For this reason, it is very important to understand the principles on which stress determinations are based, and how to make fundamental stress calculations. To account for the stress dependent behavior of soils and their increased. In 1936 professor westergaard was appointed to the gordon. Nov 22, 2016 vertical stress in soil stress below a line load the vertical stress increase due to line load, inside the soil mass can be determined by using the principles of the theory of elasticity, or 2 v p this equation can be rewritten as 2 v 1 p 1p p 53dr. We will limit ourselves to mode i, and the summary of the procedure given below is taken from the book by gdoutos 2010. Stress distribution in soil media boussinesque formula stress due to line load and circular and rectangular loaded area approximate methods use of influence charts westergaard equation for point load components of settlement immediate and.
The single stress functions approach of westergaard has often been conveniently used for a certain class of stress prescribed crack problems. Tm 580912 concrete floor slabs on grade subjected to. Pdf application of bousinesqs and westergaards formulae. In the previous study, the westergaard approach was successfully extended to displacementprescribed crack problems.
The westergaard equations 1938 are thought to provide better results for layered media, however the solution essentially smears out the effect of the different layers so. It is a common observation that the theory of elasticity is. The effect of the westergaard assumption is to reduce the stresses substantially below those obtained by. Analysis of rigid pavement stresses by finite element method. Analysis of slabsongrade for a variety of loading and. We will limit ourselves to mode i, and the summary of the procedure given. The stress distribution pattern revealed that the soil strength was lower than the imposed loadings from the structure thereby resulting in. Westergaards theory is considered good to design the rigid pavements. The boussinesq stress distribution theory is very extensively used in the determination of the distributions of. Use of linearelastic layered theory for the design of crcp overlays b. Westergaard stress functions for several periodic crack.
Earth pressure theories and problems on earth pressure on retaining wall. Application of bousinesqs and westergaards formulae in analysing foundation stress distribution for a failed telecommunication mast article pdf available july 2012 with 2,585 reads. Vertical stress in soil stress below a line load the vertical stress increase due to line load, inside the soil mass can be determined by using the principles of the theory of elasticity, or 2 v p this equation can be rewritten as 2 v 1 p 1p p 53dr. This insitu stress, also known as overburden stress see section 2. The single stress function approach of westergaard has been effective for a certain class of stressprescribed crack problems. In such materials, the stress distribution obtained from the boussinesq solution was incorrect. Analysis of rigid pavement stresses by finite element.
Pdf application of bousinesqs and westergaards formulae in. I took the first example calculation in appendix 1 of aci 360 pca method 22. He worked as an adviser to the us states bureau of reclamation during the building of the hoover dam and also published a muchquoted paper on this westergaard, 1933. In 1948 westergaard presented an equation for the stress under an elliptical loaded area equation 3 in new formulas for stresses in concrete pavements of airfields 10 i. For further information see the settle3 theory manual.
Use of linearelastic layered theory for the design of. In this step, treat the reinforced soil below the footing as a stiff soil with a large 229friction angle and check the bearing capacity of this layer. The pressure transmitted through grain to grain at the contact points through a soil mass is termed as intergranular or effective pressure. So in order to ensure the stabilization of unstable soil sample sawdust is added as a stabilizer in increasing proportions and the stress response in the. First, westergaards solution applies directly to cracks, not to an ellipse that approaches a crack in the limit. Boussinesq equations, stress isobar and pressure bulb concept, pressure distribution on horizontal and vertical planes, stresses due to point load, line load, strip load, uniformly loaded circular and rectangular areas. In this step, treat the reinforced soil below the footing as a stiff soil with a large 229friction angle. Second, the solution is expressed in rectangular coordinates rather than elliptical coordinates. The single stress function approach of westergaard has been effective for a certain class of stress prescribed crack problems. Boussinesq 1985 evolved equations that can be used to determine stresses at any point p at a depth z as a result of a surface point load. First, westergaard s solution applies directly to cracks, not to an ellipse that approaches a crack in the limit. It is a common observation that the theory of elasticity. Effective stress concept as in other materials, stresses may act in soils as a result of an external load and the volumetric weight of the material itself. Stress condition at a point in a soil mass stress conditions in soil during triaxial compression test relationship between.
Infinitely loaded area point load concentrated load circular loaded area though the surface loading is caused to increase both vertical and horizontal stresses in soils, only the vertical stress increase is discussed. Stress in concrete pavements computed by theoretical analysis, 19261. At any point in soil the stress applied from own weight of soil which called effective stress, and from external load which called net stress, the net stress which applied must be determined. The stress distribution pattern revealed that the soil strength was lower than the imposed loadings from the structure thereby resulting in differential settlements. As ell or all increase, finite element stresses become progressively higher than westergaard s. Soil mechanics and foundation engineering mcq test set. Unit 3 stress distribution copressibility and settlement. Stress distribution at predetermined depths based on the bousinesqs and westergaard s formulae. Similarly, the insitu stress in a soil mass is a function of depth and the weights of the different soil elements within that depth. Hankel transformation method for solving the westergaard. For soil layers with high stiffness contrasts, the boussinesq solution can produce large errors in stress. Methods have been developed to estimate the vertical stress increment in subsoil considering the shape of the surface loading area. Determine the vertical stress distribution in the foundation soil using the westergaard elastic layer theory.
Boedecker, united states steel corporation the design of overlay pavements for upgrading existing pave. Westergaard complex stress functions 16 i main topics a historical perspective b expression of the biharmonic function by harmonic functions c boundary conditions d use of symmetry and boundary conditions to simplify the stress function e general solution for stresses and displacements in terms of a single complex stress function. Westergaards theory for rigid pavements civil engineering. Stress distribution in soils gate boussinesq equation soil mechanics boussinesq theory in soil mechanics westergaard theory soil. Application of bousinesqs and westergaards formulae in. In this paper, the approach was further extended to the combined problem of displacementprescribed cracks and stress prescribed cracks. Comparative analysis of rigid pavement using westergaard. Westergaard presented solutions for the stress fields for such. Boussinesq equations, stress isobar and pressure bulb concept, pressure distribution on. Bina nusantara westergaard s theory of stress distribution assumptions. Stress distribution at predetermined depths based on the bousinesqs and westergaards formulae. Use of linearelastic layered theory for the design of crcp. It introduces new sections on vertical stress due to a line load of finite length, vertical stress in westergaard material due to point load, line load of finite length, circularly loaded area, and rectangularly loaded area.
About geotechnical engineering principles and practices of soil mechanics. The stresses in the concrete slab are determined using westergaards theory. Stress distribution in soils gate 2019 civil boussinesq. Comparison of illislab and westergaard corner deflections 171. Sep 10, 20 westergaard s theory is considered good to design the rigid pavements. Westergaard complex stress functions 16 i main topics a. Westergaard developed a solution for the stress field surrounding a crack that has two advantages over ingliss solution 2. Westergaard worked as technical expert to the bureau of reclamation on the design of hoover dam.
Pdf geotechnical engineering principles and practices of. Hankel transformation method for solving the westergaard problem for point, line and distributed loads on elastic halfspace. Westergaard stress functions for displacementprescribed. Pdf an approximation to the stress distribution analysis. Stress solution at crack tip westergaard 1934 general stress solution the procedure for computing the stress state near a crack tip was established by westergaard 1934. The westergaard stress solution implicitly assumes a layered soil structure, and includes poissons ratio.
W westergaard stress coefficient i w westergaard vertical stress n point load from the end bearing pile z vertical distance from the end point of pile r radial distance from z murthy, 1992. Stress distribution in soils due to surface loads 175 that ib has a maximum value of 0. Application of bousinesqs and westergaard s formulae in analysing foundation stress distribution for a failed telecommunication mast article pdf available july 2012 with 2,585 reads. So, here the upward reaction is assumed to be proportional to the deflection, i. Except for occasional happy coincidences, soil settlement computations are only best estimates of the deformation to expect when a load is applied. During settlement the soil transitions from the current body or selfweight stress state to a new one under the additional applied load. Stresses when flow takes place through the soil from top to bottom stresses when flow takes place through the soil from bottom to top effective pressure due to capillary water rise in soil problems stress distribution in soils due to surface loads introduction boussinesqs formula for point loads westergaards formula for point loads line loads.
Hydro pole, light stand, column, etc lines loads rack or rail loading, strip foundation rectangular area raft or rectangular footing circular area tank earth embankment road, railway, fill, ice, etc. In this paper, the approach was further extended to the combined problem of displacementprescribed cracks and stressprescribed. Advanced soil mechanics 4th edition pdf free download direct. Civil engineering app fadum soil stress increment apps. Sm2 lec 3 soil stresses elasticity physics contour line. Stresses in a soil mass slide 4 of 23 vertical stress increase in soils analysis methods westergaard vertical stress increase in soils analysis methods 2v. He considered rigid pavement slab as a thin elastic plate resting on soil subgrade, which is assumed to be a dense liquid.
The calculation of subsurface stress increase due to the following surface loading conditions will be discussed. Boussinesqs equation geotechnical engineering civil. Westergaards solution for cracks fracture mechanics. Pdf geotechnical engineering principles and practices. An approximation to the stress distribution analysis for anisotropic clayey soil article pdf available in scientific research and essays 42. Stresses in soil, boussinesqs theory, westergaards theory. In the present study, the westergaard approach was successfully extended to displacementprescribed crack problems. The effect of the westergaard assumption is to reduce the stresses substantially below those obtained by the boussinesq equations. The westergaard analysis is applicable to soil profiles consisting. Determine the bearing capacity of the reinforced soil foundation.
In this civil engineering app students and geotechnical engineering professionals can determine stresses under the corner of a uniformly loaded rectangular area. The single stress functions approach of westergaard has often been conveniently used for a certain class of stressprescribed crack problems. Soil engineering properties and behavior are strongly influenced by stresses and stress history. Hankel transformation method for solving the westergaard problem. It summarizes soil compaction procedures and proctor compaction tests. Sm2 lec 3 soil stresses free download as powerpoint presentation. Vertical stress in a soil mass forces that increase vertical stress in soil mass weight of soil effective stress surface loads fill large area point loads. In this brief note the expressions of zc, together with z t, z d, which are necessary to calculate the displacements, and k, the crack tip stress intensity factors, are given in closed form. The assumption is likely to be most accurate in the soil directly beneath the center of the surface load, which is the zone of most interest in settlement analyses. The pavement must also be plotted to limit the expansion and loss of density of the subgrade soil 5. Arora 2003 has reported that the westergaards analysis is used for design of rigid pavements.