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    <title>Transport Research International Documentation (TRID)</title>
    <link>https://trid.trb.org/</link>
    <atom:link href="https://trid.trb.org/Record/RSS?s=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" rel="self" type="application/rss+xml" />
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
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    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Transport Research International Documentation (TRID)</title>
      <url>https://trid.trb.org/Images/PageHeader-wTitle.jpg</url>
      <link>https://trid.trb.org/</link>
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    <item>
      <title>ELASTIC SUBSURFACE STRESS ANALYSIS FOR CIRCULAR FOUNDATIONS. I</title>
      <link>https://trid.trb.org/View/486070</link>
      <description><![CDATA[In part I of this analysis, an attempt is made to determine a simple estimate of the stresses resulting from a circular foundation subjected to concentric or eccentric loading.  It is assumed that the foundation loading can be modeled as combinations of uniform, linear, quadratic tractions applied over a circular area on the surface of an elastic half space.  The analysis for quadratic and linear loading are combined with a uniform loading solution (normal or shear traction), previously derived by the authors, to provide the requisite loading conditions and resulting internal stress fields.  The current analysis consists of using potential functions to derive closed form expressions for the elastic field in the half space. The half space is taken as cross-anisotropic (transversely isotropic), where the planes of isotropy are parallel to the free surface.  The x- and y-axes are taken in the plane of the surface with z directed into the half space.  Hence, the boundary conditions within the circular loaded area are on the shear stress components and normal stress.  The solutions presented actually comprise seven different boundary value problems for the transversely isotropic half space.  The analytical solutions for a point normal or shear force are first used to write the solution for distributed loading over a circle in the form of a double integral over the loaded area.  It is shown, with the aid of Hankel transform analysis, that the integrals appearing in the elastic field have been previously evaluated in terms of complete elliptic integrals.  The necessary integral evaluations are provided in Appendix I.  The limiting form of the expressions for an isotropic material are also included.]]></description>
      <pubDate>Fri, 29 May 1998 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/486070</guid>
    </item>
    <item>
      <title>ELASTIC SUBSURFACE STRESS ANALYSIS FOR CIRCULAR FOUNDATIONS. II</title>
      <link>https://trid.trb.org/View/486071</link>
      <description><![CDATA[In part I of this analysis, analytical expressions were derived for the elastic fields in a cross-anisotropic and isotropic half space with various loadings applied over a circular area on the surface.  Two special cases are analyzed in part II. Consideration is first given to derive the analytical expressions for the elastic field along the z-axis perpendicular to the surface.  Then the elastic field at the surface z=0 is found. Finally, numerical results reveal the effect of concentric and eccentric loading on the vertical soil pressure and the maximum shear stress below the surface.  It is found that the nature of the quadratic loading significantly effects the magnitude and distribution of the maximum shear stress.  It is also shown that some types of cross-anisotropy may also give significantly different results than those for isotropic materials.]]></description>
      <pubDate>Fri, 29 May 1998 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/486071</guid>
    </item>
    <item>
      <title>EIGENPROPERTIES OF MASSIVE RIGID BODY ON ELASTIC HALF-SPACE. TECHNICAL NOTE</title>
      <link>https://trid.trb.org/View/464391</link>
      <description><![CDATA[The author of this technical note investigates the eigenvalues and eigenvectors of a massive rigid square block bonded to an elastic medium.  Uncoupled vertical and coupled sliding-rocking modes of vibration are pondered.  The supporting medium is represented as an elastic homogeneous or layered, inertial or massless half-space.  The eigenvalues are complex-valued in a geometrically damped system and they are purely imaginary in an undamped system.  Numerical results show the effects of inertial interaction.  The data are computed via a technique that considers the mixed boundary conditions at the surface of the half-space.]]></description>
      <pubDate>Sun, 22 Sep 1996 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/464391</guid>
    </item>
    <item>
      <title>THE INFLUENCE OF SUPPORT CONDITIONS ON THE BEHAVIOR OF ELASTIC PLATES</title>
      <link>https://trid.trb.org/View/99339</link>
      <description><![CDATA[THE PURPOSE OF THIS RESEARCH IS TO STUDY THE INFLUENCE OF TYPES OF SUPPORT ON THE BEHAVIOR OF FLEXIBLE PAVEMENT SURFACE LAYERS. THE REPORT PRESENTS THE DEVELOPMENT OF COMPUTER SUBPROGRAMS FOR EVALUATING THE INFINITE INTEGRALS WHICH OCCUR IN TWO PAVEMENT SYSTEM MODELS. THESE ARE A THIN PLATE OF INFINITE EXTENT SYMMETRICALLY LOADED WITH UNIFORM CIRCULAR PRESSURE DISTRIBUTION OVER /1/ A WINKLER FOUNDATION AND /2/ AN ELASTIC HALF SPACE. THE DEFLECTION OF THE PLATE, FOR THE ELASTIC HALF SPACE, AT ANY DISTANCE FROM THE LOAD CENTER IS OBTAINED FROM TABLES OR GRAPHS OF VALUES OF INFINITE INTEGRALS CALLED DEFLECTION COEFFICIENTS. THE COEFFICIENTS WERE OBTAINED BY APPROXIMATING THE INFINITE INTEGRALS NUMERICALLY AND EVALUATING THEM ON A DIGITAL COMPUTER USING FORTRAN LANGUAGE . THE INTEGRAL IS EXPRESSED IN TERMS OF PLATE AND HALF SPACE MODULI, PLATE THICKNESS, RADIUS OF APPLIED LOAD AND DISTANCE FROM THE LOAD CENTER TO THE POINT OF DEFLECTION. THE FIRST AND SECOND DERIVATIVES OF THE DEFLECTION ARE OBTAINED IN ORDER TO DETERMINE THE RADIAL AND TANGENTIAL BENDING MOMENTS IN THE PLATE. THE DERIVATIVES WHICH ALSO CONTAIN INFINITE INTEGRALS WERE EVALUATED ON THE COMPUTER. THE THIRD DERIVATIVE IS LIKEWISE OBTAINED TO DETERMINE THE TRANSVERSE SHEAR FORCE. THE INFINITE INTEGRAL FOR REACTIVE PRESSURE WAS OBTAINED INDIRECTLY FROM THE ORIGINAL DIFFERENTIAL EQUATION GIVEN BY HOLL INSTEAD OF OBTAINING THE FOURTH DERIVATIVE. THE INTEGRAL WAS ALSO APPROXIMATED NUMERICALLY AND EVALUATED ON THE COMPUTER. COMPUTER PROGRAMS AND TABLES FOR DEFLECTION AND MOMENT ARE ALSO GIVEN FOR THE WINKLER CASE. THE INTEGRAL EQUATION FOR THE WINKLER CASE IS JUST A SIMPLIFICATION OF THE ELASTIC HALF SPACE CASE BECAUSE OF THE DIRECT PROPORTIONALITY BETWEEN DEFLECTION AND SUBGRADE REACTION. COMPARISON OF WINKLER AND HALF SPACE COEFFICIENTS WERE MADE' /A/ WINKLER DEFLECTION IS LESS THAN HALF SPACE, /B/ REACTIVE PRESSURES AGREE OUTSIDE RELATIVELY LARGE LOADED AREAS AND DISAGREE BENEATH SMALL LOADED AREAS, /C/ MOMENTS AGREE WELL UNDER ALL LOADING CONDITIONS IMPLYING THAT BOTH SYSTEMS ARE EQUIVALENT AND THAT MOMENT IS INDEPENDENT OF THE SYSTEM USED FOR SIMILAR RELATIVE STIFFNESS RATIOS. /BPR/]]></description>
      <pubDate>Sat, 01 Oct 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/99339</guid>
    </item>
    <item>
      <title>THE AXISYMMETRIC DEFORMATION OF A HOMOGENEOUS, CROSS- ANISOTROPIC ELASTIC HALF SPACE</title>
      <link>https://trid.trb.org/View/127212</link>
      <description><![CDATA[THE SOURCES OF ANISOTROPY IN THE STRUCTURE OF SOILS ARE TRACED AND IT IS SUGGESTED THAT MANY PRACTICAL SOLUTIONS FROM THE HOMOGENEOUS CROSS-ANISOTROPIC ELASTIC HALF SPACE CAN BE USED TO PREDICT THE EFFECT OF THE STRUCTURE OF AN EARTH MASS ON ITS RESPONSE TO LOADING. BASED ON PREVIOUSLY DEVELOPED METHODS, SOLUTIONS ARE PRODUCED FOR THE AXISYMMETRIC DEFORMATION OF A HOMOGENEOUS, CROSS-ANISOTROPIC ELASTIC HALF SPACE ACTED UPON BY THE FOLLOWING LOADING CONDITIONS: (1) UNIFORM VERTICAL PRESSURE, (2) UNIFORM VERTICAL DISPLACEMENT, (3) LINEARLY INCREASING RADIAL SHEAR STRESS, (4) LINEARLY INCREASING TORSIONAL SHEAR STRESS, AND (5) LINEARLY INCREASING TORSIONAL SHEAR DISPLACEMENT. IN ALL CASES, THE LOADED AREAS ARE CIRCULAR IN SHAPE AND THE SOLUTIONS INDICATE THE VARIATION OF ALL DISPLACEMENT, STRAIN, AND STRESS COMPONENTS THROUGHOUT THE HALF SPACE. /AUTHOR/]]></description>
      <pubDate>Sun, 28 Aug 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/127212</guid>
    </item>
    <item>
      <title>STRESSES INDUCED BY SURFICIAL AND DEEP LOADING IN ELASTIC MEDIUM</title>
      <link>https://trid.trb.org/View/366685</link>
      <description><![CDATA[In this study, expressions are derived to compute vertical normal stress at any point within an elastic half-space for two loading conditions: surficial polygonal surface with linearly distributed loading; and deep polygonal surface uniformly loaded.  Equations are presented which are useful in many practical soil mechanics calculations.  They can be included in stress estimation computer programs with significant savings of computing time and improvement of accuracy.]]></description>
      <pubDate>Sat, 21 Aug 1993 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/366685</guid>
    </item>
    <item>
      <title>NONDESTRUCTIVE TESTING WITH FALLING WEIGHT DEFLECTOMETER ON WHOLE AND BROKEN ASPHALT CONCRETE PAVEMENTS</title>
      <link>https://trid.trb.org/View/371685</link>
      <description><![CDATA[Extensive testing of flexible pavements with the falling weight deflectometer on various test sites in Ontario has aided the development of a rational method of deflection basin interpretation.  The goal is a fast computer program (PROBE) that calculates important mechanistic response parameters and determines the quality of data and the degree of structural integrity of the pavement layers.  Using the theory of Boussinesq and Odemark's method of equivalent layer thickness, two quantities are defined to help interpret deflection bowl data:  (a) the effective modulus of measured surface deflection and (b) the effective modulus of subgrade deflection.  Both moduli change with their radial distance from the test load. When plotted they may briefly be referred to as the surface modulus profile and the subgrade modulus profile, respectively. Both moduli provide apparent values of elastic stiffnesses, using uniform elastic half-space solutions.  They are parameters for a systematic study of the difference between the theoretically expected and the observed behavior of asphalt concrete pavements.  The surface modulus profile evaluates the quality and integrity of pavement layers.  Both the surface and subgrade modulus profile are used to estimate the subgrade modulus near the test load, which is the base for further calculation of primary response parameters by the Odemark method.  Examples are presented, ranging from very good to poor and broken conditions.  Computer simulations with various programs suggest two major points:  (a) dynamic effects have only a comparatively minor influence, so that elastostatic modeling appears to be feasible, and (b) deflections die away faster than expected with radial distance, probably because of an increase in the subgrade modulus with depth, an unrecorded presence of a bedrock face, or--more likely--discontinuities of unbound or cracked layer materials.  In short the new approach tries to obtain information and interpretations on system features of field cases by systematically studying the deviation from simple elastostatic modeling.]]></description>
      <pubDate>Mon, 05 Apr 1993 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/371685</guid>
    </item>
    <item>
      <title>ANALYSIS OF VOIDED THICK PLATES ON AN ELASTIC HALF-SPACE FOUNDATION</title>
      <link>https://trid.trb.org/View/360063</link>
      <description><![CDATA[The loading stresses in voided thick plates on an elastic half-space foundation are analysed in this paper by using the finite prism method.  The elastic half-space foundation is divided into sliding clamped prism elements.  The interface of plate and foundation is assumed smooth and rigid.  A program for calculating voided thick plates has been developed.  The results calculated with this program agree quite well with those obtained from tests.  This method requires smaller amount of storage and shorter computing time than the three-dimensional finite element method.  (TRRL)]]></description>
      <pubDate>Sat, 30 Nov 1991 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/360063</guid>
    </item>
    <item>
      <title>LOAD-TRANSFER PROBLEMS FOR TRANSVERSELY ISOTROPIC ELASTIC MEDIA</title>
      <link>https://trid.trb.org/View/349038</link>
      <description><![CDATA[This paper presents a coupled variational boundary integral equation scheme to analyze the load transfer from a cylindrical elastic bar into a transversely isotropic elastic half-space.  The displacement compatibility between the bar and the half-space is satisfied at nodal locations defined along the real contact surface.  In all cases, as the bar becomes rigid, the method yields a solution for the exact boundary value problem corresponding to the surrounding half-space.  The details of the study are described and the results are discussed.]]></description>
      <pubDate>Mon, 31 Dec 1990 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/349038</guid>
    </item>
    <item>
      <title>ROCKING COMPLIANCE FUNCTIONS FOR RIGID BASES ALLOWED TO UPLIFT</title>
      <link>https://trid.trb.org/View/308230</link>
      <description><![CDATA[A study is reported in which a static gravitational force and a static or dynamic overturning moment are applied to a rigid base on an elastic half-space, and an interative procedure is used to analyze the rocking response of the base with partial uplift.  In the two-step study, the relationship between soil surface displacements and the surface tractions that the rigid base exerts on the soil (interaction forces) is derived from a boundary element analysis in the frequency domain.  In the second step, displacements and tractions are modified in the time domain so that the boundary conditions are satisfied at the interface between the base and the soil.  It was found that, in general, uplift leads to a softer vibrating system that behaves nonlinearly, i.e., rocking compliance increases with increasing values of the rotational moment.  These and other study findings are presented and discussed.]]></description>
      <pubDate>Thu, 31 May 1990 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/308230</guid>
    </item>
    <item>
      <title>DISPLACEMENTS OF FOOTINGS ON SAND UNDER ECCENTRIC AND INCLINED LOADS</title>
      <link>https://trid.trb.org/View/283355</link>
      <description><![CDATA[Results of an investigation of the response of footings on sand, under eccentric and inclined loads, are presented. Apparatus was constructed that could simultaneously apply loads to footings at any accentricity and inclination, without imposing restraints on the footing displacements. Th experimental results are interpreted, compared with published data, and a method for predicting vertical and horizontal displacements and rotations of loaded footings on sand developed.  At low load levels the analysis generates the elastic half-space solution, which is then augmented to provide the complete nonlinear response of the footing.  In addition, interaction diagrams between the verical loads, horizontal loads, and moments that cause failure of the footing are presented.]]></description>
      <pubDate>Wed, 31 Aug 1988 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/283355</guid>
    </item>
    <item>
      <title>ANALYSIS OF PUMPING A COMPRESSIBLE PORE FLUID FROM A SATURATED ELASTIC HALF SPACE</title>
      <link>https://trid.trb.org/View/283111</link>
      <description><![CDATA[A solution method is presented for the consolidation of a saturated, porous elastic half space due to the pumping of a pore fluid at a constant rate from a point sink embedded beneath the surface.  It is assumed that the saturated medium is homogeneous and isotropic with respect to both its elastic and flow properties.  The soil skeleton is modelled as an isotropic, linear elastic solid obeying Hooke's law while the pore fluid is assumed to be compressible with its flow governed by Darcy's law.  The solution has been evaluated for a soil with a value of Poisson's ratio of 0.25 and for a number of different cases of pore fluid compressibility.  It is demonstrated that this compressibility can have a significant influence on the rate of consolidation around the sink.  The solutions presented may have application in practical problems such as the extraction of groundwater and other fluids from compressible geological media.  (Author/TRRL)]]></description>
      <pubDate>Sun, 31 Jul 1988 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/283111</guid>
    </item>
    <item>
      <title>TORSIONAL STIFFNESS OF NON-UNIFORM AND HOLLOW RIGID PIERS EMBEDDED IN ISOTROPIC ELASTIC MEDIA</title>
      <link>https://trid.trb.org/View/281818</link>
      <description><![CDATA[This paper examines the torsional response of a rigid pier type foundation, with a non-uniform or hollow cross-section which is embedded in bonded contact with a layered elastic half space.  The tractions which act at the axisymmetric boundary surface between the pier and the surrounding elastic medium are represented by discretized regions of uniform traction.  The compatibility of deformation at the boundary is used to determine the interface stress distribution.  The torque-rotation response for the rigid pier foundation is obtained for different choices of the pier geometry and shear modulus mismatch between the layer and the underlying half space.  (Author/TRRL)]]></description>
      <pubDate>Thu, 31 Mar 1988 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/281818</guid>
    </item>
    <item>
      <title>THE BEHAVIOUR OF AN ELASTIC NON-HOMOGENEOUS HALF SPACE. PART 1 - LINE AND POINT LOADS</title>
      <link>https://trid.trb.org/View/191608</link>
      <description><![CDATA[In the first part of this paper solutions are developed for the response of a non-homogeneous half-space subjected to either a surface point load or a surface line load.  The non-homogeneity considered is a variation in Young's modulus (e) with depth (z) which takes the form e = m(sub E) z alpha where m(sub e) is a constant and alpha is referred to as the non-homogeneity parameter.  The variation of these solutions as the non-homogeneity parameter alpha varies between the limits of zero (homogeneous soil) to unity (Gibson soil) gives some fresh insight into both these limiting cases.  (Author/TRRL)]]></description>
      <pubDate>Sun, 30 Oct 1983 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/191608</guid>
    </item>
    <item>
      <title>MEASUREMENTS OF THE BEARING CAPACITY OF TWO-LAYER SYSTEMS</title>
      <link>https://trid.trb.org/View/189181</link>
      <description><![CDATA[The paper deals with measurements of the subgrade bearing capacity and of the subgrade improved by a layer of different materials.  There are described the plate bearing tests on two-layer systems, constructed as models on silty soil subgrade.  The materials of the improving layer were: sand and gravel, sand and gravel with geotechnical fabrics, sand and gravel with fibres, crushed stone (quarry and waste material), crushed stone with geotechnical fabric and with fibres.  The static loading tests were made by rigid circular plates with area of 0,1 and 0,4 M2 and with double tyred wheel.  The dynamic loading test was made by a falling weight deflectometer. Using the deflection values from measurements the e-modulus was calculated for elastic halfspace.  A great difference in deflections and calculated e-modulus according to various method was estimated.  The bearing capacity of the crushed stone (quarry waste material) layer was generally 1,6 times higher than the sand and gravel one.  The significance of geotechnical fabrics under the layer of material is greater on subgrade with lower bearing capacity.  Thin layer of sand and gravel on fabric is not effective.  The additional load on surface has a great significance for measured deflection by static and dynamic load test. (a) (TRRL)]]></description>
      <pubDate>Thu, 30 Jun 1983 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/189181</guid>
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