also the wobble effect due to deviation of duct alignment from the centerline. Therefore, the pre-stress force in the mid-span or at the other end will be greatly reduced in case the frictional loss is high. Consequently, pre-stressing, from both ends for a single span i.e. pre-stressing one-half of total tendons at one end and the remaining half at the other end is carried out to enable a even distribution and to provide symmetry of pre-stress force along the structure.
In fact, stressing at one end only has the potential advantage of lower cost when compared with stressing from both ends. For multiple spans (e.g. two spans) with unequal span length, jacking is usually carried out at the end of the longer span so as to provide a higher pre-stress force at the location of maximum positive moment. On the contrary, jacking from the end of the shorter span would be conducted if the negative moment at the intermediate support controls the pre-stress force. However, if the total span length is sufficiently long, jacking from both ends should be considered.
Question No. 278
Rational Method should not be used for large catchments in estimating peak runoff. Is it true?
Answer: Rational Method is suitable for small catchments only because the time of concentration of small catchments is small. In Rational Method the peak runoff is calculated based on the assumption that the time of concentration is equal to the rainfall duration. For small catchments, this assumption may hold true in most circumstances. One of the assumptions of Rational Method is that rainfall intensity over the entire catchment remains constant during the storm duration. However, in case of a large catchment it stands a high probability that rainfall intensity varies in various part of the large catchment. In addition, for long duration of rainfall, it is rare that the rainfall intensity remains constant over the entire rainstorm and a shorter duration but a more intense rainfall could produce a higher peak runoff. Moreover, a reduction of peak runoff is also brought about by the temporary storage of storm-water like channels within the catchment.
In actual condition, the runoff rate within the catchment varies from place to place because of different soil properties and past conditions. As suggested by Bureau of Public Roads (1965), sometimes the peak discharge occurs before all of the drainage area is contributing. For instance, when a significant portion of drainage area within the catchment has very small time of concentration so that a higher rainfall intensity can be used for this portion, the runoff coming solely from this portion is higher than that of the whole catchment in which a lower rainfall intensity is adopted because the remaining part of the catchment has comparatively large time of concentration. Therefore, this results in incorrect estimation of peak runoff of large catchments if Rational Method is adopted.
Question No. 279
In bridge widening projects, the method of stitching is normally employed for connecting existing deck to the new deck. What are the problems associated with this method in terms of shrinkage of concrete?
Answer: In the method of stitching, it is a normal practice to construct the widening part of the bridge at first and let it stay undisturbed for several months. After that, concreting will then be carried out for the stitch between the existing deck and the new deck. In this way, the dead load of the widened part of bridge is supported by itself and loads arising from the newly constructed deck will not be transferred to the existing deck which is not designed to take up these extra loads.
One of the main concerns is the effect of stress induced by shrinkage of newly widened part of the bridge on the existing bridge. To address this problem, the widened part of the bridge is constructed a period of time (say 6-9 months) prior to stitching to the existing bridge so that shrinkage of the new bridge will take place within this period and the effect of shrinkage stress exerted on the new bridge is minimized.
Traffic vibration on the existing bridge causes adverse effect to the freshly placed stitches.
To solve this problem, rapid hardening cement is used for the stitching concrete so as to shorten the time of setting of concrete. Moreover, the stitching work is designed to be carried out at nights of least traffic (Saturday night) and the existing bridge may even be closed for several hours (e.g. 6 hours) to let the stitching works to left undisturbed.
Sometimes, longitudinal joints are used in connecting new bridge segments to existing bridges. The main problem associated with this design is the safety concern of vehicles. The change of frictional coefficients of bridge deck and longitudinal joints when vehicles change traffic lanes is very dangerous to the vehicles. Moreover, maintenance of longitudinal joints in bridges is quite difficult.
Note: Stitching refers to formation of a segment of bridge deck between an existing bridge and a new bridge.
Question No. 280
What are the limitations of Rational Method in calculating runoff?
Answer: Computation of runoff is a complicated matter which depends on many factors like the ground permeability, rainfall duration, rainfall pattern, catchment area characteristics etc. Basically, Rational Method is a means to find out the maximum discharge suitable for design purpose. In this method, it is assumed that the rainfall duration is the same as the time of concentration and the return period of rainfall intensity is the same as the peak run-off. Time of concentration refers to the time required for the most remote location of storm-water inside the catchment to flow to the outlet. When the time of concentration is equal to the rainfall period, the maximum discharge occurs and rainfall collected inside the catchment comes to the same outlet point.
Rational Method provides the peak discharge only and it cannot produce a hydrograph. If a more detailed pattern of runoff is required, unit hydrograph or other methods have to be used. The accuracy of rational method depends very much on our correct selection of run-off coefficient and delineation of catchment area.
Rational Method is a rather conservative method. One of the basic assumptions of the rational formula is that the rainfall intensity must be constant for an interval at least equal to the time of concentration. For long duration of rainfall, this assumption may not hold true. Moreover, the runoff coefficient in Rational Method is difficult to be determined accurately and it depends on many factors like moisture condition of soils, rainfall intensity and duration, degree of soil compaction, vegetation etc. In addition, In Rational Method the run-off coefficient is independent of rainfall intensity and this does not reflect the actual situation.
Question No. 281
Is it desirable to use concrete of very high strength i.e. exceeding 60 MPa? What are the potential problems associated with such high strength concrete?
Answer: To increase the strength of concrete, say from 40 MPa to 80 MPa, it definitely helps in improving the structural performance of the structure by producing a denser, more durable and higher load capacity concrete. The size of concrete members can be significantly reduced resulting in substantial cost savings. However, an increase of concrete strength is also accompanied by the occurrence of thermal cracking. With an increase in concrete strength, the cement content is increased and this leads to higher thermal strains. Consequently, additional reinforcement has to be introduced to control these additional cracks caused by the increase in concrete strength. Moreover, the ductility of concrete decreases with an increase in concrete strength. Attention should be paid during the design of high strength concrete to increase the ductility of concrete. In addition, fire resistance of high strength concrete is found to be less than normal strength concrete as suggested by Odd E. Gjorv (1994).
Though the tensile strength of high strength concrete is higher than that of normal concrete, the rate of increase of tensile strength is not proportional to the increase of compressive strength. For normal concrete, tensile strength is about one-tenth of compressive strength. However, for high strength concrete, it may only drop to 5% of compressive strength.
Moreover, owing to a low aggregate content of high strength concrete, creep and shrinkage increases.
Question No. 282
Why do BS8007 specify the allowable crack width of water retaining structure as 0.2 mm for severe or very severe exposure?
Answer: For crack width less than 0.2 mm, it is assumed that the mechanism of autogenous healing will take place in which the crack will automatically seal up and this would not cause the problem of leakage and reinforcement corrosion in water retaining structure.
When the cracks are in inactive state where no movement takes places, autogenous healing occurs in the presence of water. However, when there is a continuous flow of water through these cracks, autogenous healing would not take place because the flow removes the lime. One of the mechanisms of autogenous healing is that calcium hydroxide (generated from the hydration of tricalcium silicate and dicalcium silicate) in concrete cement reacts with carbon dioxide in the atmosphere, resulting in the formation of calcium carbonate crystals. Gradually these crystals accumulate and grow in these tiny cracks and form bonding so that the cracks are sealed. Since the first documented discovery of autogenous healing by the French Academy of Science in 1836, there have been numerous previous proofs that cracks are sealed up naturally by autogenous healing. Because of its self-sealing property,
Question No. 283
Why is it preferable to design storm-water drains to match soffit?
Answer: Storm-water drains collect storm-water in their corresponding catchment areas during rainstorm and convey the collected water through outlets to the sea. Therefore, in considering the hydraulic design of storm-water drains, other than normal drainage pipe capacity to be taken into consideration, one should check the backwater effect due to tidal condition at outlets if the drains are located quite close to the downstream end of outlets.
Storm-water drains are normally designed to match soffit to avoid surcharging by backwater effect or when the downstream pipes are running full. Normally pipe size increases from upstream to downstream. For the case of matching drain invert, when outlet pipes are fully surcharged by tidal effect of the sea or when the downstream pipes are fully filled with storm-water, pipe sections immediately upstream of the outlet are also surcharged too. However, for the case of matching pipe soffit, the immediate upstream sections of outlet pipes are not totally surcharged even though downstream pipes are running full. However, it is not always practical to maintain soffit for all pipelines because it requires sufficient drop to achieve this.
Moreover, the flow of storm-water is mainly by gravity in the design of storm-water drains.
In case the drains are designed to match invert, then it stands a high probability that the flow in the upstream smaller pipes has to be discharged against a head.
Note: Matching soffit means that all pipelines are aligned continuously with respect to the pipelines’ crown level.
Question No. 284
When designing a water storage tank, should movement joints be installed?
Answer: In designing water storage tanks, movement joints can be installed in parallel with steel reinforcement. To control the movement of concrete due to seasonal variation of temperature, hydration temperature drop and shrinkage etc. two principal methods in design are used: to design closely spaced steel reinforcement to shorten the spacing of cracks, thereby reducing the crack width of cracks; or to introduce movement joints to allow a portion of movement to occur in the joints.
Let’s take an example to illustrate this. For 30 m long tanks wall, for a seasonal variation of 35 degree plus the hydration temperature of 30°C, the amount of cracking is about 8.8 mm. It can either be reduced to 0.3 mm with close spacing or can be absorbed by movement joints. Anyway, the thermal movement associated with the seasonal variation of 35°C is commonly accounted for by movement joints.
For water-retaining structure like pumping stations, the crack width requirement is even more stringent in which 0.2 mm for severe and very severe exposure is specified in BS8007. It turns out to a difficult problem to designers who may choose to design a heavy reinforced structure. Obviously, a better choice other than provision of bulky reinforcement is to allow contraction movement by using the method of movement joints together with sufficient amount of reinforcement. For instance, service reservoirs in Water Supplies Department comprise grids of movement joints like expansion joints and contraction joints.
Question No. 285
What is the function of shear keys in the design of retaining walls?
Answer: In determining the external stability of retaining walls, failure modes like bearing failure, sliding and overturning are normally considered in design. In considering the criterion of sliding, the sliding resistance of retaining walls is derived from the base friction between the wall base and the foundation soils. To increase the sliding resistance of retaining walls, other than providing a large self-weight or a large retained soil mass, shear keys are to be installed at the wall base. The principle of shear keys is as follows:
The main purpose of installation of shear keys is to increase the extra passive resistance developed by the height of shear keys. However, active pressure developed by shear keys also increases simultaneously. The success of shear keys lies in the fact that the increase of passive pressure exceeds the increase in active pressure, resulting in a net improvement of sliding resistance.
On the other hand, friction between the wall base and the foundation soils is normally about a fraction of the angle of internal resistance (i.e. about 0.8 ϕ) where ϕ is the angle of internal friction of foundation soil. When a shear key is installed at the base of the retaining wall, the failure surface is changed from the wall base/soil horizontal plane to a plane within foundation soil. Therefore, the friction angle mobilized in this case is ϕ instead of 0.8ϕ in the previous case and the sliding resistance can be enhanced.
Question No. 286
In the design of watermains, how to decide the usage of double air valves and single air valves?
Answer: Single air valves allow squeezing air out of the pipeline in automatic mode in high-pressure condition and are normally designed in high points of watermain in which air voids are present. Double air valves basically serve the same purpose except that it has another important function: it can get air into/out of the pipeline during low-pressure condition.
In WSD practice, watermain are normally divided into sections by installation of sectional valves to facilitate maintenance. In a single isolated pipeline section bounded by two sectional valves, at least a double air valve should be installed. During normal maintenance operation like cleansing of watermain, water inside pipelines is drawn from washout valves. However, as normal watermain is subject to very high pressure like 1.5 MPa and the sudden withdrawn of water will cause a transient vacuum condition and will damage the watermain. Therefore at least one double air valve should be present to allow air to squeeze in to balance the pressure and this protects the pipeline from damaging.
In essence, for local high points single air valves should be installed. Within a section of pipeline, at least one double air valve should be installed.
Question No. 287
In checking the quality of weld, what are the pros and cons of various non-destructive weld inspection methods i.e. ultrasonic test, radiographic inspection and magnetic particle flaw detection test?
Answer: Currently, there are three common non-destructive testing of weld, namely radiographic inspection, ultrasonic testing and magnetic flaw detection test.
The method of radiographic approach was used commonly in the past until the arrival of ultrasonic inspection technique. The major difference between the two is that ultrasonic testing detects very narrow flaws which can hardly be detected by radiographic method. Moreover, it is very sensitive to gross discontinuities. Tiny defects, which characterize welding problems, are normally not revealed by radiographic inspection.
Moreover, ultrasonic inspection possesses the advantages that it can accurately and precisely locate a defect as well as figure out its depth, location and angle of inclination.
In the past, it was expensive to adopt ultrasonic means for inspection. Nowadays, the rates for both inspection methods are comparable. Most importantly, the x-ray and gamma ray used in radiographs are radioactive and pose potential safety hazard to testing technicians on site. Reference is made to Paul G. Jonas and Dennis L. Scharosch.
Magnetic flaw detection test can only be used for checking flaws in any metallic objects.
This method is commonly used for inspecting surface cracks and slightly sub-surface cracks. However, surface and sub-surface cracks can be readily detected by radiographs and ultrasonic inspection.
Question No. 288
If a contractor proposes to increase concrete cover beyond contractual specification (i.e. 40 mm to 70 mm), shall engineers accept the proposal?
Answer: In contractual aspect, based on the requirement of General Specification of Civil Engineering Works (1992 Edition), the tolerance of concrete cover is between +5 mm and -5 mm and engineers should not accept sub-standard work because they do not possess the authority to change the acceptance criteria. In case engineers consider contractor’s proposal acceptable in technical point of view, consent has to be sought from the employer regarding the changes in acceptance criteria.
From technical point of view, the effect on cracking due to an increase in concrete cover should be considered. In general, there are three main parameters which govern crack width, namely tensile strain at the point considered, the distance of longitudinal bar to the concerned point and the depth of tension zone.
For the second factor, i.e. proximity of longitudinal bars to point of section, the closer a bar is to this point; the smaller is the crack width. Therefore, closely spaced bars with smaller cover will give narrower cracks than widely spaced bars with larger cover. Therefore, with an increase of concrete cover, the crack width will increase which is undesirable.
Question No. 289
Can a concrete structure be completely free of expansion joints and contraction joints?
Answer: Consider that the concrete structure is not subject to the problem of differential settlement.
For contraction joints, it may be possible to design a concrete structure without any contraction joints. By using sufficient steel reinforcement to spread evenly the crack width over the span length of the structure, it may achieve the requirement of minimum crack width and cause no adverse impact to the aesthetics of the structure. However, it follows that the amount of reinforcement required is higher than that when with sufficient contraction joints.
For expansion joints, the consequence of not providing such joints may be difficult to cater for. For example, a concrete structure has the coefficient of thermal expansion of 9 × 10-6 /°C and a Young’s modulus of 34.5kN/mm². With an increase of temperature of 20°C and it is restricted to free expansion, then the structure is subject to an axial stress of 6.21 MPa. If the structure is very slender (e.g. concrete carriageway), buckling may occur. Therefore, the structure has to be designed to take up these thermal stresses if expansion joints are not provided. However, for water retaining structures, most of them are not affected by weather conditions because they are insulated from the water they contain internally and soil backfill that surround them. Therefore, it is expected that a smaller amount of thermal movement will occur when compared with normal exposed concrete structure. Consequently, expansion joints may be omitted in this case with the view that the compressive stress induced by thermal expansion toughens the structure to limit the development of tensile stress.
Question No. 290
What is the difference between “hammer efficiency” and “coefficient of restitution” when using Hiley’s formula in pile driving?
Answer: Hammer efficiency refers to the ratio of kinetic energy of the hammer to the rate energy (or potential energy). In essence, there is undoubtedly certain energy loss induced by the hammer itself prior to the actual impact on the driven pile. For instance, these losses may include misalignment of the hammer, energy losses due to guiding friction, inaccurate dropping height etc.
Coefficient of restitution refers to a value indicating the strain energy during collision regained after the bodies reverted back to their original shapes. If the coefficient of restitution is equal to unity, it means that the collision is elastic and all energy has been returned after the impact action. Hence, this is a index showing the degree the impact action in terms of elasticity.
In mathematical forms,
Coefficient of restitution = -(v₁ - v₂)/ (u₁ - u₂)
Where u = initial velocity and v = final velocity after impact
Question No. 291
What are the functions of different components of a typical expansion joint?
Answer: In a typical expansion joint, it normally contains the following components: joint sealant, joint filler, dowel bar, PVC dowel sleeve, bond breaker tape and cradle bent.
- Joint sealant: it seals the joint width and prevents water and dirt from entering the joint and causing dowel bar corrosion and unexpected joint stress resulting from restrained movement.
- Joint filler: it is compressible so that the joint can expand freely without constraint. Someone may doubt that even without its presence, the joint can still expand freely. In fact, its presence is necessary because it serves the purpose of space occupation such that even if dirt and rubbish are intruded in the joint, there is no space left for their accommodation.
- Dowel bar: This is a major component of the joint. It serves to guide the direction of movement of concrete expansion. Therefore, incorrect direction of placement of dowel bar will induce stresses in the joint during thermal expansion. On the other hand, it links the two adjacent structures by transferring loads across the joints.
- PVC dowel sleeve: It serves to facilitate the movement of dowel bar. On one side of the joint, the dowel bar is encased in concrete. On the other side, however, the PVC dowel sleeve is bonded directly to concrete so that movement of dowel bar can take place. One may notice that the detailing of normal expansion joints in Highways Standard Drawing is in such a way that part of PVC dowel sleeve is also extended to the other part of the joint where the dowel bar is directly adhered to concrete. In this case, it appears that this arrangement prevents the movement of joint. If this is the case, why should designers purposely put up such arrangement? In fact, the rationale behind this is to avoid water from getting into contact with dowel bar in case the joint sealant fails. As PVC is a flexible material, it only minutely hinders the movement of joint only under this design.
- Bond breaker tape: As the majority of joint sealant is applied in liquid form during construction, the bond breaker tape helps to prevent flowing of sealant liquid inside the joint.
- Cradle bar: It helps to uphold the dowel bar in position during construction.
Question No. 292
What are the considerations in determining whether casings should be left in for mini-piles?
Answer: Contrary to most of pile design, the design of min-piles is controlled by internal capacity instead of external carrying capacity due to their small cross-sectional area.
There are mainly two reasons to account for designing mini-piles as friction piles:
- Due to its high slenderness ratio, a pile of 200 mm diameter with 5 m long has a shaft area of 100 times greater than cross-sectional area. Therefore, the shaft friction mobilized should be greater than end resistance.
- Settlements of 10%-20% of pile diameter are necessary to mobilize full end bearing capacity, compared with 0.5%-1% of pile diameter to develop maximum shaft resistance.
Left-in casings for mini-piles have the following advantages:
- Improve resistance to corrosion of main bars;
- Provide additional restraint against lateral buckling;
- Improve the grout quality by preventing intrusion of groundwater during concreting;
- Prevent occurrence of necking during lifting up of casings during concreting.
Question No. 293
If on-site slump test fails, should engineers allow the contractor to continue the concreting works?
Answer: This is a very classical question raised by many graduate engineers. In fact, there are two schools of thought regarding this issue.
The first school of thought is rather straightforward: the contractor fails to comply with contractual requirements and therefore as per G. C. C. Clause 54 (2)(c) the engineer could order suspension of the Works. Under the conditions of G. C. C. Clause 54(2)(a) – (d), the contractor is not entitled to any claims of cost which is the main concern for most engineers. This is the contractual power given to the Engineer in case of any failure in tests required by the contract; even though some engineers argue that slump tests are not as important as other tests like compression test.
The second school of thought is to let the contractor to continue their concreting works and later on request the contractor to prove that the finished works comply with other contractual requirements e.g. compression test. This is based upon the belief that workability is mainly required to achieve design concrete compression strength. In case the compression test also fails, the contractor should demolish and reconstruct the works accordingly. In fact, this is a rather passive way of treating construction works and is not recommended because of the following reasons:
- Workability of freshly placed concrete is related not only to strength but also to durability of concrete. Even if the future compression test passes, failing in slump test indicates that it may have adverse impact to durability of completed concrete structures.
- In case the compression test fails, the contractor has to deploy extra time and resources to remove the work and reconstruct them once again and this slows down the progress of works significantly. Hence, in view of such likely probability of occurrence, why shouldn't the Engineer exercise his power to stop the contractor and save these extra time and cost?
Question No. 294
In piling works, normally founding levels of bored piles are defined by using total core recovery or rock quality designation (RQD). Are there any problems with such specification?
Answer: The use of total core recovery to determine the founding level may not be able to indicate the quality of rock foundation for piles because it depends on the drilling technique and drilling equipment (GEO (1996)). For instance, if standard core barrels are used to collect samples, it may indicate sufficient core recovery for samples full of rock joints and weathered rock. On the other hand, if triple tube barrels are used for obtaining soil samples, samples with joints and weathered rock can also achieve the requirements of total core recovery.
In case RQD is adopted for determining founding levels, it may also result in incorrect results. For instance RQD does not indicate the joints and infilling materials. Moreover, as it only measures rock segments exceeding 100 mm, rock segments exceeding 100 mm is considered to be of good quality rock without due consideration of its strength and joint spacing.
Question No. 295
What is the purpose of post-grouting for mini-piles?
Answer: Post-grouting is normally carried out some time when grout of the initial grouting work has set (e.g. within 24 hours of initial grouting). It helps to increase the bearing capacity of mini-piles by enhancing larger effective pile diameter. Moreover, it improves the behavior of soils adjacent to grouted piles and minimizes the effect of disturbance caused during construction. In essence, post-grouting helps to improve the bond between soils and grout, thereby enhancing better skin friction between them.
During the process of post-grouting, a tube with a hole at its bottom is lowered into the pile and grout is injected. The mechanism of post-grouting is as follows: the pressurized grout is initially confined by the hardened grout and can hardly get away. Then, it ruptures the grout cover and makes its way to the surrounding soils and into soft regions to develop an interlock with harder soil zones. In order to enhance the pressurized grout to rupture the initial grout depth, a maximum time limit is normally imposed between the time of initial grouting and time of post-grouting to avoid the development of high strength of initial grout. Consequently, the effect of soil disturbance by installation of casings and subsequent lifting up of casings would be lessened significantly.
Question No. 296
What is the purpose of conducting load test for piling works?
Answer: Pile load test provides information on ultimate bearing capacity but not settlement behavior. In essence, it can determine if the load is taken up by the stratum designed or if the centre of resistance is at the design location in piles as suggested by Robert D. Chellis (1961).
After conducting load tests, the curve of movement of pile head (Settlement against load) and the curve of plastic deformation can be plotted. By subtracting the curve of plastic deformation from the curve of pile head movement at each load, the curve of elastic deformation can be obtained. For piles of end-bearing type unrestrained by friction, the theoretical elastic deformation can be calculated from e = RL/AE where e is elastic deformation, ‘L’ is pile length, ‘A’ is area of pile, ‘E’ is Young’s Modulus of pile material and ‘R’ is the reaction load on pile. By substituting e in the formula, the elastic deformation read from the curve of elastic deformation, ‘L’ can be obtained which shows the location of the centre of resistance corresponding to that load.
Question No. 297
In modeling a non-rigid mat foundation by using elastic springs, should a uniform modulus of sub-grade reaction be used along the whole base of mat?
Answer: By using a bed of springs to simulate the flexible behavior of mat subject to loads, care should be taken in selection of the modulus of sub-grade reaction. In fact, the modulus of sub-grade reaction depends on many factors like the width of the mat, the shape of the mat, the depth of founding level of the mat etc. In particular, the modulus of sub-grade reaction is smaller at the center while it is larger near the mat’s edges. If a constant modulus of sub-grade reaction is adopted throughout the width of the mat, then a more or less uniform settlement will result when subject to a uniform load. However, the actual behavior is that settlement in the center is higher than that at side edges. Consequently, it leads to an underestimation of bending moment by 18% to 25% as suggested by Donald P. Coduto (1994).
In general, a constant value of modulus of sub-grade reaction is normally applied for structure with a rigid superstructure and the rigid foundation. However, a variable modulus of sub-grade reaction is adopted instead for non-rigid superstructure and non-dominance of foundation rigidity to account for the effect of pressure bulbs.