International Journal of Geomechanics

The study of strata behaviors of hard, thick stratum (HTS) and faults in underground coal mines is significant to understanding and predicting the mechanism of rock bursts. By considering the occurrence of a HTS and a normal fault (NF), the strata behaviors and rock burst–inducing mechanism were studied using the universal distinct element code (UDEC) numerical simulation and field observation. The results show that prior to failure, a HTS continues to suspend and the lower strata breaks and moves easily because of fault cutting and fault activation. This process induces microseismic events accompanied by the release of a small amount of energy that concentrates near the fault and beneath the HTS. However, the mining stress concentrates and strain energy accumulates in the surrounding rocks because of the large-scale suspension of the HTS, thereby providing sufficient energy for rock bursts to occur. When the HTS suspension increases to the ultimate span, the HTS breaks and slips along the fault plane. Moreover, the fault-plane stress varies notably and the fault slipping is clear. These conditions indicate that the fault activates and destabilizes violently. A large amount of strain energy is released because of the HTS failure and fault slipping, easily inducing violent rock bursts. Hence, the mechanism that induces rock bursts can be divided into two stages: the accumulation of strain energy prior to HTS failure and the release of strain energy because of the coupling effect of HTS failure and fault slipping. In particular, more attention should be paid to the latter stage.

The consolidation of soils is important to geotechnical engineering practice, such as when assessing the rate of settlement of shallow foundations, embankments, and landfills. In this paper, numerical analyses are performed to study the consolidation of unsaturated soils. The variations of excess pore-air and pore-water pressures and settlement with time are established by solving the governing equations. The flow and deformation of the different constituents of an unsaturated soil are fully coupled in the governing equations. The dependency of soil parameters, including the coefficients of permeability for air and water phases and the constitutive coefficients, is allowed to vary as changes to soil volume and suction occur. The effect of hydraulic hysteresis is investigated by considering different initial locations of the hydraulic states on the soil-water characteristic curve. It is shown that the different initial locations of hydraulic states result in different normalized instantaneous settlements and different initial excess pore pressures. The influence of the degree of saturation is also studied. It is shown that for the lowest degree of saturation, the most significant instantaneous settlement occurs and the total consolidation time is longest. The results of this study provide new insights into unsaturated soil consolidation. This is important because the hydraulic loading history and degree of saturation of the soil should be considered when assessing the rate and magnitude of consolidation settlement.

The freeze-thaw damage of rock is mainly induced by the 9% volumetric expansion of frozen water. It has already been demonstrated that unfrozen water exists in porous material at the freezing point. Accurate estimation of unfrozen water content is important for evaluating freeze-thaw damage and understanding freezing processes in rock. To derive the unfrozen water content, the freezing process of pore water and freezing strain of saturated rock under low temperature were studied. Based on the cumulative distribution curve of pore size, the unfrozen water content is proved to be an exponential function of freezing temperature. Unfrozen water mainly occupies nanopores and has no effect on the freezing strain of rock. The freezing strain of rock under subzero temperature is composed of matrix shrinkage caused by falling temperature and pore expansion by pore-ice pressure. Thus, a theoretical model that accommodates the relationship between freezing strain and unfrozen water content considering the phase transition is proposed according to saturated poroelasticity theory. Using this model, the unfrozen water content can be accurately calculated by measuring the freezing strain of saturated rock. Three examples of freezing strain tests demonstrate that the freezing strains derived from this theoretical model are in good agreement with the experimental values for saturated rock with different porosities and that the unfrozen water content can be easily and accurately determined.

This article presents an experimental laboratory study on the effect of plastic compression and stress history on the small strain shear modulus, G_max, of unsaturated soils. In previous studies, most of the experiments for the measurement of the G_max values of unsaturated soils were performed along the elastic unloading–reloading curve of the compression curve, and the effect of plastic compression on the measured G_max was ignored. This research aimed to provide a set of high-quality G_max data along elastoplastic paths of the compression curve that can be used to further investigate this effect. In this study, a bender element system was used to measure G_max values under different matric suctions and mean net stresses, the axis translation technique was implemented for suction control, and high values of confining pressure were applied using a high-pressure hydraulic pump. A digital image processing (DIP) method was also used to measure changes in the soil specimen’s volume during loading. Experimental results showed an increase in the small strain shear modulus during loading, with trends that follow transitions in the shape of the curve for void ratio versus mean effective stress. During unloading, the values of unsaturated small strain shear modulus were observed to decrease with a mean net stress decrease while being consistently higher than those measured during loading at the same stress levels. This study also highlighted the effects that hydraulic hysteresis and the initial loading conditions might have on the values of G_max measured during loading and unloading. Finally, the G_max values measured in this study were used to evaluate the accuracy of an existing model in predicting the small strain shear modulus of unsaturated soils along elastoplastic paths of the compression curve.

Solutions for cylindrical cavity expansion have been studied widely in many aspects, but the analysis of expanded radius and internal expanding pressure is rarely found. In practical engineering, it is of great significance to determine the relationship of the initial expanded radius (a₀) and expanding pressure (p). Based on the unified strength theory (UST), a theoretical relationship among the initial radius (a₀), the expanded radius (a), and the expanding pressure (p) of the cylindrical cavity was derived under the condition of nondrainage. By using the theoretical relationship obtained, the limit expanding pressure (p_u) and the stress and displacement fields were achieved, as well as the plastic-zone radius (r_p). The influence of the intermediate principal stress coefficient (b) on stress fields and expanding pressure (p_u) is also discussed. A parametric study showed that the stress and displacement fields in undrained conditions are only related to the initial radius (a₀) and the expanding pressure (p), and the expanded radius (a) is a function of the expanding pressure (p) under a given initial radius (a₀). In addition, the effect of intermediate principal stress on the p_u is nonnegligible, whereas the effect on the stress is limited. At last, the validation of the proposed theoretical solution was demonstrated by comparing with the conventional theoretical solution and field test results.

Numerous nonlinear theories of consolidation for clay soils have been proposed in the past. Most of them are based on constitutive models of clays whose structural property is neglected, yet the natural structured soils are widely distributed around the world. This study investigated the nonlinear consolidation of natural structured clays using a semianalytical method. Variable permeability and compressibility were considered, as were variable overburden pressure and yield stress with depth and arbitrary loading with time. Simplified models were developed, and the process of consolidation was analyzed in detail. Calculation methods and solutions were determined. Then, a computational program was developed for verification and calculation. The present regressive solutions were found to compare well with the existing solutions, indicating that the solutions are correct and reliable. Finally, the nonlinear consolidation behavior influenced by several factors was investigated using parametric analysis.

Rockfall is a common geological hazard in mountainous areas and can pose great danger to people and properties. Understanding the impact forces induced by a single rock or a rock cluster on retaining structures is considered key in the analysis and design of protection barriers. This study presents the results of small-scale laboratory experiments conducted to measure the impact forces induced by a group of rocks moving down a rough slope on a barrier wall. The effect of slope inclination angle and wall location on the impact pressure acting on the wall was examined. A three-dimensional discrete element model was then proposed and used to study the behavior of the rock cluster under different geometric conditions. Rocks were modeled using polydisperse clumps in which each clump consisted of several overlapping spherical particles to account for the shape effect of the falling rocks. First, the model was validated by comparing the measured and calculated forces, and then, it was used to investigate the role of different material and geometric parameters on the impact behavior. Conclusions were made regarding the role of modeling the irregular rock shapes and the roughness of the slope surface on the behavior impacted by the travel mode for different slope angles.

Overconsolidated unsaturated soils emerge in many engineering problems. This article presents a constitutive model for unsaturated soils using skeleton stress and degree of saturation as fundamental variables. A subloading surface is introduced into the framework to interpret the effect of overconsolidation on the coupled hydromechanical behavior of overconsolidated unsaturated soils. The main advantage of the proposed model is that it is capable of reproducing the hydromechanical behavior of unsaturated soils with different initial overconsolidation ratios, such as the overconsolidation effect on the shearing-induced saturation change. The material parameters of the proposed model can be calibrated through conventional tests. Numerical studies were conducted to assess the performance of the model for a fictional silt under two typical scenarios. The validity of the proposed model was confirmed by experimental results for both isotropic and triaxial conditions reported in the literature.

Although the pile-raft foundation is preferred for supporting a tall wind turbine, the geotechnical design and selection of suitable design parameters are based on a complex procedure. Except the foundation, all the other aboveground components are precast members that are assembled at the project site to build a wind turbine. Therefore, it is necessary to consider the possible variations in soil properties and wind speed in the design of the foundation. In this paper, a reliability-based robust design procedure for a pile-raft foundation that supports a 130-m-tall wind turbine on a layered clayey soil is presented. Upon completion of the geotechnical design for the mean wind speed and undrained shear strength, a parametric study and Monte Carlo simulation were conducted by varying the wind speed and the undrained cohesion of each layer to establish a relationship among the design variables (number and length of piles and radius of the raft) and the random variables (wind speed and undrained cohesion). Finally, a reliability-based robust design was created considering the total cost and robustness as the objectives. The standard deviation of the response of concern, which is the differential settlement, was considered the measure of robustness. The optimization yielded a set of preferred designs known as the Pareto front, and the suitable design was selected for a given cost limitation and performance requirement using the Pareto front.

This paper presents a semi-analytical solution to Fredlund and Hasan’s one-dimensional consolidation for unsaturated soils subjected to exponentially time-growing drainage-boundary conditions. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform method. Then, pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. Crump’s method is adopted to perform the inverse Laplace transform to obtain semi-analytical solutions for the time domain. It is shown that the present solution is more general and applicable to various types of boundary conditions. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, and mixed drainages. Finally, changes in pore-air and pore-water pressures and soil settlement with the time factor at different values of the boundary condition parameters are illustrated. In addition, parametric studies are conducted using different ratios of the air–water permeability coefficient to investigate the variations of pore-air and pore-water pressures.

Enhanced oil recovery (EOR) methods were processed to increase the amount of oil extracted from a reservoir after primary and secondary recoveries, typically by injecting water or gas. Fluid injection has been vastly applied in oil wells as a simple and effective EOR method. Rocks are a combination of different materials that exhibit poroelastic response. The amount of stress indexed by pore pressure depends on pore content. Rock stress around a wellbore is a function of wellbore fluid flow. On the other hand, fluid flow is the function of porosity and permeability. Nevertheless, porosity and permeability alter as stress changes. Therefore, a coupling method should be used. The purpose of this study is to propose a model to find corrected stresses and calculate the change in porosity and permeability after injection. This study focuses on wellbore results. Effective parameters, such as pressure, temperature, saturation, and stress, were obtained for the multiphase flow condition using mathematical modeling. Moreover, pressure and saturation are solved using the finite-difference method, whereas the finite-volume method is applied to obtain rock stresses. The iterative coupling method is used to improve the accuracy of results. The results of the study showed how porosity and permeability will change after drilling around the well and how they will increase during injection. The results expressed the corrected distribution of stress values after injection. Porosity and permeability were reduced from their original values after drilling; nonetheless, their values had increased after injection but not equally around the wellbore. Moreover, it was concluded that the change in porosity and permeability by injection was more significant in low-porosity formations.

The microstructure that lies within a continuum sometimes plays a very important role, and hence, mechanics associated with the microstructure cannot be disregarded during the study of elastodynamic problems in such a structure. Also, the bonding between the stratum in the composite structure is not always perfect. Therefore, the present paper investigates the effect of imperfect interfacial bonding on Love wave propagation in a vertically heterogeneous fiber-reinforced stratum lying over a micropolar elastic substrate. Under imperfect bonding conditions, the dispersion relation affecting the Love wave was derived analytically. The study reveals that wave number, k, coupling factor, N, and a imperfectness parameter, Γ disfavor the phase velocity of a Love wave, whereas reinforcement, μ_L/μ_T, heterogeneity, ν, and micropolarity, ${kH}^{\prime 2}/\gamma$, favor the phase velocity of a Love wave. The influence of a complex interface on the phase velocity of a Love wave was analyzed meticulously, and it was found that a flexibility imperfectness parameter encourages, whereas a viscoelastic imperfectness parameter discourages, the phase velocity; however, the effect of the viscoelastic imperfectness parameter is dominating.

The prediction of the bearing capacity (q_rs) of unreinforced sand bed and geogrid-reinforced sand bed resting over a group of stone columns floating in soft clay is an important task due to the complex geometry and uncertainty involved in the different geotechnical parameters. Moreover, there is no established bearing capacity equation available on this topic. Because of the complex, elaborate, and expensive estimation of q_rs, it is required to develop a precise prediction model, which is supposed to be nonlinear. In this study, the potential of the support vector regression (SVR) technique for q_rs prediction is investigated. The performance of the SVR model with three different kernel functions is examined. The prediction performance of the SVR model with exponential radial basis kernel (ERBF) is compared with the artificial neural network (ANN) model. A sensitivity analysis is also performed to demonstrate the effectiveness of each input variable on q_rs. Finally, using the SVR-ERBF model an empirical equation is proposed to predict tq_rs for practical application purposes. Obtained results approve the robustness of the SVR-ERBF model for indirect prediction of q_rs.

Cone-penetration resistance in unsaturated soils may differ from that in dry or saturated soils. A finite-element numerical model simulating the cone penetration process in soil inside a calibration chamber is explained. An arbitrary Lagrangian-Eulerian algorithm was used to overcome the mesh distortion caused by large deformation during penetration. Predicted cone-resistance profiles were validated using calibration-chamber test results and empirical data. Unsaturated soil was modeled using two different approaches: incorporating apparent cohesion in standard constitutive relations and implementing an elastoplastic constitutive model for unsaturated soils. Both approaches resulted in cone-resistance profiles that were in fair agreement with the calibration-chamber data. However, the reasonably successful use of simpler constitutive models with fewer material parameters may be an appropriate option for such applications. Investigations into the effect of degree of saturation on the cone resistance revealed the significant influence of interparticle suction on soil resistance, while they also show that neglecting the saturation effect may lead to unreliable evaluation of soil properties.

The structure of the layered rocks is characterized by oriented bedding planes, resulting in transverse isotropy in deformation and strength. An elastoplastic constitutive model was proposed for transversely isotropic (TI) rock in this study. In the model, the generalized Hooke’s law was adopted for the elastic behavior. For the plastic behavior, the yield criterion and plastic potential are formulated as functions of the generalized octahedral shear stress and the first invariant of stress tensor. A nonassociated flow rule and a stress-dependent hardening rule were adopted in the model. The plastic model can be simplified to the Drucker-Prager model for isotropic rocks. A methodology for the determination of model parameters was developed. The parameters can be determined by combining triaxial compression tests with torsion tests on specimens with different bedding directions. The constraint on plastic parameters was theoretically identified. The proposed model and the parameter determination methodology were applied to modeling the TI elastoplastic property of carbonaceous slate in triaxial compression. The results show that the model proposed in this study can well describe the transverse isotropic elastoplastic property of the rock, and the parameter determination methodology is simple and effective.

The study investigated the mechanical behavior of fine-grained sandstone. Laboratory triaxial cyclic loading tests were conducted on the sandstone under various confining pressures (5, 15, and 20 MPa). The initial yield stresses ${\sigma }_y$ were approximately 69.0–74.0% of the peak strengths under the different confining pressures, and the residual strengths ${\sigma }_s$ were 39.5–43.5% of the peak strengths. Based on the experimental results, a coupled elastoplastic damage model for the sandstone is proposed along with a nonassociated plastic potential function. In addition, an isotropic damage evolution model has been formulated with plastic coupling for the sandstone. Furthermore, the numerical formulations of a return mapping algorithm for the implementation of the coupled model are introduced in detail. The numerical results were found to be in good agreement with the experimental data, showing that the model is able to describe the main features of the mechanical behaviors of the fine-grained sandstone.

The effect of nonuniform consolidation on the average degree of consolidation (DOC) under the one-dimensional (1D) condition is investigated through a laboratory model test and finite-element analyses (FEAs). Nonuniform consolidation refers to spatial and time variations in the permeability (k_v) and coefficient of volumetric compressibility (m_v) of soil induced by the consolidation process. A 1D laboratory consolidation test was conducted and analyzed using consolidation theory and FEAs. In FEAs, the spatial variations of k_v and m_v of the soil within the domain are simulated. By comparing the results of the test and FEAs with the analytical results, the effect of nonuniform consolidation on the average DOC is confirmed. Based on the results of FEAs, a method for considering the effect of the nonuniform consolidation in Terzaghi’s 1D consolidation theory is proposed.

A semianalytical solution to determine the minimum safety thickness of the rock resisting water inrush from filling-type karst caves was investigated. Mechanical analyses of the filling materials in karst caves located in a top, bottom, and lateral position to the tunnel were carried out by referring to the principle of the slice method. The mechanical mechanism of rock resisting water inrush was analyzed by adopting the theory of elastic mechanics. The semiquantitative analytical method for calculating the minimum safety thickness of the rock for resisting water inrush was achieved according to the bending strength and shear strength of the rock. The safety-thickness-prediction models of rock for resisting water inrush were applied in practical projects of the Luzhuba tunnel. The accuracy and availability of the proposed method were proven by comparing with the rock stratum thickness–span ratio method. The minimum safety thickness affected by the depth-span ratio of the filling-type karst cave, shear strength indexes of the filling materials, and the depth of the tunnel was analyzed and discussed. The results show that the minimum safety thickness of the rock resisting water inrush (1) decreases 0.02 m for every 2-m increase in cave height and increases 0.01 m for every 2-m increase in cave span such that the influence of the karst cave height is greater than the karst cave span on the minimum safety thickness; (2) decreases gradually with an increase of effective soil cohesion and decreases 0.03 m for every 5° increase in effective internal friction angle of the soil; and (3) increases 0.18 m for every 1-m increase in tunnel depth.

Ring shear tests were performed in this work to investigate the characteristics of shear band formation and particle breakage for calcareous sands sampled from the South China Sea. The tests focused on the formation of shear band and the evolution of particle breakage under various levels of loading stress, together with sensitivity analyses of the initial sample grading and shear rate. The breakage of particles has a significant influence on the stress-strain relationship, volumetric deformation, and final grading of calcareous sands. In particular, the calcareous sand specimen tends to remain at a constant volume and a stable grading at shear strains larger than 2,000%. The change of the microstructure of calcareous sands during shearing has been illustrated by scanning electron microscopy (SEM) images, showing clear evolution of particle breakage and surface smoothness within the shear band. A considerable amount of fine particles (<0.074 mm) was produced during the tests, and the final complete particle-size distribution was obtained with a laser diffraction particle-size analyzer. The findings of this study improve the understanding of calcareous sands by showing that they can be crushed readily under normal loading stress levels as long as the shear strain continues.

Combining tomographical reconstructed volumes and direct pore-scale flow simulations has proven to be an efficient tool in modern soil sciences. The main objective of the present paper is to present an extensive study about the usage of micro–computed tomography to obtain transport properties of porous media. The transport properties are obtained by means of pore-scale simulations whose domains are the pore space of the tomographical images of three different materials: glass spheres, sand, and clay. The main discussion in the present paper regards the definition of the representative elementary volume (REV). To address this issue, statistical analyses were carried out, showing that the REV concept is scale-dependent. Also, some guidelines considering the specification of the numerical domain size are discussed. It is shown that, for the glass spheres and sand, the coefficient of variation (CV) of the permeability decreases as the simulation domain increases, reaching values as low as 20%. In contrast, for clay samples, the CV does not show a clear decreasing tendency, and its values are approximately 75% for the largest domain size considered. Hypothesis tests were used to show that more than one domain size can be considered a REV (i.e., there are different minimum domain sizes for which permeability and porosity can be evaluated), and these values can be used to predict the transport properties of a larger part of the domain at a given scale.

A new gradation equation that can describe the particle-size distribution curves of soils with continuous gradation is presented. The results obtained for a large amount of test data from soil gradations prove that the equation is applicable over a wide range of soils, including rockfill, gravel, sand, and clay. Three parameter determination methods are proposed, with the optimization method yielding the best results. The possible values of the parameters m and b in the proposed equation were intensively investigated, and the suggested ranges of the parameters were found to be b < 1 and m > 0. However, for most soils, these parameters have values of –4 < b < 1 and 0 < m < 12. The study of the features of the gradation equation and the resulting curves in P-logd coordinates revealed that the parameter b determines the gradation curve shape. If b ≤ 0.5, the gradation curve is hyperbolic, and if 0.5 < b < 1, the curve is sigmoidal. The parameter m determines the gradation curve slope, which increases with increasing m. Several soil gradations used in earth-rockfill dams worldwide were investigated to summarize the gradation characteristics, and the results revealed that the values of the parameters b and m for the rockfill fall within a narrow range. The proposed equation is more convenient for expressing the soil gradation and makes it possible to quantitatively describe the relationship between the mechanical properties of the rockfill and the gradation.

This paper presents a method to determine the optimal set spacing for rigid-type galvanized I profile (GI) and Toussaint-Heintzmann (TH)–type yielding steel sets in Section A of the Omerler underground coal mine. The rock mass rating (RMR) and geological strength index (GSI) were determined by using field data and the measured mechanical properties of intact rock samples. The support pressure was calculated using the convergence–confinement method, and the support-capacity curves were plotted for a range of set spacing values. The intersection of the support-pressure and support-capacity curves was identified as the minimum set spacing that can provide stability in the roadways. A study to determine the optimal and most cost-effective designs was conducted for hanging wall, footwall, and coal sections, and these designs were verified using FEM software. According to the FEM results, applying the GI 120 profile to the set spacing decreases the deformations around the roadways for all hanging wall, footwall, and coal sections. In contrast, TH 34–type yielding steel sets will only work for coal sections because of the low deformation rates of hanging wall and footwall.