This paper presents an elastic-plastic solution for the circular tunnel of elastic-strain softening behavior considering the pressure-dependent Young's modulus and the nonlinear dilatancy. The proposed solution is verified by the results of the field measuring and numerical simulation from a practical project, and a published closed-form analysis solution. The influence of each factor is discussed in detail, and the ability of Young's modulus and dilatancy characterizing the mechanical response of surrounding rock is investigated. It is found that, in low levels of support pressure, adopting the constant Young's modulus model will seriously misestimate the surrounding rock deformation. Using the constant dilatancy model will underestimate the surrounding rock deformation. When adopting the constant dilatancy model, as the dilation angle increases, the range of the plastic region increases, and the surrounding rock deformation weakens. When adopting the nonlinear dilatancy, the plastic region range and the surrounding rock deformation are the largest. The surrounding rock deformation using pressure-dependent Young's modulus model is between those resulted from two constant Young's modulus models. The constant α of pressuredependent Young's modulus model is the main factor affecting the tunnel displacement. The influence of α using a constant dilatancy model is much more apparent than that using a nonlinear dilatancy model.

The deformation of the rock surrounding a tunnel manifests due to the stress redistribution within the surrounding rock. By observing the deformation of the surrounding rock, we can not only determine the stability of the surrounding rock and supporting structure but also predict the future state of the surrounding rock. In this paper, we used grey system theory to analyse the factors that affect the deformation of the rock surrounding a tunnel. The results show that the 5 main influencing factors are longitudinal wave velocity, tunnel burial depth, groundwater development, surrounding rock support type and construction management level. Furthermore, we used seismic prospecting data, preliminary survey data and excavated section monitoring data to establish a neural network learning model to predict the total amount of deformation of the surrounding rock during tunnel collapse. Subsequently, the probability of a change in deformation in each predicted section was obtained by using a Bayesian method for detecting change points. Finally, through an analysis of the distribution of the change probability and a comparison with the actual situation, we deduced the survey mark at which collapse would most likely occur. Surface collapse suddenly occurred when the tunnel was excavated to this predicted distance. This work further proved that the Bayesian method can accurately detect change points for risk evaluation, enhancing the accuracy of tunnel collapse forecasting. This research provides a reference and a guide for future research on the probability analysis of tunnel collapse.

Stone columns are widely used to treat soft clay ground. Optimizing the design of stone columns based on cost-effectiveness is always an attractive subject in the practice of ground treatment. In this paper, the design of stone columns is optimized using the concept of robust geotechnical design. Standard deviation of failure probability, which is a system response of concern of the stone column-reinforced foundation, is used as a measure of the design robustness due to the uncertainty in the coefficient of variation (COV) of the noise factors in practice. The failure probability of a stone column-reinforced foundation can be readily determined using Monte Carlo simulation (MCS) based on the settlements of the stone column-reinforced foundation, which are evaluated by a deterministic method. A framework based on the concept of robust geotechnical design is proposed for determining the most preferred design of stone columns considering multiple objectives including safety, cost and design robustness. This framework is illustrated with an example, a stone column-reinforced foundation under embankment loading. Based on the outcome of this study, the most preferred design of stone columns is obtained.

This paper investigates the effect of the width of failure and tension crack (TC) on the stability of cohesive-frictional soil slopes in three dimensions. Working analytically, the slip surface and the tension crack are considered to have spheroid and cylindrical shape respectively, although the case of tension crack having planar, vertical surface is also discussed; the latter was found to return higher safety factor values. Because at the initiation of a purely rotational slide along a spheroid surface no shear forces develop inside the failure mass, the rigid body concept is conveniently used; in this respect, the validity of the rigid body concept is discussed, whilst it is supported by comparison examples. Stability tables are given for fully drained and fully saturated slopes without TC, with non-filled TC as well as with fully-filled TC. Among the main findings is that, the width of failure corresponding to the minimum safety factor value is not always infinite, but it is affected by the triggering factor for failure (e.g., water acting as pore pressures and/or as hydrostatic force in the TC). More specifically, it was found that, when a slope is near its limit equilibrium and under the influence of a triggering factor, the minimum safety factor value corresponds to a near spherical failure mechanism, even if the triggering factor (e.g., pore-water pressures) acts uniformly along the third dimension. Moreover, it was found that, the effect of tension crack is much greater when the stability of slopes is studied in three dimensions; indeed, safety factor values comparable to the 2D case are obtained.

Polyacrylamide (PAM) possesses high water absorption capacity and a unique pH-dependent behavior that confer large potential to enhance the engineering performance of clays. In this study, calcium bentonite was treated with a nonionic PAM. Flexible-wall permeability test and the consolidation test were performed at different pH values to evaluate the effects of PAM treatment on the hydraulic and consolidation properties. Test results demonstrate that index properties are affected by the adsorbed PAM on clay surface: a decrease in specific gravity, a decrease in net zeta potential, and an increase in liquid limit are observed due to the PAM treatment. At a given pH, the compressibility of the treated clay is greater than that of the untreated clay. However, the compression indices of untreated and treated clays can be expressed as a single function of the initial void ratio, regardless of pH. Hydraulic conductivity is reduced by PAM treatment about 5 times at both neutral and alkaline pH conditions under similar void ratios, because of the reduction in size of the water flow channel by PAM expansion. However, at acidic pH, the hydraulic conductivity of the treated clay is slightly higher than the untreated clay. This reflects that the treated bentonite with PAM can be beneficially used in barrier system for highly alkaline residues.

The uncertain geotechnical properties of frozen soil are important evidence for the design, operation and maintenance of the frozen ground. The complex geological, environmental and physical effects can lead to the spatial variations of the frozen soil, and the uncertain mechanical properties are the key factors for the uncertain analysis of frozen soil engineering. In this study, the elastic modulus, strength and Poisson ratio of warm frozen soil were measured, and the statistical characteristics under different temperature conditions are obtained. The autocorrelation distance (ACD) and autocorrelation function (ACF) of uncertain mechanical properties are estimated by random field (RF) method. The results show that the mean elastic modulus and mean strength decrease with the increase of temperature while the mean Poisson ratio increases with the increase of temperature. The average values of the ACD for the elastic modulus, strength and Poisson ratio are 0.64m, 0.53m and 0.48m, respectively. The standard deviation of the ACD for the elastic modulus, strength and Poisson ratio are 0.03m, 0.07m and 0.03m, respectively. The ACFs of elastic modulus, strength and Poisson ratio decrease with the increase of ratio of local average distance and scale of fluctuation. The ACF of uncertain mechanical properties is different when the temperature is different. This study can improve our understanding of the spatial autocorrelation variations of uncertain geotechnical properties and provide a basis and reference for the uncertain settlement analysis of frozen soil foundation.

Quantification of the influence of the fracture of thick magmatic rock (TMR) on the behavior of its overlying strata is a prerequisite to the understanding of the deformation behavior of the earth's surface in deep mining. A three-dimensional numerical model of a special geological mining condition of overlying TMR was developed to investigate the overburden movement and fracture law, and compare the influence of the occurrence horizon of TMR. The research results show that the movement of overlying rock was greatly affected by the TMR. Before the fracture of TMR, the TMR had shielding and controlling effects on the overlying strata, the maximum vertical and horizontal displacement values of overlying strata were 0.68 m and 0.062 m. After the fracture, the vertical and horizontal displacements suddenly increased to 3.06 m and 0.105 m, with an increase of 350% and 69.4%, respectively, and the higher the occurrence of TMR, the smaller the settlement of the overlying strata, but the wider the settlement span, the smaller the corresponding deformation value of the basin edge (the more difficult the surface to crack). These results are of tremendous importance for the control of rock strata and the revealing of surface deformation mechanism under TMR mining conditions in mines.

This paper is concerned with the thermoelastic bending of FG beams resting on two-layer elastic foundations. One of these layers is Winkler springs with a variable modulus while the other is considered as a shear layer with a constant modulus. The beams are considered simply supported and subjected to thermo-mechanical loading. Temperature-dependent material properties are considered for the FG beams, which are assumed to be graded continuously across the panel thickness. The used theories contain undetermined integral terms which lead to a reduction of unknowns functions. Several micromechanical models are used to estimate the effective two-phase FG material properties as a function of the particles' volume fraction considering thermal effects. Analytical solutions for the thermo-mechanical bending analysis are obtained based on Navier's method that satisfies the boundary conditions. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models, geometric parameters, temperature distribution and elastic foundation parameters on the thermoelastic response of FG beams.