The aim of this study is to investigate the influence of rock variability on the failure mechanism and bearing capacity of strip footings. A probabilistic analysis of the bearing capacity of footings on rock masses is conducted in this paper, where random adaptive finite-element limit analysis (RAFELA) with the Hoek-Brown yield criterion and the Monte Carlo simulation technique are combined. The stochastic bearing capacity is computed by considering various parameters, such as the mean values of the uniaxial compressive strength of intact rock, Hoek-Brown strength properties, coefficient of variance, and correlation lengths. In addition to the RAFELA, this study introduces a novel soft-computing approach for potential future applications of bearing capacity prediction by employing a machine learning model called the eXtreme Gradient Boosting (XGBoost) approach. The proposed XGBoost model underwent thorough verification and validation, demonstrating excellent agreement with the numerical results, as evidenced by an impressive R2 value of 99.99%. Furthermore, Shapley's analysis revealed that the specified factor of safety (FoS) has the most significant influence on the probability of failure (PoF), whereas the geological strength index (GSI) has the most significant effect on the random bearing capacity (mu Nran). These findings could be used to enhance engineering computations for strip footings resting on Hoek-Brown rock masses.

To understand the strengths of rocks under complex stress states, a generalized nonlinear three-dimensional (3D) Hoek-Brown failure (NGHB) criterion was proposed in this study. This criterion shares the same parameters with the generalized HB (GHB) criterion and inherits the parameter advantages of GHB. Two new parameters, b, and n, were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression, respectively. The NGHB criterion can consider the influence of intermediate principal stress (IPS), where the deviatoric plane shape satisfies the smoothness requirements, while the HB criterion not. This criterion can degenerate into the two modified 3D HB criteria, the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition. This criterion was verified using true triaxial test data for different parameters, six types of rocks, and two kinds of in situ rock masses. For comparison, three existing 3D HB criteria were selected for performance comparison research. The result showed that the NGHB criterion gave better prediction performance than other criteria. The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%-3.5091% and 1.0144%-3.2321%, respectively. The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V.

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil, hydraulic, mechanical, aerospace, military, and other engineering disciplines. Therefore, the comprehensive study of the generalized nonlinear strength theory (GNST) of geomaterials has significance for the construction of engineering rock strength. This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths. First, it systematically summarizes the research progress of GNST (classical and empirical criteria). Then, the latest research the authors conducted over the past five years on the GNST is introduced, and a generalized three-dimensional (3D) nonlinear Hoek-Brown (HB) criterion (NGHB criterion) is proposed for practical applications. This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance. The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091% and 1.0144%-3.2321%, respectively. Finally, the development and outlook of the GNST are expounded, and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed. The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

为了探究寒区板岩边坡在冻融条件下的力学参数劣化规律及其失稳机理，通过室内冻融循环力学试验，并基于广义Hoek-Brown强度准则计算岩体内聚力和内摩擦角随冻融循环次数的衰减规律，以此修正未考虑冻融损伤的白云鄂博南帮内聚力和内摩擦角块体模型，实现南帮岩体力学参数的时空演化表征，最后通过数值模拟分析白云鄂博铁矿主矿区南帮边坡在冻融效应下的循序破坏机理。结果表明：经20次冻融循环后，矽质板岩、云母化板岩、碳化板岩、断层岩内聚力降低率分别为21.64%、22.66%、28.09%、28.53%，内摩擦角降低率分别为12.76%、14.72%、19.37%、21.35%；在冻融效应下，南帮边坡稳定系数由1.19逐渐降至0.92,1 650～1 570 m区域剪应变逐渐增大，最终滑体于1 570 m平台滑移剪出。

为了探究寒区板岩边坡在冻融条件下的力学参数劣化规律及其失稳机理，通过室内冻融循环力学试验，并基于广义Hoek-Brown强度准则计算岩体内聚力和内摩擦角随冻融循环次数的衰减规律，以此修正未考虑冻融损伤的白云鄂博南帮内聚力和内摩擦角块体模型，实现南帮岩体力学参数的时空演化表征，最后通过数值模拟分析白云鄂博铁矿主矿区南帮边坡在冻融效应下的循序破坏机理。结果表明：经20次冻融循环后，矽质板岩、云母化板岩、碳化板岩、断层岩内聚力降低率分别为21.64%、22.66%、28.09%、28.53%，内摩擦角降低率分别为12.76%、14.72%、19.37%、21.35%；在冻融效应下，南帮边坡稳定系数由1.19逐渐降至0.92,1 650～1 570 m区域剪应变逐渐增大，最终滑体于1 570 m平台滑移剪出。

Excavation-induced disturbances in deep tunnels will lead to deterioration of rock properties and formation of excavation damaged zone (EDZ). This excavation damage effect may affect the potential rockburst pit depth. Taking two diversion tunnels of Jinping II hydropower station for example, the relationship between rockburst pit depth and excavation damage effect is first surveyed. The results indicate that the rockburst pit depth in tunnels with severe damage to rock masses is relatively large. Subsequently, the excavation-induced damage effect is characterized by disturbance factor D based on the Hoek-Brown criterion and wave velocity method. It is found that the EDZ could be further divided into a high-damage zone (HDZ) with D 1/4 1 and weak-damage zone (WDZ), and D decays from one to zero linearly. For this, a quantitative evaluation method for potential rockburst pit depth is established by presenting a three-element rockburst criterion considering rock strength, geostress and disturbance factor. The evaluation results obtained by this method match well with actual observations. In addition, the weakening of rock mass strength promotes the formation and expansion of potential rockburst pits. The potential rockburst pit depth is positively correlated with HDZ and WDZ depths, and the HDZ depth has a significant contribution to the potential rockburst pit depth. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

为探讨冻胀力效应对寒区圆形隧洞围岩稳定性的影响，基于考虑冻胀力影响的寒区圆形隧洞稳定性分析模型，采用内边界应力条件(σr|r=r1=σr1)推导广义Hoek-Brown强度准则下寒区圆形隧洞塑性区的径向应力、切向应力以及塑性区半径、松动圈半径的弹塑性解。并以实际工程案例为背景，对比分析已有研究方法（即采用外边界应力条件计算）,验证内边界应力条件计算方法的可行性和优越性。结果表明：地质强度指标、岩体常数、单轴抗压强度、扰动系数、隧洞开挖半径、冻胀力对寒区圆形隧洞围岩塑性区径向应力、切向应力以及塑性区半径、松动圈半径均有明显影响。其中扰动系数影响比较显著，理想爆破情况（D=0.7）与不考虑扰动情况（D=0）相比较，计算结果相对误差达到32.2%～55.8%。冻胀力的影响非常显著，冻胀力从0增大到1.02 MPa,计算结果相对误差可达到507.1%。如果忽视冻胀力影响会严重低估塑性区的径向应力和切向应力以及高估塑性区范围和松动圈范围。

为探讨冻胀力效应对寒区圆形隧洞围岩稳定性的影响，基于考虑冻胀力影响的寒区圆形隧洞稳定性分析模型，采用内边界应力条件(σr|r=r1=σr1)推导广义Hoek-Brown强度准则下寒区圆形隧洞塑性区的径向应力、切向应力以及塑性区半径、松动圈半径的弹塑性解。并以实际工程案例为背景，对比分析已有研究方法（即采用外边界应力条件计算）,验证内边界应力条件计算方法的可行性和优越性。结果表明：地质强度指标、岩体常数、单轴抗压强度、扰动系数、隧洞开挖半径、冻胀力对寒区圆形隧洞围岩塑性区径向应力、切向应力以及塑性区半径、松动圈半径均有明显影响。其中扰动系数影响比较显著，理想爆破情况（D=0.7）与不考虑扰动情况（D=0）相比较，计算结果相对误差达到32.2%～55.8%。冻胀力的影响非常显著，冻胀力从0增大到1.02 MPa,计算结果相对误差可达到507.1%。如果忽视冻胀力影响会严重低估塑性区的径向应力和切向应力以及高估塑性区范围和松动圈范围。

针对北方寒区岩体在冻融循环和外荷载作用下产生的耦合损伤问题,基于广义Hoek-Brown准则及连续损伤力学理论,引入冻融-荷载耦合损伤因子,建立了可以表征耦合损伤对岩体强度参数mb、s和弹性模量E产生弱化效应的弹塑性损伤模型;为解决模型在数值实施过程中的奇异点问题,推导了其在主应力空间中的隐式返回映射算法,包括弹性预测、塑性修正和损伤修正30个计算步骤;通过ABAQUS软件的用户子程序接口Umat,实现了模型的有限元求解过程,并利用室内冻融循环试验对模型进行了验证.最后将模型应用于吉林某边坡工程当中,计算了不同冻融次数下边坡安全系数的变化规律.研究结果表明:所建模型能够较好地描述冻融循环与塑性损伤对材料强度和刚度的弱化效应,所编程序能够用于寒区岩土工程安全性评价,对施工设计起到指导作用.

针对北方寒区岩体在冻融循环和外荷载作用下产生的耦合损伤问题,基于广义Hoek-Brown准则及连续损伤力学理论,引入冻融-荷载耦合损伤因子,建立了可以表征耦合损伤对岩体强度参数mb、s和弹性模量E产生弱化效应的弹塑性损伤模型;为解决模型在数值实施过程中的奇异点问题,推导了其在主应力空间中的隐式返回映射算法,包括弹性预测、塑性修正和损伤修正30个计算步骤;通过ABAQUS软件的用户子程序接口Umat,实现了模型的有限元求解过程,并利用室内冻融循环试验对模型进行了验证.最后将模型应用于吉林某边坡工程当中,计算了不同冻融次数下边坡安全系数的变化规律.研究结果表明:所建模型能够较好地描述冻融循环与塑性损伤对材料强度和刚度的弱化效应,所编程序能够用于寒区岩土工程安全性评价,对施工设计起到指导作用.