International Journal of Geomechanics

In this paper, by analyzing evolution of aperture and contact forces of joints as well as parallel bond breakage, the effect of joint strength mobilization on mechanical behavior of jointed rock masses was studied numerically through particle flow modeling package PFC2D. With the calibrated microparameters of the particles, parallel bond contacts, and the smooth-joint contacts, the numerical tests reproduced the dependence of strength reduction and multipeak deformation behaviors of the specimens with large nonpersistent open joints on joint orientation and spacing that was observed in the laboratory tests. Four types of stress–strain curves [i.e., the single-peak curve (Type I) and the three multipeak curves (Types II–IV)] were related to the different closing and strength mobilization processes of the joint system. Strength immobilization of the joint system with the opening of most joints and slight strength mobilization of the joint system with partial closing of some joints after peak strength led to Type I (strain softening) and Type II (general strain softening with oscillations) behaviors, respectively. Full strength mobilization of the joint system with entire closing of all joints accompanied by severe damage developing in the matrix at the first peak (peak strength) led to Type III (yield platform-strain softening) behavior. Salient strength mobilization of the joint system with entire closing of most joints at the last peak (peak strength) as well as damage in the matrix mainly developing after the first peak led to Type IV (yield platform-strain hardening-strain softening) behavior. Salient or full strength mobilization of the joint system for the specimens with small joint inclination angles, or little interruption in axial load transferring for the specimens with large joint inclination angles induced slight or moderate strength reduction, whereas both slight strength mobilization of the joint system and strong interruption in axial load transferring for the specimens with medium joint inclination angles induced sharp strength reduction.

Despite the increase in offshore wind turbine (OWT) capacities, the preferred foundations for these marine structures are large-diameter monopiles due to their ease of installation in shallow to medium water depth. The current design methodologies based on p-y curves [the American Petroleum Institute (API) method, for instance] have gained a confirmed recognition in designing slender monopiles, such as those used for supporting offshore gas and oil platforms. However, when applied to large-diameter monopiles, these regulation codes failed to properly address the behavior of these extremely stiff structures, which is why many researchers tried to enhance the p-y method performance by suggesting new p-y formulas incorporating monopile properties. The paper reviews the analytical formulas of the p-y curves adopted by the current offshore guidelines and documents in detail the limitations and the shortcomings inherent to their formulations. The latest versions of p-y curves proposed to improve the performance of the Winkler model were also given. To show how well the finite-element (FE) analysis predicts the lateral response of large-diameter monopiles under horizontal loading on one hand, and how inappropriate the models using p-y curves are in studying this crucial problem on the other hand, two Fortran computer programs were considered. The first program, a computer code called NAMPULAL, combines the FE vertical slices method (VSM) and the hyperbolic model to describe the behavior of cohesionless soils. The second program, called Winkler-ROWKSS, is written using the finite-differences method. In the latter, the original and the newly developed p-y curves were implemented. The comparative study was made by considering two case histories. The first case is a monopile embedded in a multilayer sandy soil, which serves as a support foundation to 5-MW National Renewable Energy Laboratory (NREL) wind turbines, and the second case is a monopile supporting OWTs at Horns Rev in the Danish sector of the North Sea. At the first site, the evolution of the monopile head movements with applied loading provided by the different models of beams on nonlinear Winkler foundations (BNWFs) as well as the FEM was examined and compared. However, at the second site, only the monopile lateral displacement profile was studied.

This paper aims to experimentally study the performance of inclined micropiles under dynamic loading conditions. Analysis is performed using data obtained from shaking table tests on a small-scale physical model of micropiles with different inclination angles. The physical model includes a 4 × 4 micropile system inserted in sandy soil with low relative density. Inclination angle of micropiles in the direction of shaking is varied in the range of field applications. A sine wave is applied to the physical model as the input excitation and acceleration response at different points of the physical model are recorded and analyzed to investigate the effects of inclination angle of micropiles on their seismic performance. After describing the small-scale physical model used in this study, results of shaking table tests are presented, and effects of inclination angle on the dynamic response of the soil–micropile system are examined. Results of this study indicate that inclined micropiles exhibit a better seismic performance than vertical micropiles. Dynamic amplifications of acceleration on micropiles and soil surface can be reduced by inclining the micropiles.

Particle breakage has a significant impact on the mechanical properties of soils and has drawn continuous concerns among researchers. This study aims to deepen the current understanding on the particle breakage phenomenon through insights of high frequency acoustic emission (AE) signals. Two series of physical model pile tests were performed with AE instrumentation, using two different materials: silica sand and coral sand. The AE signals were digitalized continuously throughout the tests with a sampling interval of 0.5 μs (2 Mps), which enabled the signals with a maximum frequency of 1 MHz to be captured, and the AE signals with a frequency higher than 100 kHz were interpreted to be associated with particle breakage mechanism. Results show that the high frequency AE (i.e., particle breakage) occurred throughout the tests. An initial period of rapid rising and a following period of relatively stable high frequency AE signals were observed in all tests. Based on AE characteristics, the extent of particle breakage was found to be related to the material property, the pile penetration depth, and the ground density. In general, silica sand was found to be more emissive, although coral sand was more prone to break, and the dense ground was more emissive and more prone to break than the loose ground. In conclusion, the asymptotic evolving trend is suggested for simplified estimation of particle breakage during the pile penetration process.

A number of landslides occurred in the soil slopes deposited on the bedrock. The bedrock significantly influenced the failure behavior of the overlying slope, which should be reasonably captured in the slope stability analysis. To elucidate the deformation and failure mechanism of slopes overlying the bedrock, a series of centrifuge model tests were conducted to simulate different shapes and roughnesses of the bedrocks, together with a pure soil slope without any bedrock for comparison. The failure mode of the slope could be categorized to three types: sliding along the bedrock, failing inside the soil, and their combination. The steep and smooth bedrock decreased the safety limit of a slope and served as a weak surface so that the soil slope slid along it. The gentle or rough bedrock increased the safety limit of a slope and changed the failure behavior of the slope. The bedrock also changed the direction and magnitude of the slope displacement, and the extent of variation depended on the properties of the bedrock. The slope exhibited significant coupling of deformation localization and failure. This could be used to explain the influencing mechanism of the bedrock on the failure behavior of slope. The bedrock significantly changed deformation behavior of the slope, accordingly changed the location and development process of the deformation localization, and finally affect the shape of the slip surface and stability level of the slope.

At railway transition zones between soft ground and stiffer structures, dynamic actions between the railcar, track, and subgrade induce differential settlements that may cause vibration and noise, compromise ride quality, and incur relatively high maintenance costs. Using a semianalytical spectral Galerkin method, this study attempted to examine stiffness transitions for point loads traveling on a pinned beam resting on a Winkler spring foundation with damping. Generally, a different deflection behavior occurs when moving from stiff-to-soft or soft-to-stiff regions. Multiple loads induce additional oscillatory behavior that is not typical of single loads. This study showed that a minimum transition length of 8–10 times the system’s characteristic length appears necessary to avoid stiffness transition deflection spikes. A real rail transition zone taken from a case study in Portugal was also analyzed.

During excavation unloading, highly stressed rock masses at great depth exhibit failure modes with different scales, for instance, zonal disintegration, rockbursts, and super-low friction. The root cause of the failure mechanisms of highly stressed rock masses differs. In recent years, research on the failure mechanism of highly stressed rock masses during unloading has become a frontier topic in geotechnical engineering. This paper relies on the deep mining process laboratory of the China Hongtoushan Copper Mine, where it has been observed that the deep rock unloading process causes macroscopic deformation and opens microscopic joints in deep rock. Analysis of monitoring data has shown that compressional deformation occurs in the surrounding rock masses subjected to unloading during mining. It has also verified the engineering phenomenon of local compression in rockbolts. Test materials similar to deep rock were used to simulate the unloading process of in situ rock mass and verify the physical phenomenon of shrinkage of the rock mass in the unloading area. Based on this phenomenon, the stress arch theory for rock mass failure mode has been established. Finally, numerical simulation analysis of the influence of different radii of the curvature fissures in surrounding rock and the displacement field distribution of the stress field was used to verify the stress arch theory for the failure mechanism of highly stressed rock mass during unloading.

In the Federal Highway Administration (FHWA) laboratory, a phenomenon was identified that reduces soil bearing capacity. This phenomenon arises in common situations, for example, reinforced soil, triaxial tests, mat foundations on sand over bedrock, and other stratified media. In reinforced soil, this reduction is based on reinforcement spacing S and soil particle diameter D. This study provided a generic derivation showing that Coulomb’s failure criterion is triggered by shear stress associated with not only S and D, but also the other dimensions of a soil structure. Although identified and validated in experiments, the S:D instability was verified by finite-element analysis when the number of elements equals the number of soil particles. Static liquefaction was identified with instability and collapse of force chains. Although analysis was performed in the idealized context of unfaced soil structures, FHWA test data demonstrated violent effects on faced structures when the S:D stability limit was exceeded. For narrow structures, this study also evaluated the S:B instability, where B is the breadth of the reinforcement, triaxial test specimen, or foundation mat.

Understanding the mechanical and hydraulic behaviors in a single fracture is important for underground rock engineering. In this study, coupled shear-flow tests were performed on five single fractures with regular dentate asperities, under different constant normal stresses and high inlet hydraulic pressures, to investigate the change of stress, displacement, and flow rate during shear. A new radial flow cubic law was established to estimate the hydraulic behavior, and a two-dimensional (2D) finite-element model, obtained by solving the Navier-Stokes equations, was used to analyze the discrepancy of the values between the new cubic law and experiments. Infilling materials had a strong influence in both mechanical and hydraulic behaviors. The discrepancy and e_m:e_h ratio were influenced by recirculation zones, infilling materials, roughness, contact areas, and inertia force. The nonlinearity of fluid flow caused by inertia force had remarkable influence on hydraulic behavior with high hydraulic pressure. Increasing hydraulic pressure decreased hydraulic conductivity, the e_m:e_h ratio, and discrepancy during the whole shear process.

A straight-shafted cemented stone column technique for effective improvement of soft clay ground was reported in 2017. The method involved transforming the conventionally used uncemented stone or granular mix fill material from a bulging type to a cemented porous fill material of a semirigid nonbulging type. This paper addresses further improvement in the performance of cemented stone columns by incorporating an underreamed enlarged bulb in the column at its bottom or at a suitable intermediate level. Analytical and experimental studies were conducted on such underreamed cemented stone columns in soft clay. Considering an idealized load-transfer mechanism and failure mode, expressions were then developed for predicting the load-carrying capacity of soft clay ground treated with underreamed cemented stone columns. Two cases were considered in the present study: one for an enlarged bulb at the bottom of the stone column and another with a bulb at an intermediate level (at a depth of 5 times the column diameter). The laboratory investigations involved load tests of six unit cells of bulbed cemented stone columns in soft clayey soil, corresponding to area replacement ratios of 4% and 9% and column length ratios of 10, 11.67, and 13.33. The measured values of load-carrying capacity agreed very closely with theoretically computed values. Additionally, straight-shafted conventional uncemented stone columns with four other unit cells were also load tested. The test data of these 10 unit cells in the present study along with the six-unit-cell test data reported earlier were combined and analyzed to evaluate the performance of underreamed cemented stone columns in comparison to other systems of stone columns in soft clays. It was found that the cemented stone columns with an underreamed enlarged bulb at the bottom or at a depth 5 times the shaft diameter were highly effective in improving the soft clay ground condition with respect to both the load-carrying capacity and ground stiffness. The provision of a bulb at the intermediate level was found to be better than a bulb at the bottom of the cemented stone columns.

Protecting the environment from hazardous pollutants associated with waste generation and disposal is a major concern that warrants further investigation. Chemical stabilization is commonly used to improve the engineering properties of soils. The current study examines the characteristics of uncontaminated and copper-contaminated clays stabilized by gypsum. Two clay types, including bentonite (with predominantly montmorillonite mineralogy) and kaolin (with predominantly kaolinite mineralogy), were tested, representing high-swelling and low-strength clays, respectively. An extensive laboratory-testing matrix was developed to investigate the effects of gypsum and copper (Cu) concentrations on the engineering properties of the tested clays, including compaction, Atterberg limits, and unconfined compressive strength (UCS). Additionally, X-ray diffraction, field-emission scanning electron microscopy (FESEM), and X-ray fluorescence tests were conducted to understand the microstructural mechanisms controlling the changes in the engineering properties of the stabilized clays. The UCS test results showed that 7 and 9% gypsum content were optimal for uncontaminated bentonite and kaolin, respectively. The microstructural tests revealed that the added gypsum modified the porous network of the stabilized clays. The level of Cu concentration was found to have a considerable influence on the engineering properties, phases of hydration products formed, and microstructural characteristics of the stabilized clays. These changes are attributed to the retardant effect of Cu on hydration and pozzolanic reactions, which in turn alter the phases of hydration products and cementation structure—the bonding of the clays. The findings suggest that gypsum can offer an economic and effective additive for clay stabilization.

The objectives of this study were to evaluate the fatigue resistance of asphalt binders in relation to their composition and establish the correlation of the fatigue property of asphalt binders with that of mixtures using the viscoelastic continuum damage (VECD) approach. Materials used in the research incorporated reclaimed asphalt pavement, recycled asphalt shingles, warm-mix technologies, and two grades of base binder. Dynamic modulus and direct-tension cyclic fatigue tests were used to assess the linear viscoelastic and fatigue properties of mixtures, respectively. Asphalt binders were extracted, and their linear viscoelastic and fatigue characteristics were determined using frequency sweep at multiple temperatures and the linear-amplitude sweep (LAS) test, respectively. The LAS data were analyzed using the revised VECD formulation, and the parameter denoted as A_LAS was proposed as an indicator of the fatigue resistance of asphalt binders. Mixtures’ fatigue resistance was represented by the newly developed parameter of material fatigue sensitivity (MFS). The experimental evidence suggested that the proposed A_LAS parameter was a valid indicator of the fatigue resistance of asphalt binders. Further, a reasonable correlation was identified between the fatigue resistance of asphalt binders and mixtures, as represented respectively by A_LAS and MFS.

Suction bucket foundations are promising foundation options for offshore wind turbines, which are usually subjected to a relative high lateral-moment loading. To investigate the lateral-moment loading capacity of bucket foundations, a group of three-dimensional finite-element simulations with different bucket dimensions in both loose and dense saturated sand was carried out based on centrifuge tests. The numerical methods were validated by comparisons with the results of centrifuge tests and assessed by sensitivity analyses regarding the influences of soil properties and soil–foundation interface parameters. The interaction between the bucket and surrounding soil was illustrated in order to investigate the bearing behavior and failure mechanism of the bucket foundation. It was shown that in the ultimate state, the maximum passive earth pressure acting on the external skirt in the loading direction is approximately four times larger than that on the internal skirt. Furthermore, parametric studies on the L:D ratios (L is the skirt length and D is the bucket diameter) and loading eccentricity were conducted and discussed. Consequently, a modified calculation method was proposed to predict the ultimate lateral-moment loading capacity of bucket foundations and the method was validated by field and laboratory data.

The creep behaviors of stressed rock are of great practical significance because time-dependent deformation processes can lead to stable dissipation of energy, thereby reducing violent rockbursts or outbursts in underground mines. The numerical manifold method (NMM) is an effective approach to studying the nonlinear creep deformation of rock since it involves the continuous deformation of intact rock, as well as the discontinuous deformation of cracked rock. In this paper, the incremental viscoelastoplastic constitutive relation based on the extended Nishihara model (ENM) has been incorporated into the NMM to study creep deformation of stressed rock. First, an incremental viscoelastoplastic NMM formulation was derived to perform the treatments in the NMM. Using a time-step–initial strain method, viscous strain and the large timescales of typical creep were divided into a series of incremental time-step values in the improved NMM program to calculate the creep deformation of rocks. Parameter sensitivity analysis, which can reveal the influence of different parameters on the creep of rocks, was performed for the improved NMM program, and then the improved NMM program was validated against experimental data. Finally, the influence of axial stress and confining pressure on the creep of rocks was investigated. The fact that numerical simulations were in good agreement with experimental results shows that improving the NMM by combining it with the ENM is suitable for modeling the creep behavior of rocks.

This paper uses finite-element formulation of the lower bound theorem to determine the bearing capacity of ring foundations on dense sand. The results are validated with the plasticity solutions, numerical analyses, laboratory small-scale model tests, and field plate loading tests available in the literature. The Bolton strength–dilatancy relation is then adopted to consider the dependency of the friction angle on the stress level. For solid circular footings, the present results agree well with centrifuge model tests. However, a considerable discrepancy exists between numerical analyses and centrifuge model tests for the ring foundation, particularly when the radii ratio exceeds 0.5. An alternative method is proposed, in which a resistance ratio of the ring foundation to the solid circular footing with the same size is applied to an approximate equation for the bearing capacity of the solid circular footing regarding the stress level effect. The proposed approach is verified with centrifuge model tests.

A stability analysis of slopes is presented using the discretization-based kinematic analysis. By generating a discretized failure mechanism satisfying the kinematic admissibility condition with the use of a discretization technique, the initial analysis of the stability of a steep slope is performed, with the upper bound solutions of critical slope height and stability factor γH/c formulated according to the work rate-based balance equation. Nonuniformity of soil properties is accounted for in the analysis. The log-spiral kinematic solution is also calculated considering the pore water effect and a linearly increased soil cohesion with depth, which shows good agreement with numerical results obtained from different approaches. To analyze a secondary failure due to seismic loading following an initial collapse, the initial failure block is removed, and secondary failure analysis is performed based on the remaining curved sloping surface. Such a slope is deemed stable unless sufficient additional driving forces, such as earthquake loading, cause the slope to fail the second time. In this secondary failure, the focus is placed on the determination of yield seismic acceleration at ultimate failure. Because of the short duration of an earthquake, an undrained stability analysis is presented with a circular rotational failure mechanism; hence, it is not affected by the pore water effect. Following a similar kinematic procedure, the critical seismic acceleration is derived using the work rate-based formula. A parametric study specific to initial and secondary failure is performed to better understand the implications of influential factors affecting slope stability.

Granular collapse is a common issue in natural hazards. This paper proposes a novel numerical approach on modeling granular column collapse. A newly developed critical state–based constitutive model, SIMSAND, was adopted to combine with the smoothed particle hydrodynamics (SPH) method for realistically reproducing large deformation during collapse. A rectangular channel and two-dimensional column tests were first simulated for the validation. The effects of aspect ratio and initial soil density were further investigated by additional simulations. It was demonstrated that the novel SPH-SIMSAND approach is helpful in improving the understanding of granular collapse and should be an effective computational tool for the analysis of real-scale granular flow.

Young loess deposits are the most well-known collapsible soils because of their small unit masses, high void ratios, and open metastable structures. Properly assessing the collapse of loess sites covered by very thick interbedded loess–paleosol strata is complicated because the loess and paleosol layers possess significantly different permeability and collapsibility. The Tongchuan Loess Tableland is one site of such strata, and for this research, laboratory and field tests were conducted to obtain the physical and mechanical properties of the soil for each of the loess and paleosol layers. An in situ soaking test and corresponding computation were also conducted to explore the soaking process, seepage field, and collapse settlement characteristics of the site. Significant differences in collapse settlements were observed between the in situ soaking test and the computed result. The authors deduced that the strata of the test site, disturbances during extraction, drainage conditions, stress history, loading conditions, sampling interval, and magnitude of the collapse criteria could have been the reasons for the differences.

In this study, the bearing capacity of a strip footing placed on the top of a cohesionless soil slope was computed with the use of lower-bound finite-element limit analysis. A single layer of reinforcement was placed below the footing at various depths. The magnitude of N_γ, which is related to the unit weight of soil, was computed by varying the slope angle (β), footing setback distance (b), soil friction angle (ϕ), and depth of the single layer of reinforcement below the footing base (d). As expected, with the use of a reinforcement layer, the bearing capacity increased. The efficiency of reinforcement is expressed by the term η_γ, which is the ratio between the N_γ values obtained for the reinforced and unreinforced slopes. It was observed that η_γ increased with an increase in d up to a certain critical depth (d_cr), after which it decreased. The obtained results are presented as design charts. The axial tension that developed along the reinforcement layer because of the footing load was also calculated, and the variation of the axial tension along the length of the reinforcement is presented graphically. The optimum length of the reinforcement (L_opt) was also computed. The results attained from the present study were compared with the available results from the literature. In addition to the extensive research regarding the foregoing parameters, the effects of ground inclination (α), soil layering, and the water table were also investigated by placing a strip footing on the edge of the cohesionless soil slope. Failure patterns are plotted for some representative cases.

It is widely accepted that the results of wetting tests conducted on collapsible soils by reducing matric suction in consecutive steps in the laboratory provide reliable experimental data for interpreting the soil collapse behavior. The variation of void ratio derived using such a testing technique is similar to that of water content in response to decrease associated with matric suction. For this reason, van Genuchten’s equation for the soil–water characteristic curve was extended to fit the measured data of collapse behavior to describe the variation of void ratio with matric suction. Two of the three fitting parameters in the extended equation, n and m, change negligibly with the applied stress, p whereas another parameter, α, could be represented as a power function of p at a given initial matric suction. For this reason, using the results of two wetting tests performed on identical soil specimens under different applied stresses, the power function is developed for α and the values of n and m are determined; thus, the collapse behavior can be predicted. A good agreement is observed between the collapse behavior predicted using the proposed method and the measured data on collapsible soils in the literature. The proposed method requires less experimental data and hence is simple for use in engineering practice applications.

The strength–dilatancy relationship, which is significantly influenced by the shearing mode, is of great importance in modeling evolution of the mobilized strength and predicting deformations of granular soils. In this paper, the effects of the shearing mode on the strength–dilatancy relation were investigated by performing the multiaxial tests on gravelly soils. It was interestingly found that the gradient of the fitting line for the relationship between the peak–failure friction angle and maximum dilatancy angle increased with increasing the intermediate principal stress ratio b. In particular, for b = 0, the gradient of the fitting line was 0.44 (which was smaller than the Bolton dilatancy index of 0.48). In addition, a strength–dilatancy equation incorporating the effects of shearing mode was proposed for this gravel soil. Thereafter, a general equation between peak friction–failure angle and maximum dilatancy was obtained by using experimental data from the literature and current work for different shearing modes. The two equations were then validated by other independent test data on sands and gravels. It was observed that the general strength–dilatancy equation could well capture the strength–dilatancy relationships on various granular soils, including sands and gravel under different shearing modes.

This note presents a numerical model and investigation of one-dimensional large strain consolidation-induced land subsidence due to groundwater pumping. The model, called CLS1, employs the CS2 methodology and is applicable for settlement of a compressible soil layer due to a reduction in boundary pore pressure under constant overburden stress. Verification checks show excellent agreement with analytical solutions for local degree of consolidation through time. Several numeric examples are presented to highlight capabilities of the new model and emphasize the effect of soil constitutive relationships, soil self-weight, and variable groundwater pumping on consolidation-induced land subsidence. The examples indicate that failure to account for these aspects can yield significant errors in predictions of settlement through time.

Stability of slurry trenches during excavation is a major concern in design and construction. This paper presents an approach for stability analysis of slurry trenches based on Rankine’s theory of earth pressure. The proposed approach is verified via analysis of previously reported problems and is applied to a scenario with a nearby slope. The proposed approach gives the same factor of safety as that found by Coulomb force equilibrium methods. Scenarios with soil stratification and variably distributed surcharges can be analyzed by hand calculation when the proposed approach is used. The investigation also indicates that slurry trench stability is sensitive to surcharges from nearby slopes and that they require particular attention in design.

This paper aims to propose a new method to analyze the stability of a tunnel using P-wave seismic velocity (V_p) with the help of the Tunnel Seismic Prediction 203 plus system (TSP203_PLUS). On one hand, the relationship between Hoek-Brown constants such as the geological strength index (GSI) and the disturbed parameter (D) and V_p is investigated. On the other hand, the displacement of the tunnel is derived using the Hoek-Brown criterion, but it is hard to determine the Hoek-Brown constants because uncertainties are abundant in geomaterials. Fortunately, V_p can be read from TSP203_PLUS, which is an essential approach to predict geohazards in tunnels, and it is widely used during tunnel excavation. A series of parameters such as Young’s modulus, Poisson’s ratio, and the V_p of rocks can be read from TSPwin (the software for processing data in TSP203_PLUS). However, a precise prediction of V_p and other parameters depends mostly on the experience of the engineers. In order to eliminate the uncertainties due to the different engineers, it is reasonable to standardize the parameters as normal variables; then the stability of the tunnel can be calculated based on the response surface method (RSM), and the stability of the tunnel is represented by the probability of failure. To demonstrate the usefulness of this approach, a tunnel located in China is assessed and the results are validated by Monte Carlo simulations. The proposed method provides a convenient and effective method to study the reliability assessment of tunnels.

In this study, an analytical model is proposed to calculate earth pressure considering the displacement of a rigid wall, and this model is developed based on the hyperbolic soil stress-strain relationship. By introducing the soil–failure ratio, the classic limit earth pressure theories can be incorporated into this analytical model. Using the axis-translation method, the earth pressure at rest is the initial state without wall movement. As the wall moves away from the soil mass, the earth pressure decreases and reaches the limit active earth pressure if the wall displacement reaches a threshold value. Similarly, the earth pressure increases to the limit passive earth pressure as the wall moves against the soil mass. This analytical model is verified when compared with experimental and numerical results and can predict the nonlinear earth pressure distribution under various modes of wall movement. This proposed analytical model provides an effective approach to predict the variation of earth pressure, with various wall displacements ranging from the limit active state to the limit passive state.

There are no analytical solutions concerning the consolidation of a clay layer subjected to a ramp load with consideration of the variation of the consolidation coefficient and the nonlinearity of compressibility and permeability of the clay layer. Based on the assumption that the initial effective stress of the clay layer remains constant with depth, an analytical solution for one-dimensional consolidation of a clay layer with variable compressibility and permeability under a ramp load is derived in this study. The solution is validated against the results of the finite-difference method for the same problem. With the proposed solution, the influence of the ratio (C_c/C_k) of the compressibility index (C_c) to the permeability index (C_k) and the final external load (q_u) on the consolidation of clay layer is studied. The results show that C_c/C_k and q_u have significant influence on the behavior of nonlinear consolidation. Both the dissipation rate of the excess pore-water pressure and the average consolidation rate of the clay layer decrease when C_c/C_k increases. When C_c/C_k < 1, the average degree of consolidation represented by the settlement at the same time increases as the final external load (q_u) increases. When C_c/C_k > 1, however, the average degree of consolidation represented by the settlement at the same time decreases when q_u increases. The loading rate has a great influence on the dissipation of excess pore-water pressure, and the rate of nonlinear consolidation decreases when T_vc increases.