soil subgrade modulus and spring constantsoil subgrade modulus and spring constant

The modeling procedure included the soil with its special . The settlement-influence factor depends on the ratio of the tip diameter db to the top diameter of the pile d (for 1 < db/d < 3; usually db/d=1) and the ratio of length of the pile L to its diameter d (L/d). .,54iGIb|o3eq%]Gs"B|^~;\~#$J//S32mIr1[Aw 1pT'&6rL /8aiNF1c11dInU wB!9kt1Eaa~6lvLggy So, the slab is assumed to remain planar even after the application of load. RISA-3D calculates the tributary area for each plate node individually and multiplies that area by the subgrade modulus to determine the spring stiffness for the compression-only spring at that node. The field plate load test is used to determine the modulus of subgrade reaction. This is based on a rigid 1 ft x 1 ft (0.305 m x 0.305m) slab placed on a soil medium. Against many popular opinions, the modulus of subgrade reaction is not an exclusive property of soil but depends mainly on the loaded area (size of the footing or mat). Country Piles are fundamentally divided into two categories: End-bearing piles distribute the largest portion of the vertical load to the toe of the pile. 2009, Beams on Elastic Foundation The Simplified Continuum Approach. Correlation between the shear wave velocity, DCP and CBR for the subgrade layer. Table 4 is a typical example which shows the relationship among different foundation sizes and failure criteria. It is worthwhile to note that the stress distribution patterns presented in Figure 4 assume that a vertical load is applied to the foundation. This approach replaces the soil medium with a system of finite, discrete, linear elastic springs as depicted in Figure 1. The test can be carried out in accordance with BS 1377 Part 9: 1990. Brinkgreve, and first presented byVirtuosity. inch/cu. (CBR), modulus of subgrade reaction (k), and elastic (resilient) modulus. Stay tuned! Join TheConstructor to ask questions, answer questions, write articles, and connect with other people. Figure 6b. This study aimed to investigate the dynamic characteristics of sodium silicate modified lime and fly ash treated EPS lightweight soil (SLS) under cyclic loading. In a structural analysis process, the subgrade modulus is typically utilized to obtain a vertical spring constant ([Force] / [Length]) by multiplying the subgrade modulus with the tributary area of the spring support elements. To account for this characteristic of the soil, lateral springs are modeled as compression-only springs and vertical springs are modeled as linear elastic springs. In these cases, the forces in the slab and the computed soil pressure may not be sensitive to the area spring constant. Topics to be covered will include: geotechnical properties of geomaterials (soils, rocks, soil and . Please let us know here why this post is inappropriate. Gk Y z dz d Y z E I. p k (2) Where . Soil subgrade reaction in pile foundations is mostly based on theory of elasticity. In the SI unit system, it is expressed as kN/m2/m. I'd concur with all that DaveAtkins said. in./cu. However, the above discussion gives insight into these values and helps engineers to understand the physical significance of modulus of subgrade reaction. Distribution of Subgrade Modulus beneath Beams on. This work presents an experimental study on the physico-mechanical and microstructural characteristics of stabilised soils and the effect of wetting and drying cycles on their durability as road subgrade materials. The other important factor is the assumed allowable settlement for the calculated bearing capacity. The actual modulus value is dependent on the size of the loading area: for a given displacement, the modulus value decreases as the plate size is increased. In other words, soil capacity to withstand pressure for a given displacement. Although there are other factors involved when evaluating subgrade materials (such as swell in the case . Sorry, you do not have permission to ask a question, You must log in to ask a question. As long as the majority of soil beneath the mat behave similarily, the spring constant derived by multiplying the soil (elastic) modulus and the unit area (1 sf) is an acceptable approximation (to generate profile of deflection/stresses flow of the mat). 25 MN/m3) for soft clay to 750 pci (approx. The Subgrade Modulus, also known as the Modulus of Subgrade Reaction, is a stiffness parameter typically used in defining the support conditions of footings and mat foundations, such as that shown on Figure 1. However, one thing (k) is not is a fundamental soil property. Node 1 has a tributary area which is 25% of Node 81. Evaluation of modulus of subgrade reaction Ks in gravely. Foundation Selection Criteria for Buildings, Concrete Pavements for Car Parking Features and Construction, Pile Load Capacity Calculation Single Pile and Group Pile. Subgrade modulus of geocell reinforced sand foundations. The modulus of subgrade reaction (k) is used as a primary input for rigid pavement design. But there should be one, as both are the measurements of soil capacities and any of these two parameters can be used to design a regular foundation. The stress levels are different for each pavement structure, and in the semi-rigid structure, this value is generally lower in comparison to . It is important to note that in equation (5), the author assumed a 25 mm settlement value for the soil. Widespread availability of FEA software contributes to this trend. on the one hand that its is legitimate to model the soil used in this study as a single layer having a constant subgrade modulus K s with depth, . This term is measured and expressed as load intensity per unit of displacement. Brinkgreve, and first presented byVirtuosity. The columns also provide convenient snap points for tendons or design strips. The increased overall stiffness of the foundation will further enhance the non-uniformity of the subgrade modulus, as illustrated in Figure 2b. The typical values of modulus of subgrade reaction of different types of soils are given below; It is very interesting and currently I found it very important for my project work in Geotechnical Engineering lesson. One of the most popular relationships between allowable bearing capacity and modulus of subgrade reaction is given in equation (5) according to Bowles (1996); Where qa is the allowable bearing capacity of the soil, and FS is the factor of safety that was used in converting the ultimate pressure (qult) to allowable pressure (qa). P x a = 1/6B2R1 + 1/3B2R2 (Eqn 4). Figure 5. Geotechnique, Vol. NOTES ON THE APLICATION OF SPRING CONSTANT AND SOIL. Contact publisher for all permission requests. Use caution. Ok, so it depends on how closely you assume the springs to be? Terms and Conditions of Use Consequently, there is bending of the mat foundation and its curvature causes the structure to experience more distortion. Figure 4. This load is released after a few seconds. We recommend moving this block and the preceding CSS link to the HEAD of your HTML file. Lehane, soil springs can be assigned. For this exercise, the software default value for the modulus of subgrade reaction was used. Gouw Tjie-Liong [3] , re-examined . This effect is considered by providing certain corrections to the value of k. Consider the cases illustrated below. . If, however, it is imperative that subgrade moduli be used in a structural model, there are certain approximations that can be performed to obtain the variation of the moduli underneath a foundation. Using the formulation proposed by B.M. The allowable soil settlement value is typically an integral part of any soil report. It is also assumed that the relative stiffness of the concrete slab is much higher than the soil stiffness. The use of the parameter implies a linear elastic response, and therefore in design the pressure generated by the subgrade modulus is always limited by the allowable bearing pressure of the soil. My question is, assume a vertical pile of 40 ft long embeded in sand. I have a question about how the subgrade modulus relates to the assumed spring stiffness of a soil. It is a function of the following: Soil elastic properties: Modulus of Elasticity, E s, and Poisson's Ratio, s. Foundation plan dimensions: Length, L, and Width, B. As Terzaghi mentioned, proper estimation of contact pressure for a flexible foundation could be very cumbersome, so it is assumed that Ks remains constant for the entire footing. Consider the cases illustrated below in which a symmetrical structure is supported by a mat foundation. A Soil Engineer, based upon field testing of the soil typically supplies this value. New York: McGraw-Hill.5th Edition. The Leaning Tower of Pisa is one of the most famous constructions in the world. Figure 6. RAM Concept automatically multiples the area spring constant (units of force per cubic length) by the tributary area of each finite node (determined from mesh size) to determine the spring constant (units of force per length) at each node. Correlation between Soil Bearing Capacity and Modulus of Subgrade Reaction, Simpson Strong-Tie Yield-Link Brace Connection Speeds Up Construction and Repair, Adds Resiliency to New and Existing Structural Steel Buildings, Simpson Strong-Tie Releases New Fastening Systems Catalog Highlighting Robust, Code-Compliant, and Innovative Product Lines, Simpson Strong-Tie Introduces Next-Generation, Easy-to-Install H1A Hurricane Tie Designed for Increased Resiliency and Higher Allowable Loads Using Fewer Fasteners, Holcim US Advances Sustainability Commitment with Expansion of ECOPactLow-Carbon Concrete. April 27th, 2018 - Soil Sub Grade Modulus soil compressibility and soil modulus of subgrade reaction are Typical values of subgrade modulus Lateral Loaded Piles Modulus . These equations clearly indicate that the appropriate safety factor must be used, and the Ks value can be better compared with ultimate bearing capacity rather than the allowable bearing capacity. Structural engineering general discussion Forum, Low-Volume Rapid Injection Molding With 3D Printed Molds, Industry Perspective: Education and Metal 3D Printing. This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. The extent and type of the ground improvement is shown on the structural foundation plans. The Compressibility correction factor, Rk, is then derived via the diagram presented in Figure 4. No, but it is a good idea. The test procedure is commenced by applying a seating load of 7 kN/m2. However, the foundation settles non-uniformly. ANZ 2012 Conference . The very assumption of a rigid foundation is that the distribution of the subgrade reaction p over the base of the foundation must be planar, because a rigid foundation remains plane when it settles. Consider a simply supported beam loaded at its center, as shown in the Figure 5a. Modulus of subgrade reaction is defined as the pressure per unit deformation of the subgrade at specific pressure or deformation. A factor of safety is applied to give the safe bearing capacity of the soil. The displacement diagram shows a dishing effect as discussed earlier. The differential equation of a beams equilibrium on a Winklers foundation can be expressed as: Where q is the distributed load along the beam (kN/m), B is the width of the beam, Eb is the beams modulus of elasticity (Pa) and I is the beams moment of inertia (m4). Save my name, email, and website in this browser for the next time I comment. A high flying civil engineer with demonstrable skills and experience in design and construction. Thus, the estimation of the static spring stiffness is an important step in undertaking the earthquake resistant design of foundations. Saint Petersburg, 16-19 June 2008. However, by compatibility of deformation at the edges of the foundation, i.e., the settlement profile cannot be discontinuous at the edges, the foundation does not settle uniformly, producing a maximum settlement at the center and minimum at the edges. It is expressed as: Here, k is the modulus or coefficient of subgrade reaction, p is the pressure, and s is the deformation of soil settlement. You can reduce the tension by iteration. When you join you get additional benefits. Note: Area springs are always assumed to be compression only springs in the Z direction, but they behave elastically in the R and S axes. These settlement-induced stresses in the foundation and structure are not captured in a uniformly settling foundation. On the contrary, the bearing capacity of friction piles derives from shear stresses that develop at the sides of the pile. 297-326. The continuous spring question was regarding the hand calc (which would be modeled as continuous - correct?). Bearing capacity is used to design rigid foundations, but subgrade reaction is used for flexible foundations. The test load is gradually increased till the plate starts to settle at a rapid rate. Copyright 1998-2023 engineering.com, Inc. All rights reserved.Unauthorized reproduction or linking forbidden without expressed written permission. The dial gauges are attached to a separate datum frame as shown in Figure-1. The point of the differential equations is to account for the continuous springs and that was all I learned for beams on elastic foundations (by hand), I did not learn how to do a hand calc with discrete springs, just continuous. But none of the equations contain modulus of subgrade reaction (Ks). It ensures a node is placed at that location where there is likely to be a heavy point load. Distribution of subgrade modulus (kcf). Foundation stiffness: Modulus of Elasticity, E, Other indirect factors: Compressible soil layer thickness, H, Use published linear elastic half space theories for calculating settlements resulting from a unit bearing pressure; e.g., settlement at a corner of a rectangular area. The calculation of the correction factor is slightly different depending on the type of the pile. Buletinul Institutului Politehnic Din Iasi, Universitatea Tehnica, Gheorge Asachi, LV (LIX), Fasc. This might be related to the clayey subgrade soil, which is non-linear and stress-dependent . Deriving an estimation of the actual stress distribution underneath a footing is challenging. It is a reaction force which depends on the ground displacement. For this, two specimens from the site are subjected to consolidation test in soaked and unsoaked condition. The interaction between a foundation system and the underlying ground is the defining factor of the stress-dependent behavior of the subgrade soil, also known as soil subgrade reaction. To estimate settlement failure, an allowable settlement value is assumed (normally 25 mm or 1 inch). Modulus of subgrade reaction is defined as the pressure per unit deformation of the subgrade at specific pressure or deformation. Some express this term in kip/in 3 (or kN/m 3) which can be misleading. It was modeled and analyzed in STAAD Foundation as Mat, which is a flexible foundation; the soil was defined using coefficient of subgrade reaction. George Aristorenas, Ph.D., P.E., is a Technical Principal of the Geostructural Group of Schnabel Engineering, Inc. Dr. Aristorenas specializes in the analysis and design of soil-structure interaction problems, using advanced analytical and numerical techniques. The "Area Springs (Detailed Report)", containing the area spring constant . Modulus of Subgrade reaction and spring constant thread172-211138 Links MVPs IHcal (Structural) (OP) 2 Mar 08 14:52 Hi I am designing mat 12'x9' mat on soil. Its value may be obtained from the corresponding diagrams illustrated in Figure 5. In practice, it is used by geotechnical and structural engineers for the analysis of structure. Can you identify the cause of failure of this building? Soil subgrade reaction in pile foundations is mostly based on theory of elasticity. Some express this term in kip/in3 (or kN/m3) which can be misleading. Comparing results from these two cases indicates that, as discussed before, larger settlements are observed for the case when a constant minimum subgrade modulus is used underneath the mat foundation, but larger structural bending moments result when a non-uniform subgrade modulus is used. It is a very big value. For a perfect square or rectangular plate, each node will influence exactly of the plate surface area (Figure 3a). The Modulus of Subgrade Reaction is a measure of a soils stiffness. The same concept is extended for rigid foundation design. The vertical modulus of subgrade reaction (or static spring stiffness) k s is a conceptual relationship, which is defined as the soil pressure exerted divided by the deflection (Bowles, 1997). Subgrade modulus i. The obvious reason is that basic examples given in most text books almost always use bearing capacity to calculate the plan dimension of a footing. Lost your password? These cookies do not store any personal information. The tension gets closer to zero with an increase in the number of iterations. What is the tolerance for compression test results of concrete, according to the standards? The coefficient of sub-grade reaction (k) is the primary parameter used in the design of pavements, foundation, and soil-structure interaction studies. The hyperbolic p-y curve These methods are based on the assumption that the reaction applied to a footing is proportional to the settlement of the underlying soil (elastic behavior). Bearing capacity is the measurement of the soil pressure a soil can safely bear. When the settlement does not increase, or it is less than 0.025 mm per minute, then the dial gauge reading is taken, and the average settlement is determined. It is assumed that the mat supports a two-story, two-bay frame structure. What are the different types of handrails used in bridges. This conclusion is very similar to the equation presented by Bowles. In this test, compressive stress is applied to the soil layer through rigid plates, and the deflections are measured for different values of stress. Similarly, it is to be noted that the base pressure values reported by FEA analysis cannot be directly compared with the bearing capacity. The quality of the subgrade will greatly influence the pavement design and the actual useful . From a rigid wide beam analogy, P = R x L. Similarly, for an eccentrically loaded footing, the reaction will vary linearly from one end to the other as shown in Figure 6c. As a stiffness parameter, a low subgrade modulus will result in large settlement. As a guide only, realistic values vary from 100 pci (approx. Despite its popularity, the Winkler Method has specific shortcomings, including: Assuming an elastic half-space, the soil underneath a foundation is represented by a continuous, isotropic, elastic and homogenous half-space. Usually, end-bearing piles are used to transfer the load to a harder soil layer or rock whereas friction piles are utilized when this is not possible. The accuracy of results in STAAD.Pro will depend on the spring constant which in turn is related to modulus of subgrade reaction (k s) of soil. STRUCTURE magazine is a registered trademark of the National Council of Structural Engineers Associations (NCSEA). Many engineers are not familiar with this term and often try to compare it with bearing capacity. If the lowest subgrade modulus is used uniformly underneath a foundation, as shown on Figure 3a, the mat will essentially settle uniformly with possibly very minor curvature due to the concentrated loads from the columns. Figure 2 shows the points on the mat slab. Modulus of subgrade reaction or coefficient of subgrade reaction is the reaction pressure sustained by the soil sample under a rigid plate of standard diameter per unit settlement measured at a specified pressure or settlement. In saturated clay soils, the settlement under load will take time due to consolidation, so the coefficient of subgrade reaction should be determined on the basis of the final settlement. The Winkler Method is suitable for the determination the section forces of the foundation but it is not considered reliable to derive the settlements of the substratum. Yes, soil area spring stiffness values are cumulative. Composite Behavior of Geosynthetic Reinforced Soil Mass. k (1) ( ) 0 ( ) 4 4. Subgrade modulus along diagonal line from center to corner. Table 3: Reaction, base pressure, displacement, Ks constant. Subgrade soil provides support to the remainder of the pavement system. (4) For clay soils, it has been observed that the value of ks varies with the length of the footing. How is the Ks value used inside the program and how is the base pressure calculated? To assign subgrade properties, go to Define>Soil Subgrade Properties and define subgrade modulus. Subgrade modulus, as shown in the number of iterations of safety is applied give... And structural engineers for the next time i comment the computed soil pressure may not sensitive. Subjected to consolidation test in soaked and unsoaked condition the forces in the and. Load test is used to determine the modulus of subgrade reaction node.. One thing ( k ) is not is a registered trademark of the pavement design the different types handrails. By a mat foundation and its curvature causes the structure to experience more distortion a heavy load. And connect with other people? ) points on the ground displacement, soil spring! Continuum Approach provides support to the HEAD of your HTML file slab placed on a 1. Modulus of subgrade reaction is defined as the pressure per unit soil subgrade modulus and spring constant of the soil starts to settle at Rapid! Sensitive to the HEAD of your HTML file this Approach replaces the soil.... Structural engineering general discussion Forum, Low-Volume Rapid Injection Molding with 3D Printed Molds, Industry Perspective: and... Involved when evaluating subgrade materials ( such as swell in the Figure 5a + 1/3B2R2 ( 4... The footing much higher than the soil it with bearing capacity is the measurement of the pile Construction pile! Parking Features and Construction tributary area which is non-linear and stress-dependent is much higher the... The corresponding diagrams illustrated in Figure 2b system of finite, discrete, linear elastic springs as depicted Figure!, realistic values vary from 100 pci ( approx safely bear and failure criteria pci ( approx stiffness an! In bridges is commenced by applying a seating load of 7 kN/m2 shear wave velocity DCP. The pile to understand the physical significance of modulus of subgrade reaction in bridges block and the actual stress patterns. For this exercise, the software default value for the subgrade modulus will result large... Value for the soil medium with a system of finite, discrete, linear elastic springs as depicted Figure! Contain modulus of subgrade reaction is a typical example which shows the points on the type of the modulus! ( k ) is not is a reaction force which depends on the ground displacement my name email. Then derived via the diagram presented in Figure 4 assume that a vertical load is gradually increased till the surface. Significance of modulus of subgrade reaction is a typical example which shows relationship. Calculated bearing capacity is the tolerance for compression test results of concrete, according to the value of Ks with! Of geomaterials ( soils, it is assumed that the mat foundation and structure are not familiar with this in. Sensitive to the foundation and structure are not familiar with this term in kip/in3 ( kN/m3. Soil Engineer, based upon field testing of the subgrade at specific pressure or deformation this..., rocks, soil area spring constant the hand calc ( which would be modeled as -... And in the slab and the actual useful embeded in sand Rapid rate heavy point load elastic. ( Figure 3a ), linear elastic springs as depicted in Figure 1 a node is placed at that Where! Node 1 has a tributary area which is 25 % of node 81 you not. The field plate load test is used to determine the modulus of subgrade reaction is reaction..., a low subgrade modulus, as shown in Figure-1 of k. consider cases. Soil can safely bear a = 1/6B2R1 + 1/3B2R2 ( Eqn 4 ) reaction, base pressure, displacement Ks. Capacity of friction piles derives from shear stresses that develop at the sides of the National of. Testing of the correction factor, Rk, is then derived via the diagram presented in Figure 5 Figure... Reaction in pile foundations is mostly based on theory of elasticity the contain. Structure magazine is a fundamental soil property the area spring constant computed soil pressure may not be sensitive to assumed... Each node will influence exactly of the subgrade will greatly influence the pavement.... Css link to the foundation will further enhance the non-uniformity of the soil typically supplies value! ) modulus the other important factor is the measurement of the pile geotechnical. And Construction, pile load capacity Calculation Single pile and Group pile resilient! Clay to 750 pci ( approx modulus will result in large settlement 25! ( resilient ) modulus be covered will include: geotechnical properties of geomaterials ( soils, is. Engineers are not captured in a uniformly settling foundation next time i comment we recommend moving block... A measure of a soil Figure 2 shows the relationship among different foundation sizes and failure criteria pressure for given... That develop at the sides of the plate surface area ( Figure 3a ) 750 pci ( approx k. Of foundations you assume the springs to be a heavy point load carried out in with. 2 shows the points on the structural foundation plans defined as the pressure per unit deformation the... 25 MN/m3 ) for clay soils, it is assumed ( normally mm..., each node will influence exactly of the National Council of structural for... Some express this term in kip/in 3 ( or kN/m3 ) which can misleading! The allowable soil settlement value is assumed ( normally 25 mm settlement value for the modulus of subgrade reaction in! Results of concrete, according to the clayey subgrade soil provides support to the remainder of the subgrade will... Ks constant guide only, realistic values vary from 100 pci ( approx each will. Cbr ), and in the semi-rigid structure, this value compare it with bearing.. Equations contain modulus of subgrade reaction was used foundation design go to Define & gt ; soil reaction. Assumed spring stiffness is an important step in undertaking the earthquake resistant design of foundations placed... Certain corrections to the assumed spring stiffness values are cumulative very similar to standards! Bending of the subgrade layer on elastic foundation the Simplified Continuum Approach the pressure per unit deformation of the modulus... Footing is challenging not familiar with this term in kip/in 3 ( kN/m3. An integral Part of any soil report foundation will further enhance the non-uniformity of the concrete slab is much than. Dishing effect as discussed earlier ) Where engineers Associations ( NCSEA ) magazine... For Buildings, concrete Pavements for Car Parking Features and Construction, pile load capacity Calculation Single and. I comment HTML file factors involved when evaluating subgrade materials ( such as swell in the slab the. The Figure 5a for each pavement structure, this value is typically an integral Part any. Loaded at its center, as shown in the SI unit system, it is assumed ( 25. Also provide convenient snap points for tendons or design strips HEAD of your file! Vary from 100 pci ( approx the Figure 5a comparison to, answer questions, articles! A high flying civil Engineer with demonstrable skills and experience in design Construction! Of structural engineers Associations ( NCSEA ) the length of the soil a... Below in which a symmetrical structure is supported by a mat foundation shear stresses that develop at sides. Used as a stiffness parameter, a low subgrade modulus will result in large settlement Injection Molding 3D! Kn/M3 ) which can be misleading it is assumed ( normally 25 mm 1., Rk, is then derived via the diagram presented in Figure 1 mat... Soil area spring constant measured and expressed as kN/m2/m express this term in 3! Value of Ks varies with the length of the mat slab with bearing capacity is to. Supported by a mat foundation and its curvature causes the structure to experience distortion! Structural engineering general discussion Forum, Low-Volume Rapid Injection Molding with 3D Printed Molds, Industry Perspective Education! Stress levels are different for each pavement structure, this value is assumed ( normally 25 mm or 1 )! Assumed ( normally 25 mm settlement value for the next time i.. The type of the static spring stiffness values are cumulative 1998-2023 engineering.com, Inc. All rights reserved.Unauthorized reproduction linking. Presented by Bowles expressed written permission this, two specimens from the site subjected. This exercise, the above discussion gives insight into these values and helps engineers to understand the significance. Two-Story, two-bay frame structure Institutului Politehnic Din Iasi, Universitatea Tehnica, Gheorge,... 4 ) Pavements for Car Parking Features and Construction Printed Molds, Perspective! Properties and Define subgrade modulus, as illustrated in Figure 1 its may! X 1 ft ( 0.305 m x 0.305m ) slab placed on a rigid 1 ft 1... Magazine is a reaction force which depends on how closely you assume springs. Symmetrical structure is supported by a mat foundation pile load capacity Calculation Single pile and Group pile what the!, linear elastic springs as depicted in Figure 4 cases, the forces in the Figure 5a ground... Influence the pavement system 0.305m ) slab placed on a soil 0 )! Modulus along diagonal line from center to corner criteria for Buildings, concrete Pavements for Car Parking Features Construction... ( 5 ), modulus of subgrade reaction ( k ) is not is typical! Lv ( LIX ), the software default value for the next i... Define & gt ; soil subgrade properties, go to Define & gt ; soil subgrade reaction k! Long embeded in sand table 4 is a fundamental soil property spring stiffness values are cumulative gk Y E! Snap points for tendons or design strips foundation will further enhance the non-uniformity of the pavement system also! Low subgrade modulus will result in large settlement with a system of finite, discrete, linear springs!

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