This paper presents a rigorous, semi-analytical solution for the drained cylindrical cavity expansion in transversely isotropic sand. The constitutive model used for the sand is the SANISAND-F model, which is developed within the anisotropic critical state theory framework that can account for the essential fabric anisotropy of soils. By introducing an auxiliary variable, the governing equations of the cylindrical expansion problem are transformed into a system of ten first-order ordinary differential equations. Three of these correspond to the stress components, three are associated with the kinematic hardening tensor, three describe the fabric tensor, and the last one represents the specific volume. The solution is validated through comparison with finite element analysis, using Toyoura sand as the reference material. Parametric analyses and discussion on the impact of initial void ratio, initial mean stress level, at-rest earth pressure coefficient and initial fabric anisotropy intensity are presented. The results demonstrate that the fabric anisotropy of sand significantly influences the distribution of stress components and void ratio around the cavity. When fabric anisotropy is considered, the solution predicts lower values of radial, circumferential and vertical stresses near the cavity wall compared to those obtained without considering fabric anisotropy. The proposed solution is expected to enhance the accuracy of cavity expansion predictions in sand, which will have significant practical applications, including interpreting pressuremeter tests, predicting effects of driven pile installation, and improving the understanding of sand mechanics under complex loading scenarios.

The leakage of drainage pipes is the primary cause of underground cavity formation, and the cavity diameter-to-depth ratio significantly affects the overall stability of roads. However, studies on the quantitative calculation for road comprehensive bearing capacity considering the cavity diameter-to-depth ratio have not been extensively explored. This study employed physical model tests to examine the influence of the cavity diameter-to-depth ratio on road collapse and soil erosion characteristics. Based on limit analysis theorems, a mechanical model between the road comprehensive bearing capacity and the cavity diameter-to-depth ratio (FB-L model) was established, and damage parameters of the pavement and soil layers were introduced to modify the FB-L model. The effectiveness of the FB-L model was validated by the data derived from eight physical model tests, with an average deviation of 14.0%. The results indicate a nonlinear increase in both the maximum diameter and fracture thickness of the collapse pit as the cavity diameter-to-depth ratio increased. The pavement and soil layers adjusted the diameter and fracture thickness of the collapse pit to maintain their load-bearing capacity when the cavity diameter-to-depth ratio changed. The fluid erosion range increased continuously with increasing depth of buried soil and was influenced predominantly by gravity and seepage duration. Conversely, the cavity diameter decreased as the buried depth increased, which is associated with the rheological repose angle of the soil. Furthermore, the damage parameters of the pavement and soil layers decrease as the distance from the collapse pit diminishes, with the pavement exhibiting more severe damage than the soil layer. This study provides a theoretical basis for preventing road collapses.

At present, the theory of cavity expansion applied to pipe piles is mostly limited to the assumption of isotropic soil. However, the natural sedimentary site has strong anisotropy, which has an nonnegligible influence on the deformation and failure characteristics of stratum soil. (1) The proposed Von-Matsuoka-Lade(VML) strength criterion is used to describe the failure and yield characteristics of clay, sand and rock. (2) The fabric tensor is introduced to describe the anisotropic properties of clay, and the joint stress tensor is derived based on the isotropic representation of the anisotropic properties. The joint stress tensor Rij is used to represent the isotropic stress space. By mapping the VML criterion in the ordinary stress space to the Von-Mises criterion in the Rij space, the transformed stress method reflecting the anisotropy property can be established. (3) The Unified hardening (UH) model is generalized based on the above anisotropic transform stress method, and the corresponding constitutive equation is derived. (4) Based on the self-similar property of soil deformation around pipe pile in the formation, a new self-similar property solution is proposed and the corresponding radial strain and tangential strain are obtained according to the assumption of radial displacement during pipe pile pressing into the formation, and a new anisotropic soil stress analysis equation reflecting pipe pile static pressing into the formation is obtained by combining with the constitutive equation. The analysis and comparison with the experimental data show that the proposed method of soil stress analysis in anisotropic strata is reasonable and applicable.

The cyclic response in saturated sand is gaining increasing interest owing to the soil-structure interaction in seismic regions. The evolution of the pore water pressure in liquefiable soil can significantly reduce soil strength and impact the structural dynamic response. This paper proposes a semi-analytical solution for a cylindrical cavity subjected to cyclic loading in saturated sands, incorporating an anisotropic, non-associated SANISAND model. The problem is formulated as a set of first-order partial differential equations (PDEs) by combining geometric equations, equilibrium equations, stress-strain relationships and boundary conditions. Due to the non-self-similar nature of this problem, these PDEs are solved by the hybrid Eulerian-Lagrangian approach to determine the cyclic response of the cavity. Then finite-element simulations with a user-defined subroutine are performed to validate the proposed solution. Finally, parametric studies are presented with the focus on soil parameters and cyclic loading history. It is found that the cyclic responses of the cavity in saturated sands are sensitive to the initial void ratio, and the at-rest coefficient of earth pressure primarily affects the monotonic response but marginally affects the cyclic response. Cylindrical cavities are more likely to liquefy when the sands are compacted in a loose state and under lower displacement amplitudes. The proposed solution has potential use for future research on the cyclic response of the soil-structure interaction in geotechnical engineering.

This study introduces a unified cylindrical and spherical cavity reverse expansion model to simulate the formation of compaction grouting bodies and grout diffusion along pile shafts. Stress field expression employs the superposition method, while displacement field analysis utilizes the nonassociated Mohr-Coulomb criterion. By combining the displacement expression for cylindrical cavity reverse expansion with the fluid flow equation, a calculation method is proposed to compute the upward and downward diffusion heights of grout, considering the unloading effect. The parameter analysis demonstrates that ultimate grouting pressure increases with increasing soil strength and grouting depth, with the ultimate grouting pressure at the pile tip being greater than that at the pile side. The value of grout diffusion height is negatively correlated with unloading ratio and grouting depth while positively correlated with grouting pressure and pile diameter. The deeper the grouting depth, the greater the impact of unloading on grout diffusion height. Three case studies validate the effectiveness of the proposed model. Analysis reveals that when grouting pressure exceeds the ultimate pressure, the size of the grout body is related to the grouting volume. Neglecting the unloading effect in the prediction of grout diffusion height for pile foundations would lead to conservative results.

This paper presents a novel analytical framework to predict short-term pile setup in natural structure clay, considering the influence of soil destructuration in installation and consolidation. Based on the cavity expansion method, a simulation of pile installation has been conducted, with an analytical solution formulated for cavity expansion under undrained conditions to capture soil destructuration effectively. The flow rate in the unit cell is determined by Darcy's law based on the soil mass volume change, leading to the consolidation equation, which is obtained in a fully analytical form for excess pore water pressure (EPWP) dissipation. The utilization of the average compression curve aimed to depict a partially disturbed state due to the effects of installation. Based on the rewritten effective stress method (beta method), which involves the time-dependent factor while properly incorporating the effects of relaxation and thixotropy by introducing the requisite parameters. Finally, the analytical framework for predicting short-term pile setup is established and validated through a comprehensive pile field test conducted at St-Alban. The close correspondence between the analytical results and the empirical data indicates the effectiveness of the proposed framework in forecasting short-term pile behaviour with reasonable accuracy.

This paper proposes a coupled hydro-mechanical constitutive model for unsaturated clay and sand (CASM-U) in a critical state framework. The mechanical behaviour of unsaturated soils is modelled by modifying the unified clay and sand model (CASM) with Bishop's effective stress, bounding surface concept and loading collapse (LC) yield surface. The hydraulic behaviour is described by a soil-water characteristic curve (SWCC) with nonlinear scanning law, considering the coupled effects of soil deformation and hysteresis. CASM-U is implemented into a commercial finite element software through the user-defined material subroutine (UMAT), and the implementation is benchmarked by a new semi-analytical cavity expansion solution adopting CASM-U. Finally, the performance of CASM-U in predicting hydro-mechanical behaviour of unsaturated clays and sands is examined by comparing with experimental data from tests along various loading paths, including isotropic compression, cyclic drying-wetting, triaxial shearing, and their combinations. It is shown that CASM-U can provide reasonable predictions for hydro-mechanical behaviour of unsaturated soils with a total of 15 material parameters.

Many geotechnical scenarios involve cavity unloading from a loaded state, particularly in pressuremeter tests, and the unloading data of pressuremeter tests has exceptional attraction as it is less disturbed by the insertion process. However, the analyses for continuous cavity loading and unloading (i.e., cavity initially experiences expansion and then contracts) in critical state soils are rarely studied. To this end, a novel semi-analytical solution based on the unified state parameter model for clay and sand (CASM) is proposed for the whole expansion-contraction of spherical and cylindrical cavities under undrained conditions. The problem assumes that the cavity is unloaded after a monotonic loading stage, leading to plastic regions during both loading and unloading periods. The cavity response for the whole expansion-contraction process is investigated, with the total pressure and stress paths at the cavity wall presented and validated against numerical simulation. The developed solution is successfully implemented to interpret both loading and unloading data of pressuremeter tests. The undrained shear strength, in situ effective horizontal stress and initial overconsolidation ratio are back analyzed by using a curve fitting method based on the proposed solution.

Cylindrical cavity exhibits non-self-similarity during contraction process following expansion. Previous studies solve this problem with total strain approach and simple constitutive models, but the approach is not applicable when using an advanced constitutive model. This paper presents a semi-analytical solution for a cylindrical cavity undergoing expansion-contraction in undrained soils with auxiliary variable approach, incorporating the Modified Cam-Clay (MCC) model. The stress states around the cavity are formed by the superposition of initial and superimposed stress states. By treating superimposed effective stresses as self-similar, a semi-analytical solution is derived for solving the cavity expansion-contraction problem. The elastoplastic stress-strain relationship is formulated as a set of first-order differential equations, which can be solved as an initial value problem though Runge-Kutta (RK) method. Then the stress distribution around the cavity during expansion-contraction process can be determined. To validate the proposed approach, a series of well-conduced self-boring pressuremeter (SBP) tests are used to verify the proposed approach, which shows good agreements. Additionally, a FEM simulation incorporating the MCC model is performed, and the simulation results are presented to carry out parametric studies on soil parameters. A significant influence on the range of the plastic and reverse plastic zones is shown for overconsolidation ratio, while the in-situ coefficient of the earth pressure only quantitatively affects the stress distribution.

Minimizing the damage caused by landslide disasters in regions with complex geological conditions requires the development of effective and reliable methods for assessing slope stability. This study aims to generate and analyze the stability of random soil-rock mixture slope models, considering the rock block content, spatial distribution, and convexity-concavity feature of rock blocks in the slope. A Python script was developed to create these random soil-rock mixture models using the ABAQUS finite element software. Additionally, the strength reduction technique was applied to calculate the factor of safety via a USDFLD subroutine implemented in ABAQUS. A series of numerical analyses were conducted to assess the impact of rock block content and the convexity-concavity feature of rock blocks on the stability of soil-rock mixture slopes. Moreover, the impact of the random spatial distribution of rock blocks on the stability of soil-rock mixture slopes was discussed. The results show that rock block content below 20% can affect slope stability both negatively and positively. Notably, significant improvements in the stability of soil-rock mixture slopes are observed only when the rock block content exceeds 30%. Furthermore, the convexity-concavity feature of rock blocks can improve the safety factor of the slopes. This study provides a comprehensive methodology and serves as a valuable reference for estimating the safety factor of soil-rock mixture slopes using the finite element method.