Mohr-Coulomb Yield Criterion Research Articles

A Novel Strength Reduction Method for a Slope Stability Assessment Based on a Finite Element Method

Ensuring the stability of slopes is critical to the safe operation of geotechnical engineering. Evaluating slope stability to minimize geologic risks induced by destabilization is significant in reducing casualties and property damage. A conventional, single-coefficient strength reduction method is widely applied in slope stability analyses, but this method ignores the attenuation degree of different parameters in the slope destabilization. A new double-strength reduction method considering different contributions of the mechanics’ parameters is proposed in this study for evaluating the stability of nonhomogeneous slope. First, the role of each mechanic’s parameters in the slope destabilization was investigated theoretically and numerically using ABAQUS software 2022. The results indicate that the effect of elasticity (E), Poisson’s ratio (v), and soil gravity (γ) on the evolution of factor of safety (FOS) are insignificant and can be neglected compared with cohesive force (c), and angle of internal friction (φ). Next, an improved method was constructed to correlate the FOS with cohesive force (c) and the angle of internal friction (φ). Then, a numerical method was constructed based on the computation of the mathematical–mechanical relationship between FOS and the mechanical parameters, and the stability of slope is estimation based on the Mohr–Coulomb yield criterion. Finally, the double-strength reduction coefficient method proposed in this study, the limit equilibrium method, and the traditional finite element strength reduction coefficient method were applied to nonhomogeneous slopes and slopes containing a soft underlying layer for comparison, and the difference between them was within the range of ±5%. The results indicate that both the limit equilibrium method and the traditional finite element strength reduction method tend to overestimate the FOS of intricate slopes compared with the evaluated method proposed in this study. This parallel comparison serves to validate the accuracy of the double-strength reduction method proposed in the present study. Further, based on the proposed method, the relationship between slope stability and slope displacement is established, which provides a theoretical basis for the safety assessment of slope engineering.

A numerical strain-softening solution of a circular opening in nonlinear yield rock masses

Strain-softening behavior occurs when the surrounding rock reaches its peak load, complicating the prediction of stress and displacement. The linear Mohr-Coulomb yield criterion and semi-linear Hoek-Brown yield criterion are widely used in elastoplastic analysis. However, the established criteria struggle to universally describe the nonlinear behavior of various rock types. This study aims to overcome the difficulty and propose the solution of surrounding rock in a circular tunnel following any nonlinear yield criterion and plastic potential function. The derivation of the equivalent cohesive strength and frictional angle for an arbitrary nonlinear yield criterion in the form of σ1=fσ3 using the secant method, along with the determination of the equivalent dilatancy angle for any nonlinear plastic potential functions, was conducted. Concerning the elastoplastic solution of a thick-cylinder, a numerical strain-softening solution for a circular tunnel in nonlinear yield rock masses was derived. Verification of the proposed solution was performed against the established analytical and/or numerical elasto-(brittle-)plastic and strain-softening solutions in rock masses following the Mohr-Coulomb, (generalized) Hoek-Brown, and unified strength criteria. The impact of critical plastic shear strain on displacement, plastic radius, and residual radius was further analyzed. The predictions of displacement and residual region for the Jinping II project also meet the field test results.

Numerical Modeling of Cantilever Retaining Wall Using EPS Geofoam

Earth retaining wall structures are common civil engineering structures. Estimation of magnitude and distribution of earth pressure on retaining structures under different surcharge loading conditions is essential as they influence the design and overall economy of retaining structures. Numerical modeling using finite element code PLAXIS is used static analysis. 7 m height of non-yielding cantilever retaining wall with and without EPS geofoam structure is studied and 20 m backfill width was considered. In the present study backfill was modeled as Mohr-Coulomb yield criteria and EPS geofoam and wall were modeled as Linear-elastic. EPS geofoam densities namely 12 kg/m3 and 15 kg/m3 and two different geofoam thicknesses 0.107H and 0.143H were used for static analysis. Three different surcharge loading namely 10 kPa,30kPa and 50kPa which were kept at a distance of 2.0 m away from the wall face. In the static analysis earth pressure distribution for wall with and without geofoam were analyzed. Approximately 50% isolation efficiency was reported. At lower surcharge loads the effectiveness of EPS is more as compare to higher surcharge load and with increase in surcharge load, isolation efficiency gradually decreases and isolation efficiency decreases with increase in buffer modulus. Apart from these serviceability criteria was also checked. Serviceability criteria comprise of lateral deformation of EPS geofoam at sand-geofoam interface and backfill surface settlement were studied. Lower EPS geofoam density and higher EPS geofoam thickness reduces higher magnitude of earth pressure but in this combination the backfill surface settlement was coming very high.

A numerical investigation into the equivalent parameters of a compressible soil treated by stone columns

A series of triaxial test simulations are adopted to estimate the equivalent strength parameters for compressible soil samples reinforced with stone columns. The simulations utilize the finite difference code, Fast Lagrangian Analysis of Continua in three dimensions FLAC3D. An elasto-plastic model is applied to utilize a Mohr-Coulomb yield criterion. The equivalent strength parameters are estimated using newly proposed formulas for geo-composite materials. The researchers compare the obtained results to the analytical formulas proposed in the literature. Additionally, the equivalent parameters are used in equivalent area models. This study investigates the effect of the replacement area ratio. This study offers two applications. Firstly, it evaluates the safety factor of embankments constructed on compressible soil improved with stone columns. Secondly, it estimates the bearing capacity of strip footings on compressible soil treated with stone columns. In all applications, both individual column and equivalent area models are considered. The proposed equations for the equivalent elastic parameters (E, ν) and the mechanical properties, equivalent cohesion, and internal frictional angle (c and φ) give results that agree with the solutions reported in the existing literature.

Analysis of fracture toughness deterioration and instability model of dangerous rock masses under freeze–thaw cycles

The instability of dangerous rock masses is primarily caused by the stress intensity factor at the primary structural plane exceeding the fracture toughness of the rock bridge section, which results in the propagation of fractures. Additionally, in cold regions, the fracture toughness of these rock masses gradually decreases due to freeze–thaw cycles. Initially, considering the deterioration of type I and type II fracture toughness in the rock bridge section and the frost heaving force between structural planes, an assessment model for the stability of dangerous rock mass under freeze–thaw cycles is established. Secondly, utilizing the theory of circular hole expansion, along with the Mohr-Coulomb yield criterion and maximum tensile stress criterion, a model is constructed to simulate the degradation of type I and type II fracture toughness in rock bridge segments under the influence of freeze–thaw cycles. The validity of this model was subsequently verified through experimental validation. Finally, through engineering case studies, the degradation pattern of the stability of dangerous rock formations under the action of freeze–thaw cycles was analyzed. The study reveals that the decreasing stability of dangerous rock mass under freeze–thaw conditions is intricately linked to the internal friction angle, elastic modulus, and initial tensile strength of the rocks. Notably, the long-term stability of hard and coarsely textured dangerous rock mass under such conditions generally improves. Conversely, the tensile strength of the rock bridge segment elevates, which is beneficial for the long-term stability of the rock mass. When the residual debris ratio exceeds 0.25, the instability of the rock mass deteriorates more modestly. To maintain long-term stability, managing debris loss or injecting fillers into the pores can be effective strategies.

Ultimate Load-Bearing Capacity and Sustainable Performance of Pile Foundations of Yanji Suspension Bridge in Fault Zone Based on Refined Geological Model

Pile foundation is the most important foundation type of long-span bridges, of which the ultimate load-bearing capacity affects the safety and sustainable performance of bridges. When constructing large-span bridges, the bridge site may be close to the adjacent fault zones, which seriously affects the safety and long-term performance of pile foundations, causing the failure and unsustainability of long-span bridges in their life-cycle service life. At present, there are no engineering design rules or methods for assessing the load-bearing capacity of the pile foundation near the fault zones. To study the influence of the fault zone on the loading-bearing capacity and sustainable performance of pile foundations, triaxial compression tests were carried out on the mylonite at the Yanji suspension bridge site near the Xiangfan–Guangji fault zone in Hubei Province. The mechanical properties of mylonite were reflected by the Mohr–Coulomb yield criterion, and a topographic and geological modeling method based on the multi-platform was established. Then, the ABAQUS finite element software was used to study the deformation, stress, failure modes, and sustainable performance of the pile foundation under different bridge load levels, analyze the safety of the pile foundation in the fracture zone, and summarize the ultimate bearing characteristics of the pile foundation. The results show that the whole pile and surrounding rock are basically elastic under the pressure of the designed load, the plastic zone of the pile foundation is mainly concentrated at the pile bottom, and the shear stress concentration zone of the pile is mainly manifested in the joint of the cap and pile and the interface between soft and hard rock. When the load is increased to 4 times the designed load, the stress concentration area of the pile body gradually shifts upward from the pile bottom, and the surrounding rock at the bottom forms an “X-shaped” shear failure zone. After 100 years of operation, the maximum compressive stress of piles reaches 28.6 MPa, which is 120% higher than that at the beginning of the bridge construction, indicating that the sustainable performance of the piles can withstand the effect of the fault zone over the designed service years.

A new method of solving plane-strain boundary value problems for the double slip and rotation model

Abstract A method of solving plane-strain boundary value problems for a reduced version of the double slip and rotation model is developed. It is assumed that the intrinsic spin vanishes. Elastic strains are neglected. The Mohr–Coulomb yield criterion is adopted. An analogy between the solutions for this model and classical rigid plastic solutions of pressure-independent plasticity is revealed. The method is based on introducing auxiliary variables that satisfy the equation of telegraphy in regions where both families of characteristics are curved. Therefore, Riemann's method can conveniently be applied to solving boundary value problems. The method is employed for analyzing the processes of plane-strain drawing and extrusion through a wedge-shaped die. Friction is neglected. The solution is given in terms of ordinary integrals. The effect of the angle of internal friction on processes’ parameters is revealed. The solution reduces to available solutions of pressure-independent plasticity if the angle of internal friction vanishes.

Bearing capacity factor for strip foundations on unsaturated clay

ABSTRACT The matric suction in unsaturated soil depends on the type of soil and various flux conditions i.e., infiltration, evaporation and no flow. The shear strength of unsaturated soil changes with change in matric suction leading to varying resistance of soil under various flow conditions. In this study, the bearing capacity of strip foundations resting over unsaturated clay considering variation of matric suction with depth for different surface flux conditions and position of water table, has been obtained using finite element lower bound limit analysis. Modified Mohr-Coulomb yield criteria based on unified effective stress approach has been employed to incorporate the contribution of matric suction stress to the failure condition. A non-dimensional bearing capacity factor was introduced to estimate the bearing capacity of strip foundations and presented as a function of different influencing parameters such as foundation width, water table depth, soil properties, various flow conditions and their flow rate, and surcharge pressure. The influence of variation of unit weight of soil in the unsaturated zone, air entry and pore size distribution parameters, residual degree of saturation of soil, specific gravity of soil solids, and foundation-soil interface roughness on the bearing capacity has also been examined and found to be insignificant.

Inversion study on elastic–plastic material parameters of red sandstone in uniaxial compression test

In order to obtain the real material parameters of heterogeneous rock, the material parameters of red sandstone specimens under uniaxial compression tests are inverted based on the Digital Image Correlation (DIC) method and the Finite Element Model Updating (FEMU) method. The DIC method is employed to calculate the displacement field of red sandstone specimens during uniaxial compression loading. Concurrently, a uniaxial compression elastic–plastic finite element numerical model with non-uniform material parameters is developed based on the FEMU method. The model adopts the Mohr–Coulomb yield criterion and adjusts the boundary conditions in real-time to maintain consistency with the test. The vertical displacement field of the numerical model is juxtaposed with that of the test to construct the objective function. Optimization is achieved using the Artificial Fish Swarm algorithm, which enables the acquisition of the non-uniform distribution and evolution process of the material parameters of specimens at different loading moments. The results indicate that this method can spatially obtain the non-uniform distribution field of material parameters and temporally track the evolution of material parameters during the loading process. This research lays a solid foundation for enhancing the accuracy of intelligent coal mining and dynamic disaster monitoring and early warning in coal mines.

Elastoplastic solution of a circular tunnel in surrounding rock with any nonlinear yield criteria and plastic flow envelopes

Besides the (semi-)linear Mohr-Coulomb and Hoek-Brown criteria, other nonlinear functions are also used to describe the plastic response of rock mass. For a nonlinear yield and plastic flow function in the form of τ=fσn and/or σ1=fσ3, the equivalent cohesive strength and frictional angle corresponding to the Mohr-Coulomb yield criterion were derived. The normal stress was further related to the minimum principal stress using the geometrical relationship of a Mohr circle. The equivalent dilatancy angle was also derived using the same method. According to the solution of a circular tunnel in Mohr-Coulomb rock mass, this paper derived a semi-analytical solution of a circular tunnel in any nonlinear yield and plastic flow rock masses with a form of τ=fσn and/or σ1=fσ3. A numerical procedure was developed for the stresses and displacement using a reserve method. The proposed solution was verified by the results of a circular tunnel in elasto-perfectly(brittle-)-plastic and/or strain-softening rock mass. The strain-softening analysis of a circular tunnel in the assumed two nonlinear yield criteria and/or plastic flow rock masses was studied. For a linear deteriorated material parameters leads to a nonlinear evolution of equivalent cohesive strength, frictional angle and dilatancy angle in the plastic region.

Evaluating Pile-Supported Embankment Considering the Soil Anisotropy Effect

It is an economical way to use the pile-supported embankment for the construction of the embankment over soft soil. The combined use of piles and reinforcement effectively reduces the differential settlement of the embankment surface. However, the previous analysis of embankment stress and settlement did not take into account the anisotropy in the embankment filler. In this paper, the UMAT subroutine is developed by using the material subroutine interface in ABAQUS 2016 finite element software. The anisotropy of soil cohesion and friction angle has been incorporated into the Mohr–Coulomb yield criterion so that it can consider the anisotropy of soil. The accuracy of the anisotropic yield criterion in this paper is verified by an ABAQUS source program and related engineering examples. It is found that the anisotropy value of soil cohesion is inversely proportional to the stress ratio on the pile–soil interface while being directly proportional to the tensile stress applied to the geogrid. The results show that the anisotropy of the friction angle decreases with the soil arching effect but increases by 23.1% with the tensile stress on the geogrid. The position of the settlement plane remains relatively constant at 2.3 m as the friction angle anisotropy coefficient increases. These research results provide valuable theoretical guidance for on-site construction design.

Application of Cross model for granular flow and impact analysis using three-dimensional B-spline material point method

Granular flow and impact, such as landslides and debris flows, are typical problems involving large deformations of non-Newtonian free surfaces, which are of great interest in geological engineering and also pose challenges for traditional mesh-based numerical methods. As an enhancement of the traditional Material Point Method (MPM), the B-Spline Material Point Method (BSMPM) can not only effectively reduce mesh-crossing and quadrature errors, but also facilitate the tracking and capturing of free surfaces and contact interfaces. In this paper, the non-Newtonian general Cross model, the rheological parameters of which are determined by the Bingham model and the Mohr-Coulomb yield criterion, is introduced into the three-dimensional BSMPM (3D BSMPM) for simulating granular flow and impact problems. Interparticle effects of granular materials are represented by artificial damping forces. Dynamic simulations are carried out on the collapse of sand column and glass beads, the flow of bentonite suspensions, and the impact between granular mass and elastic obstacles. The overall evolution of granular flow and impact behavior are presented and compared with existing experimental and/or original MPM results. It is found that the proposed method well reproduces the overall process of granular flow and impact behavior, including its various stages of formation, acceleration, deceleration, and deposition, as well as the impact pressure. The results show that the granular flow and impact behavior can be well represented by the proposed 3D BSMPM with the Cross rheological model, demonstrating the effectiveness of the proposed method in simulating complicated environmental fluid dynamics.

Two-phase MPM modeling of dry granular fronts and watery tails formed in debris flows

Debris flow is a mixture involving complicated interactions between granules and liquids. In the process of sliding down at high speed, it may pose a great threat to the life and health of people and property safety. In nature, the debris flows often show a dry granular front and a more watery tail, which makes the debris flows the most destructive geological disaster. Therefore, it is of great significance to deeply understand the kinematic characteristics of the landslide body and to accurately predict the flow of granular-liquid mixture in practical applications. In this paper, a two-phase material point method (MPM) based on mixture theory is used to model the formation of watery tails and dry granular fronts observed in debris flows. In the proposed model, the debris flow is idealized as a granular-liquid mixture, the liquid phase is assumed to be a weakly compressible viscous fluid, and an elastic-plastic model with Mohr-Coulomb yield criterion is used to model the granular response, and the granular-liquid interaction is realized through momentum exchange. The accuracy and effectiveness of the proposed method were verified by comparing the numerical results with the experimental data through two tests of a dry granular collapse and a granular-liquid mixture destabilization. Then, we applied the validated method to simulate the phenomenon of watery tails and dry granular fronts formed in debris flows, and investigated the effects of the angle of the inclined plane, the initial saturation (defined as the initial depth ratio of water to granular material), the granular density, internal friction angle, particle diameter and the initial porosity on the time evolution of the front end of the granules and the liquid.

Design of Dies of Minimum Length Using the Ideal Flow Theory for Pressure-Dependent Materials

This paper develops the ideal plastic flow theory for the stationary planar flow of pressure-dependent materials. Two rigid plastic material models are considered. One of these models is the double-shearing model, and the other is the double slip and rotation model. Both are based on the Mohr–Coulomb yield criterion. It is shown that the general ideal plastic flow theory is only possible for the double slip and rotation model if the intrinsic spin vanishes. The theory applies to calculating the shape of optimal extrusion and drawing dies of minimum length. The latter condition requires a singular characteristic field. The solution is facilitated using the extended R–S method, commonly employed in the classical plasticity of pressure-independent materials. In particular, Riemann’s method is used in a region where all characteristics are curved. It is advantageous since determining the optimal shape does not require the characteristic field inside the region. The solution is semi-analytical. A numerical procedure is only required to evaluate ordinary integrals. It is shown that the optimal shape depends on the angle of internal friction involved in the yield criterion.

An implicit stress update algorithm for the plastic nonlocal damage model of concrete

The numerical implementation of advanced plastic damage models has been challenging due to the diverse computational difficulties caused by material nonlinearity. In this study, firstly, a plastic damage model is developed by a nonsmoothed Mohr–Coulomb yield criterion. The nonorthogonal flow rule without plastic potential function is employed to describe the dilatancy behavior of concrete. The stiffness degradation is considered through two tensile and compressive damage variables. Subsequently, an implicit stress update algorithm incorporating several advanced numerical methods is proposed to tackle difficulties arising in the numerical calculation of the plastic damage model. In the model implementation, the Mohr–Coulomb yield function with corners is replaced by a single smooth expression to ensure the stability of the numerical calculation. A line search method is used to solve nonlinear systems of integral stress equations to obtain better convergence than Newton method. The complex step derivative approximation is used to evaluate the consistent tangent operator to provide quadratic convergence speed of the global equilibrium iterations, thus avoiding tedious analytical derivative operations. The integral nonlocal method is also used to regularize the finite element solution. At the material point scale, the ability of the proposed model to describe the complex mechanical behavior of concrete is verified by utilizing nine sets of monotonic and cyclic loading and unloading tests. Finally, the algorithm and model’s performance is well tested by the failure analysis of five numerical examples. The code of this work will be freely available at https://github.com/zhouxin615/PD_model.

Cohesion and aggregates in unsaturated wet granular flows down a rough incline

Multi-phase flows, encountered in nature or in industry, exhibit non-trivial rheological properties, which we attempt to better understand thanks to model materials and appropriate rheometers. Unsaturated wet granular flows down a rough inclined plane turn out to be steady and uniform for a wide range of parameters, despite the cohesion and the grain aggregates. The cohesive Mohr–Coulomb yield criterion extended to inertial granular flows, with a cohesion stress dependent on the liquid content and an internal friction coefficient dependent on the inertial number, allows for predictions in good agreement with our experimental measurements, when one introduces a grain aggregate size, which defines the appropriate length and relaxation time scales in the inertial number. We found that the grain aggregate size depends not monotonically on the liquid content and does not scale with the cohesion length induced by the cohesion stress, due to the non-trivial distribution of the liquid within the granular material.

Numerical study of water wave generation by granular-liquid mixture collapse using two-phase material point method

Debris flow sliding with high-speed and its possible interactions with a confined water body may lead to dangerous hazard. Therefore, it is important in practical applications to accurately predict the granular-liquid flows and their possible interactions with the water body. A two-phase material point method (MPM) with double-point formulation was applied in this paper to simulate the generation of the water wave by granular-liquid mixtures collapse into water. In our study, the debris flow was idealized as a granular-liquid mixture, the liquid phase was considered as a compressible viscous fluid, the granular response was modeled using the Mohr–Coulomb yield criterion and the granular-liquid interaction forces including viscous drag force and buoyancy force. Two experimental tests of dam-breaking flow and the wave generation by a dry granular column collapse were simulated, the accuracy and effectiveness of the proposed approach has been proven by comparing the numerical results with experimental data. We performed an experiment of saturated granular column collapsed into water and the test results were used to validate the proposed method, then applied the validated method to simulate the water wave generation by granular-liquid mixture collapse into water and investigate the effects of the initial degree of saturation defined as the initial depth ratio of water to granular material on the time evolution of the granular front and the amplitude of leading wave.

Seismic combined bearing capacity of strip footings on partially saturated soils using lower bound theorem of finite element limit analysis and second-order cone programming

The seismic bearing capacity of strip footings resting on unsaturated soils subjected to combined loading is investigated in this study using a combination of lower bound limit analysis and finite element discretization. Second-order cone programming (SOCP) is used in this instance to simulate the nonlinear form of the universal perfectly-plastic Mohr-Coulomb yield criterion during the stress field optimization process. Under no-flow and steady-state infiltration/evaporation flow conditions, the significant influence of matric suction induced below the surface footing is accounted for using the suction stress concept. The load eccentricity and inclination applied to the footing and pseudo-static forces exerted simultaneously to the footing (superstructure) and underlying soil are all incorporated into the equilibrium equations, resulting in combinations of limit moment (M), and vertical (V), and shear (H) forces, under the influence of seismic loading. The results demonstrate that the matric suction induced within the porous structure of the underlying soil stratum increases the capacity of the surface footing to withstand various combinations of eccentric and inclined loadings under seismic excitation. Moreover, at a given hydraulic condition, the failure envelopes of obliquely/eccentrically loaded shallow foundations shrink significantly with the increase in the seismic intensity; the process which is more highlighted in sand (no-suction and all flow conditions). As the flow state in the unsaturated clay changes from infiltration to evaporation, the failure envelopes are observed to enlarge. In addition, as the load inclination angle reaches the soil-footing interface friction angle, the ultimate horizontal bearing capacity of the foundation resting on sand (no-suction) drops to zero; however, there still exists a residual shear resistance in the underlying clay layer or unsaturated sand, posing non-zero horizontal bearing capacity even at extremely high angles of inclination. Last but not least, the influence of earthquake horizontal loading on the bearing capacity envelopes of a shallow footing resting on a sand deposit was corroborated to be more pronounced than on a cohesive soil deposit. Indeed, the intrinsic (residual) cohesion, normally found in cohesive soils, was realized to contribute significantly to suppress the detrimental effect of earthquake horizontal loading.

Stability Analysis of Geosynthetic-Reinforced Shallow Foundations with a Lower-Bound FELA Approach Adopting the Nonassociated Plastic Flow Rule

Finite-element limit analysis (FELA) is an effective numerical method to evaluate the stability of reinforced geostructures. Such an analysis has been commonly performed in the literature by assuming the earthen material to follow the well-defined associated plastic flow rule. In this study, the effect of adopting the nonassociated plastic flow rule on the ultimate bearing capacity of eccentrically-obliquely loaded shallow footings placed over geosynthetic-reinforced granular soil is rigorously examined through a comprehensive set of lower-bound FELA simulations along with second-order cone programming. The nonassociativity of the plastic flow rule is incorporated into the formulation of the Mohr–Coulomb yield criterion by considering a wide range of dilation angles (ψ) varying between 0 and the soil internal friction angle (φ). Unlike the previous FELA studies, both pull-out (sliding) and tensile (structural) modes of geosynthetic failure are taken into account. Accordingly, the impact of considering the nonassociated flow rule for the sand deposit on the bearing capacity ratio, failure envelopes, and the failure mechanism of overlying shallow foundation is investigated and discussed. The results show that failing to consider the significant influence of nonassociativity in the FELA simulations leads to overestimations of the tensile forces mobilized in the reinforcement layer as well as the ultimate bearing capacity of the overlying shallow foundation, thus yielding nonconservative and insecure designs.

Theoretical analysis of grouting reinforcement for surrounding rock of deep shaft based on stability and water inflow control

To address the challenge of designing grouting reinforcement in a deep shaft to control water, this study established an elastic-plastic analytical formula for the grouted rock surrounding a shaft under the combined action of thermal, hydraulic, and mechanical fields based on the Mohr–Coulomb yield criterion. The various rules and influencing factors of stability and impermeability of the grouted rock surrounding the shaft are calculated and analyzed. The analysis shows that damage to the surrounding rock is aggravated by the action of high ground temperature and high water pressure in deep shafts, and the influence of water pressure is particularly significant. The larger the radius and cohesion of the grouted surrounding rock, the smaller the radius of its plastic zone. With an increase in the elastic modulus ratio between the grouted surrounding rock and the original rock, the radius of its plastic zone increases, so the elastic modulus of the grouted surrounding rock design should consider the original surrounding rock. With a decrease in the permeability coefficient of the grouted surrounding rock, the radial stress decreases, the tangential stress increases, and the radius of the plastic zone increases. The development of plastic zone not only affects the stability but also causes an increase in the permeability coefficient. There is mutual restriction and influence between the shaft water inflow, the permeability coefficient, the radius of the grouted surrounding rock, and the radius of its plastic zone. In the design of grouting reinforcement, the stability of surrounding rock and the control requirements of shaft water inflow should be comprehensively considered and the optimal parameters should be selected based on theoretical calculation. This study provides a theoretical basis for the optimization of grouting reinforcement parameters in a deep shaft.