Limited laboratory studies have investigated the cyclic behavior of sands under plane strain state, despite the current extensive applications of the plane strain hypothesis in modeling the behavior of subgrade soils beneath long road embankments. This study aims to explore the traffic-induced deformation behavior of sand under plane strain state and compare it to the conventional triaxial stress state. A series of one-way high-cyclic tests were performed on Fujian sand under both states using a true triaxial apparatus, considering different cyclic stress levels, consolidation stresses, consolidation anisotropies, and relative densities. In the plane strain scenario, the deformation of the specimen in the direction of intermediate principal stress was restricted when the cyclic major principal stress was applied. The test results indicate that during long-term cyclic loading, the sand exhibits substantially lower accumulated axial and volumetric strains when subjected to plane strain state as opposed to the conventional triaxial state. The reduction effect of plane strain state on the accumulated axial strain was found to be distinctively correlated with the strain levels, regardless of the cyclic stress amplitude and relative density. A practical formula was developed to estimate the difference in accumulated axial strain between the plane strain and triaxial states. Additionally, the intermediate principal stress of specimens under plane strain state was observed to oscillate cyclically in accordance with the one-way vertical cyclic stress. The intermediate principal stress coefficient, triggered by vertical cyclic loading, is more pronounced under high deformation, with its magnitude dependent on the specific loading conditions.

To investigate the mechanical characteristics of frozen silty clay under complex stress paths, using the true triaxial instrument for permafrost, tests were carried out under triaxial compressive and plane strain stress states using the true triaxial instrument for permafrost to analyze deformation characteristics and strength evolution law under different stress paths and minor principal stresses (sigma(3)) and establish strength criterion under plane strain conditions. PFC3D numerical simulation results were compared to test results and meso-crack evolution law was discussed. The results showed that stress-strain curves were characterized by strain hardening. Destructive strength showed a gradual increase with the increase of sigma(3) and the values obtained from plane strain tests were higher than those of triaxial compression tests. Volume strains basically showed shear shrinkage characteristics and all sigma(3) directions were expansion deformation. Strength at damage under plane strain state was approximated based on generalized Mises and Lade-Duncan plane strain strength criterion using generalized plane strain strength criterion. Stress-strain curves obtained from numerical simulation tests in PFC3D basically agreed well with those obtained from indoor test results. The number of tensile and shear cracks in the developed numerical model under various stress paths were increased with generalized shear strain.

Prefabricated vertical drains (PVDs) are highly effective in hastening the consolidation process of soil and enhancing the strength of the foundation. Enhanced computational precision is achieved by utilizing a twodimensional (2D) plane strain model throughout the analytical procedure. The pronounced layering characteristic of saturated soils, coupled with the obstruction of pore water drainage across interfaces, results in a pronounced flow contact resistance effect. A comprehensive investigation into the 2D plane strain consolidation behavior of layered saturated soils under continuous drainage boundary conditions is facilitated by the presentation of the interfacial flow contact model. Subsequently, semi-analytical solutions for pore water pressure and the degree of consolidation are derived using the Laplace transform and the Crump inverse method. The proposed solution is analyzed for its degradation and compared against the experimental results and numerical solutions, to ascertain the accuracy and reliability of the presented solution. The research delves into the effects of flow contact resistance on parameters, including the permeability coefficient ratio (kv / kh) and boundary coefficients (rt and rb) throughout the consolidation process. Additionally, the impact of the flow contact resistance on the degree of consolidation is discussed. The results indicate that both the permeability coefficient ratio and boundary parameters have a close association with the flow contact resistance effect. Ignoring this effect may lead to inaccurate predictions of pore water pressure distribution and an overestimation of the soil consolidation.

Dispersive clay is widely distributed in the Songnen Plain of northeast China, causing serious embankment damage to hydraulic engineering, and the research on the relevant failure mechanism is still incomplete. In this study, based on the real stress path of dispersive clay failure, a mechanical experimental method under plane strain conditions was adopted to investigate the strength properties of dispersive clay. The results showed that under plane strain conditions, the stress-strain curve of dispersive clay exhibited the strain hardening type, distincted from the conventional strain softening type under triaxial vertical conditions, and the strength difference was approximately twice at a consolidation stress of 50 kPa. The stress-strain relationship of the principal stress also showed the strain hardening type, and the relationship between the stress-strain was approximately linear. Under low consolidation stress, the coefficient of the intermediate principal stress reached 0.44, indicated a significant influence of the intermediate principal stress on the strength of the clay. Under low consolidation stress, the failure mode of dispersive clay was characterized by swelling with no obvious spatial shear band, while under high consolidation stress, the failure mode exhibited a shear band located diagonally. Additionally, the strength properties of dispersive clay were weakened by the leaching of chemical ions in the clay, showed different compaction and strength under different consolidation stresses.

This study conducts several triaxial cyclic and plane strain cyclic impact tests on fissured soil under varying effective consolidation pressures, impact peak loads, and frequencies through the true triaxial test system to investigate the mechanical response characteristics. The results indicated that, under plane strain conditions, the specimens' shear resistance increases compared to that under triaxial loading. Moreover, the influence of fissures is challenging to quantify under triaxial loading compare to the mechanical response to fissure failure under the plane strain condition. As a result of the lateral confinement under plane strain conditions, the excess pore pressure, stress path, and lateral stress coefficient exhibit changes in sensitivity due to fissure damage, facilitating the analysis of the fissures' influence. Lower consolidation stress tends to increase the likelihood of fissure failure. As the peak impact stress escalates, the specimen deformation and excess pore pressure rise. When the impact peak stress reaches a critical value, the sample undergoes substantial deformation and fails rapidly. The impact of the frequency on specimen deformation correlates with the peak impact stress. Under low-impact peak stress, higher frequencies result in smaller deformations. However, under high-impact peak stress, a critical frequency exists. As the frequency increases, the difference between the maximum and minimum pore water pressure expands, with the change in this difference relating to fissure damage. Inherently, fissures in the soil significantly affect the mechanical properties under the impact load in the plane strain condition. The findings from this study can provide technical support for determining and evaluating the mechanical parameters of the fissured soil layer in light of the impact load.

Rapid dynamic loads, such as those caused by earthquakes or traffic, induce medium strain rates in expansive soil, impacting its mechanical properties, which are vital for geotechnical engineering design. This study aims to deepen understanding of the rate effect on expansive clay under plane strain conditions. It conducts various isotropic triaxial and plane strain shearing tests at different medium strain rates. Post-testing, the microstructures of the clay, affected by varying shearing rates, are examined using scanning electron microscope and nuclear magnetic resonance. The experimental findings revealed that the strength at higher strain rates surpasses that at lower ones. In addition, the strength under plane strain at the same consolidation stress level exceeds that under triaxial loading. The strain rate effect is more pronounced in the clay studied under low consolidation pressure, which is more significant in the triaxial state than under plane strain. Excess pore water pressure initially peaks at low strain rates before decreasing but increases at higher strain rates. The specimen's intermediate principal stress coefficient (b) rises with the increase in consolidation pressure and strain rate. In addition, the expansion of fissures and changes in internal structure account for the strain rate effect in undisturbed expansive soil under specific loading rates. These new insights aid in better understanding the behavior of expansive clay under medium strain rates, enabling engineers to establish appropriate design parameters and criteria. This ensures the safety and stability of structures under dynamic loading.

An important characteristic of some clays is their abundance of fissures. In the case study reported here, to investigate how the fissure inclination angle affects the deformation and strength of fissured clay, samples of undisturbed fissured clay with different inclination angles of its inherent fissures (0 degrees, 45 degrees, and 90 degrees) were subjected to consolidated undrained plane-strain shear tests using a true triaxial apparatus. Moreover, consolidated undrained triaxial tests were carried out on samples with the same inclination angles for comparison. The results showed that compared with the triaxial state, the degree of fissure influence on samples with different fissure angles is different under plane strain, which weakens the influence of the fissure inclination angle on the soil's mechanical behavior. Under the designed consolidation pressures, the peak stress of the 45 degrees fissured soil samples was the smallest, with a stress-strain curve that exhibits strain softening. The 0 degrees fissured soil samples exhibited the highest peak stress, with a stress-strain curve that exhibits strain hardening. The 90 degrees fissured soil samples fell in between, with a stress-strain curve that exhibits a relatively stable trend. The intermediate principal stress coefficient b-value showed different trends at different fissure angles, which also reflects the influence of fissure dip angle. According to the von Mises and Lade-Duncan strength criteria, the generalized plane-strain criterion for fissured soil was obtained. The dip angle of the shear band was calculated from Mohr-Coulomb theory, and the difference between the calculated and measured dip angles was found to be small.

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories. The purpose of this review is to provide information about the existing works on the subject, critically discuss them and make suggestions for further research. The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems. Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic, viscoelastic or poroelastic material behavior. Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements. The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed. The above pavement-vehicle models are dynamically analyzed by analytical, analytical/numerical or purely numerical methods working in the time or frequency domain. Representative examples are presented to illustrate the models and methods of analysis, demonstrate their merits and assess the effects of the various parameters on pavement response. The paper closes with conclusions and suggestions for further research in the area. The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Unbound granular materials (UGMs) are extensively used in pavements mostly as subgrade and subbase materials. Excessive permanent settlement or rutting is the main damage mechanism encountered in UGMs. Rutting is a result of accumulated gradual plastic strain in the subbase and subgrade layers subjected to repetitive traffic loadings. Axisymmetric triaxial apparatus or repeated lateral triaxial (RLT) devices are commonly used to explore the rutting of UGMs. However, these devices are not able to capture the actual stress state generated in traffic. A soil element in pavement layers is in a three-dimensional (3D) stress state and includes all three components of cyclic principal stresses. A typical pavement also can be considered geometrically as a plane strain structure. Accordingly, aim of this study is to carry out experiments to determine the long-term deformation of a silty sand in plane strain and in a 3D stress state using a multistage true triaxial apparatus (TTA). It is found that the permanent deformation of UGMs under plane strain and 3D anisotropic stress state differs significantly from that under axisymmetric stress. An increase in the intermediate principal stress was observed to decrease the total and permanent deformation. An increase in cyclic stress level was also found to increase the rutting in UGMs. The deformation of soil under the plane strain state was found to be less than that in the axisymmetric stress state but falls into an intermediate range when compared to tests involving 3D cyclic loading.

To address loading and unloading issues in civil and hydraulic engineering projects that employ coarse-grained soil as fill material under plane strain conditions during construction and operation, cyclic loading-unloading large-scale plane strain tests were conducted on two types of coarse-grained soils. The effects of coarse-grained soil properties on shear behavior and various modulus relationships were analyzed. The research results showed that coarse-grained soils with better particle roundness exhibit significant shear dilation deformation; it was also found that low parent rock strength can lead to strain softening, and an increase in confining pressure suppresses shear dilation deformation. During the cyclic loading-unloading process, the initial unloading modulus (E-iu) > unloading-reloading modulus (E-ur) > initial reloading modulus (E-ir) > initial tangent modulus (E-i), with the unloading modulus considerably greater than the others. In finite element simulations and model calculations, it is essential to select appropriate modulus parameters based on the stress conditions of the soil to ensure calculation accuracy. In this work, an elastoplastic and nonlinear elastic theory was used to establish a cyclic loading-unloading constitutive model. By comparing the values obtained using this model with experimental measurements, it was found that the model can reasonably predict stress-strain variations during cyclic loading-unloading of coarse-grained soils under plane strain conditions.