In Situ Soil Response to Vibratory Loading and Its Relationship to Roller-Measured Soil Stiffness

An investigation was conducted to characterize and relate in situ soil stress-strain behavior to roller-measured soil stiffness. Continuous assessment of soil stiffness via roller vibration monitoring has the potential to significantly advance performance based quality assurance of earthwork. One vertically homogeneous and two layered test beds were carefully constructed with embedded sensors for the field testing program. Total normal stress and strain measurements at multiple depths reveal complex triaxial soil behavior during vibratory roller loading. Measured cyclic strain amplitudes were 15–25% of those measured during static roller passes due to viscoelasticity and curved drum/soil interaction. Low amplitude vibratory roller loading induces nonlinear in situ modulus behavior. Roller-measured stiffness and its dependence on excitation force is influenced by the stress-dependent modulus function of each soil, the varying drum/soil contact area, and by layer characteristics (modulus ratio, thickness) when layering is present. On vertically homogeneous clayey sand, roller-measured stiffness decreased with increasing excitation force, a behavior attributed to stress-dependent modulus reduction observed in situ. On the crushed rock over silt test bed, roller-measured stiffness increased with increasing excitation force despite the mild stress-dependent modulus reduction observed in the crushed rock. In this case, the stiffer crushed rock takes on a greater portion of the load, resulting in the increase in roller-measured stiffness.     

Nonlinear Stress-Strain Relationship of Soil Reinforced with Flexible Geofibers

A nonlinear stress-strain relationship of soil reinforced with flexible geofibers under static loading is derived based on a nonlinear elastic stress-strain relationship of soil and a linear elastic stress-strain relationship of geofibers in the paper. This investigation includes the following aspects: First, the homogenization technique is introduced to find the volume average stress tensor and volume average strain tensor and further an elastic incremental stress-strain relation is introduced to describe deviatoric shear stress-axial strain relationship of equivalent homogeneous geofiber-reinforced soil. Second, the relation of geofiber numbers, content, mechanical behavior, distribution, and geometrical features to shear modulus of geofiber-reinforced soil is expressed and assessed by employing an elastic energy method. Third, the deviatoric shear stress and axial strain curves of geofiber-reinforced soil are calibrated by laboratory testing data of geofiber reinforced soil samples. Finally, the theoretical computational curves of geofiber reinforced soil are compared with the curves calibrated by testing data of geofiber reinforced soil. The model prediction has a good agreement with experimental results.     

Displacements and Stresses Due to a Uniform Vertical Circular Load in an Inhomogeneous Cross-Anisotropic Half-Space

In this work, we present the solutions for displacements and stresses along the centerline of a uniform vertical circular load in an inhomogeneous cross-anisotropic half-space with its Young’s and shear moduli varying exponentially with depth. The planes of cross anisotropy are assumed to be parallel to the horizontal surface. The presented solutions can be directly integrated from the point load solution in a cylindrical coordinate system, which were derived by the writers. However, the resulting integrals of the circular solution for displacements and stresses cannot be given in closed form; hence, numerical integrations are required. For a homogeneous cross-anisotropic half-space, the numerical results agree very well with the exact solutions of Hanson and Puja, published in 1996. Two examples are given to elucidate the effect of inhomogeneity, and the type and degree of soil anisotropy on the vertical displacement and vertical normal stress in the inhomogeneous isotropic/cross-anisotropic soils subjected to a uniform vertical circular load acting on the surface. The proposed solutions can more realistically simulate the actual stratum of loading problem in many areas of engineering practice.     

红砂岩单轴压缩试验的率效应研究

利用MTS 322试验机对均质红砂岩进行了低加载（应变）率范围内不同量级的单轴压缩试验，考察了加载率对压缩强度、切线弹模和破坏应变的率效应影响规律。试验过程中采用位移控制加载，对应的加载量级分别为0.12，1.2，12，120 mm/min。研究结果表明：位移控制加载率与试样实际加载率、应变率之间均存在良好的线性关系。不同加载速率下岩石材料的单轴压缩强度、切线弹模随着加载率的增加呈现增加趋势，单轴压缩强度增加了11%，切线弹模增加了13%，率效应显著。通过试验数据发现，破坏应变与应变率（加载率）之间无相关性，不具有率效应规律，故强度准则应该是应力准则而不是应变准则。     

Effects of misalignment on the pre-macroyield region of the uniaxial stress-strain curve

Some bending usually occurs in uniaxial testing systems due to small unavoidable misalignment. The resulting elastic strain gradient can lead to significant differences between axial strain and extreme surface bending strains, especially at small strains. A three-point microstrain measurement around a cylindrical sample permits evaluation of the extreme strains and of the precision of alignment. A three-point, parallel-plate capacitance strain gage having a linear output with displacement was designed to evaluate bending of tensile samples in the microstrain range. The resolution of the gage was 3 parts in 10,000 at plate separations of 0.010 in. Varying misalignment resulted in extreme elastic bending strains at the sample surface of the order of tens to hundreds of micro-in. per in. larger than the axial strain. Analysis of the mechanics of bending in uniaxial loading demonstrated that: 1) the average applied stress divided by the average elastic strain always gives a unique number, Young's modulus, and 2) the average microplastic strain is not uniquely related to the average applied stress, but rather depends upon precision of alignment. The influence of bending on the determination of the average stress at which microplastic flow initiates is discussed, and a method for making meaningful comparisons of plastic microstrain data generated with significant misalignment is suggested.     

Mixture Theory for a Fluid-Saturated Isotropic Elastic Matrix

The theory for a fluid saturated linearly isotropic elastic matrix is still the basis for many geophysical applications, and commonly adopts Biot’s symmetric stress–strain laws for the matrix stress and fluid pressure. These involve a shear modulus and three elastic moduli governing the mixture and constituent compressions, in contrast to four compression moduli if Biot’s invalid potential energy argument is not applied. We now show that an energy argument applied to undrained loading also leads to three compression moduli, but distinct from those derived by Biot (Biot symmetry). However, there are two distinct solutions of this energy balance, corresponding to the Voigt and Reuss limits of the analogous theory of a linear two-phase elastic composite, whereas a unique undrained modulus not at either limit would be expected. It is proposed that an energy contribution is lost due to the idealised assumptions made for undrained loading, which therefore does not determine a further restriction, so that there are four independent compression moduli. The general and restricted combinations of the total pressure and fluid pressure (effective stress) governing the matrix compression are then presented, together with the alternative forms of the partial differential equations governing the deformation and flow.     

Pressure-Level Dependency and Densification Behavior of Sand Through Generalized Plasticity Model

Natural soil deposits and man-made earth structures exhibit complicated engineering behavior that is influenced by factors such as the stress level and drainage conditions. The stress conditions within a soil structure vary greatly, ranging from very low to very high values, due to the dead weight, loading and boundary conditions. Saturated sand deposits that exhibit drained conditions under static loading become undrained when subject to earthquake excitations. The Pastor–Zienkiewicz–Chan model has demonstrated considerable success in describing the inelastic behavior of soils under isotropic monotonic and cyclic loadings, including liquefaction and cyclic mobility. This study proposed modifications to the Pastor–Zienkiewicz–Chan model so that effects of stress level and densification behavior are simulated. The proposed model suggested that the angle of internal friction, elastic and plastic moduli are dependent on the pressure levels. Relevant modifications were made to incorporate a power term of mean effective stress on the loading plastic modulus so that a stress-level dependent volume change is obtained in combination with the stress-dilatancy relationship. To better simulate cyclic loading with reference to densification behavior, an exponential term of plastic volumetric strain is included for the unloading and reloading plastic moduli. A total of 11 parameters are needed for monotonic loading, whereas 15 parameters are needed in describing the cyclic behavior. The model simulations were compared with undrained and drained triaxial test results of several kinds of sand under dense and loose states. The predictive capability for monotonic and cyclic loading conditions was also demonstrated.     

Approximate Displacement Influence Factors for Elastic Shallow Foundations

Displacement influence factors for calculating the magnitudes of drained and undrained settlements of shallow foundations are approximated by simple numerical integration of elastic stress distributions within a spreadsheet. Influence factors for circular foundations resting on soils having homogeneous (constant modulus with depth) to Gibson-type (linearly increasing modulus) profiles with finite layer thicknesses are obtained by summing the unit strains from incremental vertical and radial stress changes. The effects of foundation rigidity and embedment are addressed by approximate modifier terms obtained from prior finite-element studies. Results are compared with closed-form analytical and rigorous numerical solutions, where available. A new solution for Gibson soil of finite thickness is presented.     

Plate Load Test on Fiber-Reinforced Soil

This technical note discusses the load–settlement response from two steel plate load tests (0.3 m diameter, 25 mm thick) carried out on a thick homogeneous stratum of compacted sandy soil, reinforced with polypropylene fibers, as well as on the same soil without the reinforcement. In addition to the field test program, laboratory triaxial compression tests were performed to determine the static stress–strain response of the compacted sandy soil reinforced with randomly distributed polypropylene fibers. The laboratory test results showed that the reinforcement changed dramatically the stress–strain behavior at very large strains. The strength was found to increase continuously at a constant rate, regardless of the confining pressure applied, not reaching an asymptotic upper limit, even at axial strains as large as 25%. The plate load test on the soil–fiber stratum was performed to relatively high pressures, and gave a noticeable stiffer response than that carried out on the nonreinforced stratum.     

Buckling of Column with Base Attached to Elastic Half-Space

Buckling of a heavy elastic column loaded by a concentrated force at the top is analyzed. It is assumed that the base of the column is fixed to a rigid circular plate that is positioned on a homogeneous, isotropic, linearly elastic half-space. The plate has adhesive contact with the half-space. The constitutive equations for the column are assumed in the form that allows axial compressibility and takes into account the influence of shear stresses. It is shown that eigenvalues of the linearized equations determine the bifurcation points of the full nonlinear system of equilibrium equations. The type of bifurcation at the lowest eigenvalue is examined and is shown that it could be super- or subcritical. The postcritical shape of the column is determined by numerical integration of the equilibrium equations.     

Variable Bulk Modulus Constitutive Model for Sand

A quasi-linear elastic constitutive model is proposed to describe the behavior of sand well below failure. It is based on isotropic compression tests and captures the increase in stiffness due to confinement—a unique property that makes sand stiffer under certain applied loads. The model traces the increase in stiffness by describing the instantaneous bulk modulus in terms of the effective mean stress and two constitutive parameters: the initial bulk modulus and the ultimate volumetric strain. The validity of the model is examined by checking how closely the proposed mathematical formulation represents high quality isotropic compression tests reported in the literature.     

Stress Integration Approach in Resonant Column and Torsional Shear Testing for Soils

Determination of strain in resonant column and torsional shear (RC/TS) tests is complicated due to nonuniform stress–strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate levels, however, the approach is less accurate when performing the tests at higher strains. The stress integration approach involving integration of an assumed soil stress–strain model was developed to account for this problem more precisely. This approach was used to generate the plots of equivalent radius ratio versus strain developed based upon shear modulus and damping. Results showed that the equivalent radius ratio curves converge to a value of approximately 0.8 at low strains and decrease as strain increases. The equivalent radius ratio curves based upon damping decrease to significantly lower values at high strain than curves based upon shear modulus. This study suggests that using the same values of equivalent radius ratio to calculate strains for both shear modulus and damping is not appropriate. The stress integration approach provides an accurate analysis technique for evaluating both modulus and damping behavior of soil, over any range of strains in RC/TS testing.     

Damage Theory Based on Composite Mechanics

A new theory of composite damage mechanics is developed. A material with damage is considered as a composite comprised of two different phases (called matrix and inclusion). Both phases are linearly elastic isotropic materials. The matrix is considered as the intact material, and the inclusion is the damaged material. Three different composite models, Voigt (parallel), Reuss (serial), and generalized self-consistent (spherical), are introduced for three types of damage distributions. These composite models are usually used for initial tangential modulus of a composite material, here we use them for secant modulus of a distressed material. Since the parallel and the serial models represent the upper and lower bounds for stiffness of materials, the composite damage theory obtains the upper and lower bounds for postpeak stress and the level of damage for the material beyond the elastic limit. The spherical model is in between the two bounds. Depending on the “elastic limit” of the inclusion, the theory can be used to describe elastic perfectly plastic behavior, strain hardening, and strain softening. Two different degradations, the linear and exponential degradations of the stress–strain response curve are introduced. The two degradation models are used in two different failure surfaces, i.e., Tresca and Mohr–Coulomb failure surfaces, to predict the postpeak behavior of distressed material.     

Strain Localization in Combined Axial-Torsional Testing on Kaolin Clay

A series of combined axial-torsional tests were performed to study the 3D mechanical behavior of kaolin clay in an undrained condition. Using the digital image analysis technique, discrete local deformation of the surface of a hollow cylindrical specimen under loading was recorded. A linear interpolation method was used to generate a continuous deformation and strain field of the specimen based on the recorded discrete local deformations. Evolution of shear band was vividly visualized and recorded during the loading process for various inclinations of major principal stress. The theory of strain localization on continuous bifurcation was briefly reviewed and applied to the Mohr-Coulomb model, and a single hardening model incorporating the concept of loading-history-dependent plastic potential was developed by the writers. The largest critical plastic modulus and orientation of the shear bands were predicted by using the theoretical solution. Significant disagreement was observed between the experimental results and theoretical predictions related to the initial occurrence of strain localization and the inclination of fully developed shear bands.     

Lateral Behavior of Pile Groups in Layered Soils

Assessment of the response of a laterally loaded pile group based on soil–pile interaction is presented in this paper. The behavior of a pile group in uniform and layered soil (sand and/or clay) is evaluated based on the strain wedge model approach that was developed to analyze the response of a long flexible pile under lateral loading. Accordingly, the pile’s response is characterized in terms of three-dimensional soil–pile interaction which is then transformed into its one-dimensional beam on elastic foundation equivalent and the associated parameter (modulus of subgrade reaction Es) variation along pile length. The interaction among the piles in a group is determined based on the geometry and interaction of the mobilized passive wedges of soil in front of the piles in association with the pile spacing. The overlap of shear zones among the piles in the group varies along the length of the pile and changes from one soil layer to another in the soil profile. Also, the interaction among the piles grows with the increase in lateral loading, and the increasing depth and fan angles of the developing wedges. The value of Es so determined accounts for the additional strains (i.e., stresses) in the adjacent soil due to pile interaction within the group. Based on the approach presented, the p–y curve for different piles in the pile group can be determined. The reduction in the resistance of the individual piles in the group compared to the isolated pile is governed by soil and pile properties, level of loading, and pile spacing.     

Acoustic Measurements of the Anisotropy of Dynamic Elastic and Poromechanics Moduli under Three Stress/Strain Pathways

A series of triaxial compression experiments have been conducted to investigate the effects of induced stress on the anisotropy developed in dynamic elastic and poroelastic parameters in rocks. The measurements were accomplished by utilizing an array of piezoelectric compressional and shear wave sensors mounted around a cylindrical sample of porous Berea sandstone. Three different types of applied states of stress were investigated using hydrostatic, triaxial, and uniaxial strain experiments. During the hydrostatic experiment, where an isotropic state of stress was applied to an isotropic porous rock, the vertical and horizontal acoustic velocities and dynamic elastic moduli increased as pressure was applied and no evidence of stress induced anisotropy was visible. The poroelastic moduli (Biot’s effective stress parameter, α) decreased during the test but also with no evidence of anisotropy. The triaxial compression test involved an axisymmetric application of stress with an axial stress greater than the two constant equal lateral stresses. During this test a marked anisotropy developed in the acoustic velocities, and in the dynamic elastic and poroelastic moduli. As axial stress increased the magnitude of the anisotropy increased as well. The uniaxial strain test involved axisymmetric application of stresses with increasing axial and lateral stresses but while maintaining a zero lateral strain condition. The uniaxial strain test exhibited a quite different behavior from either the triaxial or hydrostatic tests. As both the axial and lateral stresses were increased, an anisotropy developed early in the loading phase but then was effectively “locked in” with little or no change in the magnitude of the values of the acoustic velocities, or the dynamic elastic and poroelastic parameters as stresses were increased. These experimental results show that the application of triaxial states of stress induced significant anisotropy in the elastic and poroelastic parameters in porous rock, while under the uniaxial strain condition the poromechanics, Biot’s effective stress parameter, exhibited the largest variation among the three test conditions.     

Elastic Anisotropic Viscoplastic Modeling of the Strain-Rate-Dependent Stress–Strain Behavior of K0-Consolidated Natural Marine Clays in Triaxial Shear Tests

This paper presents a new three-dimensional (3D) anisotropic elastic viscoplastic (EVP) model for the time-dependent stress–strain behavior of K0-consolidated marine clays. A nonlinear creep function with a limit for the creep volumetric strain under an isotropic or odometer K0-consolidated stressing condition and a nonsymmetrical elliptical loading locus are incorporated in the 3D anisotropic EVP model. An α-line defines the inclination of the nonsymmetrical elliptical loading locus in the p′-q plane and is commonly used for natural soils. All model parameters are determined from the results of one set of consolidated undrained compression tests and an isotropic consolidation/creep test. With the parameters determined, the 3D anisotropic EVP model is used to simulate the behavior of K0-consolidation tests and the strain-rate-dependent stress–strain behaviors of the K0-consolidated triaxial compression and extension tests on natural Hong Kong marine deposit clay specimens. These triaxial K0-consolidated specimens were sheared at step-changed axial strain rates from +2?to?+0.2, +20, ?2 (unloading) and +2%/h (reloading) for compression tests; or from ?2?to??0.2, ?20, +2 (unloading), and ?2%/h (reloading) for extension tests, all in an undrained condition. The simulation results of all these tests are compared with the test results. The validation and limitations of the model are then evaluated and discussed.     

Influence of deformation history on the yield locus and stress-strain behavior of aluminum and copper

Thin-walled tubular specimens of 1100-0 aluminum and OFHC copper were loaded biaxially through the application of simultaneous axial load and internal pressure. The effects of loading path and deformation history on the stress-strain and yield locus characteristics were studied at strains less than 2.0 pct. The observed plastic strains for both materials depended on the loading path to a given stress point, whereas the loading path during prestraining did not affect subsequent deformation. Deformation subsequent to prestraining depended on the prestraining magnitude and direction at strains less than 0.2 pct and only on the magnitude at larger strains. The resulting plastic response was, therefore, anisotropic at small strains and isotropic at large strains. The small strain behavior cannot be predicted by present continuum plasticity theories, whereas the large strain behavior agrees with the isotropic hardening rule. It was also found that a prestraining operation of sufficient plastic strain can erase some of the prior deformation history. Formerly with the Los Alamos Scientific Laboratory, Los Alamos, N. M.     

Buckling and Postbuckling Behavior of Cross-Ply Composite Plate Subjected to Nonuniform In-Plane Loads

This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin’s approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (a/b = 0.5, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible.     

Viscoelastic Analysis of Constant Creep Tests on Silicate-Grouted Sands at Low Stress Levels

This paper presents the mechanical properties of silicate-grouted sands subjected to creep loadings at low stress levels. Uniaxial compressive tests were performed in order to determine the stress levels of constant creep tests. The uniaxial compressive strength rapidly increased with time over the first 7 days of curing and then approached a constant level. A series of creep tests were performed for three stress levels and viscoelastic theory was employed to assess the creep behavior. During the loading process elastic, plastic, and viscoelastic strains existed together. The recoverable portions contained elastic and time-dependent viscoelastic strains, and both were approximately linear. Test results showed that the magnitude of the instantaneous recoverable strains was independent of the unloading time. A constitutive model to predict the permanent deformation was developed.