Sep 10, 20 westergaard s theory is considered good to design the rigid pavements. The modulus of subgrade reaction k is used as a primary input for rigid pavement design. Evaluation of coefficients of subgrade reaction soil. Pdf experimental evaluation of the subgrade reaction and. Westergaard equations have often been misquoted or misapplied. Potts, austin 2009 modulus of subgrade reaction and deflection,undergraduate journal of mathematical modeling. Evaluating the coefficient of subgrade reaction main problem with the accuracy of k. Materials, road construction, deflection, subgrade reaction. Modulus of subgrade reaction geotechnical engineering. It serves as a resource for contractors, government agencies, consultants, and others in. The winkler type subgrade assumed by westergaard is modelled as a uniform, distributed subgrade through an. The soil reaction p at any point at a distance x along the axis of the pile may be expressed as p e sy eqn 3.
Determining composite modulus of subgrade reaction by use of. Modulus of subgrade reaction which one should be used. The kvalue can be determined by field tests or by correlation with other tests. The modulus of subgrade reaction came about because work done by westergaard during the 1920s developed the kvalue as a spring constant to model the support beneath the slab figure 1. Subgrade characterization plays a key role in the thickness design of airport pavements. The modulus of subgrade reaction is a calculation expedient, and nothing more. Bases and subbases for concrete pavements aashto classification a6 or a7 soil groups or the unified soil classification system ch, mh, and oh soils. Modulus of subgrade reaction and deflection scholar commons.
The correlation between subgrade reaction modulus k s, modulus of elasticity e s and corrected standard penetration test blow counts n are presented for clayey deposits of the qazvin alluvium. Modulus of subgrade reaction is the reaction pressure sustained by the soil sample under a rigid plate of standard diameter per unit settlement measured at. The modulus of subgrade reaction is an often misunderstood and misused concept. Identifying critical parameters, such as the maximum deflection and maximum bending moments of a street supported by an elastic subgrade, is key to designing safe and reliable roadways. Evaluation of modulus of subgrade reaction ks in gravely. The subgrade reaction modulus k30 obtained from the uplt test has been popular for use in asia. The answer lies in the underlying assumptions of how a foundation might behave. The modulus of subgrade reaction has a direct relation with clayey soils consistencies. Westergaard american concrete pavement association. The use of the k value is appropriate for the design of pavements and floor slabs that do not support columns or loadbearing walls.
The theories of vertical and horizontal subgrade reaction are based on the simplifying assumptions that the subgrade obeys hookes law, and that the subgrade reaction on the base of a rigid centrally loaded plate resting on the horizontal surface of the subgrade has the same value at every point of the base. As discussed above, modulus of subgrade reaction is the ratio between the contact pressure q and its corresponding settlement s. California bearing ratio cbr, plate load test plt, modulus of elasticity e, modulus of subgrade reaction k. Analysis of embedded retaining wall using the subgrade reaction method 61 2 2 m x dx d w x ej 4 3 3 t x dx d w x ej 5 where mx is the bending moment and tx is the shearing force. There is no direct laboratory procedure for determining kvalue. Amount of deflection which will occur on the pavement surface depends on the stiffness of the slab and also on the stiffness of the subgrade. To obtain the interior stress in the case ofa square loaded area, radius a is replaced in equation ic by a. Westergaard 1925 assumed that a rigid pavement could be considered as a slab on a winkler foundation.
Structure magazine correlation between soil bearing. Comparative study of methods of determination of coefficient. The modulus of subgrade reaction may be interpreted as the pressure exerted on the subgrade and is measured in pound per squared inches. Determining modulus of subgrade reaction k value txdot designation.
Once a subgrade modulus is known, the behavior of a laterally loaded pile may be eval. It is the ratio of applied pressure divided by the corresponding soil or rock movement. The construction and design of concrete slabs on grade. Feb 25, 2016 historical modulus of subgrade reaction kvalue primary subgrade design variable for concrete pavement design in the good old days westergaard models pca design procedure, etc. The stresses in the concrete slab are determined using westergaards theory. The modulus of subgrade reaction, which is defined as the ratio between an applied pressure q and the deflection. Design of rigid pavements is based on westergaards analysis, where modulus of subgrade reaction, radius of relative stiffness, radius of wheel load distribution are used. The results showed that the 28day qu, the soaked cbr, the modulus of rupture mr and the modulus of subgrade reaction k of the 3 stabilized subgrade materials increased with an increase in. The site is a repository for encyclopedic articles, news, and information on all topics related to pavements. Fol rigid pavements, a rational method for including department of civil engineering, university of arkansas, fayetteville, ark. Ive already provided a modulus of subgrade reaction for the design their request is apparently about a dynamic subgrade modulus. It means that as the consistency of soil decreases the modulus of subgrade reaction decreases. To evaluate the subgrade strength is important during construction and design stage.
Ziaie moayed and janbaz 12 proposed equation 5 which. The volume of traffic during the design life is important for fatigue considerations. Experimental evaluation of subgrade modulus and its. It was also found that the composite modulus of subgrade reaction depends on several variables, including slab thickness, modulus of elasticity of the subbase, and modulus of subgrade reaction. Differential equations govern the bending and deflection of roads under a concentrated load. In this paper, an integrated methodology is introduced for estimating the static vertical subgrade reaction modulus from cpt for shallow foundations on cohesionless soils.
Plate load test how it works measuring ev2 and ev1. Effect of fwd testing position on modulus of subgrade reaction. A sdvosb service disabled veteran owned small business. Plateload tests have been conducted to asses the effect of soil density on the subgrade reaction and soil modulii.
A third measure of soil strength, westergaards modulus of subgrade reaction, k, is the most commonly used soil parameter in the design of concrete pavements and slabs on grade. A third measure of soil strength, westergaards modulus of subgrade reaction, k, is commonly used in design procedures for concrete pavements and floorson. It seems that the terzaghis equation as bowles shows deteriorates when foundation dimension is 3 times of plate dimension. It estimates the support of the layers below a rigid pavement surface course the pcc slab. So, here the upward reaction is assumed to be proportional to the deflection, i. Modulus of subgrade reaction and deflection scholar. In other words, the foundation reaction or vertical stress equals to the deflection times a constant k called modulus of subgrade reaction. To remedy this situation a re examination of these solutions using the finite element method has been conducted. For critical design, a combination of load stress, frictional stress and warping stress is considered. Different types of joints are required like expansion and contraction. Note that the modulus of subgrade reaction k has unit of pci. This paper discusses the variation of the modulus of subgrade reaction k backcalculated from slab deflection basins, interactive with the location of the falling weight deflectometer fwd load.
Hence, the modulus of subgrade reaction, which is the function of soil settlement and the external pressure,is used for flexible foundation design. The effects of different parameters on subgrade reaction modulus are studied and the following results are obtained. Subgrade reaction modulus k s of clayey soils based on field tests 2025 the ultimate soil pressure is at a settlement of. Plate bearing tests, penetration tests, alluvium, gravel, subgrade modulus, case studies. Analysis of pile foundation subjected to lateral and vertical. Comparative analysis of rigid pavement using westergaard. Vertical modulus of subgrade reaction modulus of subgrade reaction k is it a soil property. No footing, rafts, pavement design westergaards work in 1920s q k d used by structural engineers q applied or contact pressure fl2 d settlement of footing under q l k qd slope linear spring. The modulus of the unbound base materials depends on the stress state ie, on the subgrade modulus and the thickness of base course. Modulus of subgrade reaction is decreased as the side dimension of foundation is increased.
The traffic effects are characterized with an equivalent 80 kn esal, which is a dual wheel on one axle, with each wheel weighing 20 kn with 600 kpa uniform tirepavement contact pressure and 105 mm in contact radius. This course is adapted from the unified facilities criteria of the united states government, which is in the public domain, is authorized for unlimited distribution, and is not ed. Missouri university of science and technology scholars mine. A third measure of soil strength, westergaards modulus of subgrade reaction, k, is commonly used in design procedures for concrete pavements and floorsongrade that are not structural elements in the building floors not supporting columns and loadbearing walls. The data developed in the static load test is used in the calculation of the modulus of subgrade reaction in section 6. Winkler model, soft soil model, coefficient of subgrade reaction, modulus of elasticity, settlement.
The usual practical way to deal with heterogeneous. He considered rigid pavement slab as a thin elastic plate resting on soil subgrade, which is assumed to be a dense liquid. However, the strain modulus is determined by the curve fitting method for the overall normal stresssettlement data. Pdf correlation between subgrade reaction modulus and. Pdf correlation between subgrade reaction modulus and cbr. Table 31 lists va lues for maximum stationary live loads on floo r slabs. Evaluation of modulus of elasticity and modulus of subgrade. Pdf subgrade reaction modulus k s of clayey soils based. The two methods show similar trends, although the finiteelement technique appears to be siffer than westergaard s theory. Fatigue failure due to slab flexure erosion failure due to foundation compression edge loads produce the worst stresses fatigue based on tensile stress due to edge loads corner loads produce the worst deflections erosion based on deflections due to corner loads 2.
Other factors responsible for non uniform foundation include variability due to a number of reasons including, natural causes, excavation and. Tm 580912 concrete floor slabs on grade subjected to. Westergaard is considered the pioneer in providing the rational treatment of the rigid pavement analysis. Measure of soil resistance to vertical pressure pressure deflection k 18. Estimation of the static vertical subgrade reaction. In this study, five different backfill materials of known relative densities have been prepared in a large scale testing facility. This is due to the fact that the modulus of elasticity is the only factor by which the effect of subsurface soil properties on the value of k. The subgrade reaction modulus is determined as the ratio between the normal stress and the settlement from 0 to 1. Westergaards theory for rigid pavements civil engineering. The pavement must also be plotted to limit the expansion and loss of density of the subgrade soil 5. Effective parameters on modulus of subgrade reaction in. The theory of subgrade reaction assumes that the unit soil reaction p with respect to a laterally loaded pile increases linearly with the lateral deflection y, as expressed in the fol lowing equation. Tm 580912 concrete floor slabs on grade subjected to heavy.
Th e floor slab design procedure presented the maximum allowable stationary live load is lim. Manual computation of flexible analysis could be challenging and, in almost all. This is hardly a surprise as, by definition, the modulus of subgrade reaction. As a result, it cannot be determined using a cbr test, plate load test or any other test, for that matter. Modulus of subgrade reaction westergaard considered the rigid pavement slab as a thin elastic plate resting on soil subgrade, which is assumed as a dense liquid. With constant width and with constant load intensity, the modulus of subgrade reaction in strip foundation has the. The modulus of subgrade reaction is not a soil property. The intensity of this load can be quantified by westergaards modulus of subgrade reaction i. Design of slabs on grade aci 360r is specifically oriented to the determination of modulus of subgrade reaction using a 760mm 30in. More recently, the strain modulus ev was newly introduced. For a uniformly loaded flexible foundation, contact pressure remains uniform throughout the foundation, but settlement decreases from the center towards the edge, so qs or modulus of subgrade reaction increases from the center towards the edge figure 2. Facilities development manual wisconsin department of. Design of rigid pavements is based on westergaard s analysis, where modulus of subgrade reaction, radius of relative stiffness, radius of wheel load distribution are used. The winkler type subgrade assumed by westergaard is modelled as a uniform, distributed subgrade through an equivalent mass formation.
The most common and probably the safest answer to the question of correlation between bearing capacity and the modulus of subgrade reaction is that there is no correlation. Since floor slabs are designed for moving live loa ds, the design should be checked for stationary live loading conditions. It is used for continuous footing, mats and various types of. The plate load test ax01 is the simple solution to determine the strain moduli ev2 and ev1 a figure for the bearing capacity and the ratio ev2ev1 a figure for the compaction level. Pavement interactive is a free online knowledge base for the paving industry. Westergaards theory is considered good to design the rigid pavements. Variable modulus of subgrade reaction civil engineering.
An introduction to engineering properties of soil and rock. Arora 2003 has reported that the westergaards analysis is used for design of rigid pavements. From a mechanical point of view, a subgrade soil represents a highly diverse heterogeneous structure. Concrete mixture proportioner iphone concrete mixture proportioner ipad evaporation rate calculator. Modulus of soil reaction, e the modified iowa formula includes a term referred to as the modulus of soil reaction, e, and is defined as an empirical value used to express the stiffness of the embedment soil in predicting flexible pipe deflection. Correlation between soil bearing capacity and modulus of. Modulus of subgrade reaction and deflection usf scholar. Introduction the modulus of subgrade reaction is a conceptual relationship between soil pressure and deflection that is widely used in the structural analysis of foundation members.
Subgrade modulus of laterally loaded piles in clays. No footing, rafts, pavement design westergaards work in 1920s q k d used by structural engineers q applied or contact pressure fl2 d settlement of footing under q l. I do not believe that it is the dynamic shear modulus g that the engineer has asked for as ive given them a value for that. The modulus of subgrade reaction is an often misunderstood and misused concept for the thickness design of slabsonground. The proposed methodology relies on fundamental concepts of soil mechanics and foundation engineering applicable to flexible foundations. In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to. June 1979, after the draft finalized by the soil engineering and rock mechanics sectional committee had been approved by the civil engineering division council. E modulus of elasticity of concrete 4,200,000 psi k modulus of subgrade reaction psi refer to soils report figure 5. It serves as a resource for contractors, government agencies, consultants, and others in the transportation infrastructure industry. Same amount of deflection will occur on the top surface of the subgrade.
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