Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.     

基于三剪统一强度准则的隧道围岩抗力系数计算

基于三剪统一强度准则对隧道围岩抗力系数进行了分析,并导出了围岩抗力系数的计算公式。在表征岩石的强度和变形特征时采用了三剪统一强度准则以反映中间主应力对岩石强度和变形的影响,在描述隧道围岩塑性区内的应力状态时,采用中间主应力参数法来表达不同岩体可能具有的不同塑性区应力状态。计算实例表明：隧道围岩的中间主应力对隧道围岩抗力系数有影响,考虑中间主应力效应后所得的隧道围岩抗力系数增大。     

一种考虑主应力空间的岩石非线性真三轴强度准则

为评估岩石的真三轴强度特性,首先根据常规三轴试验岩石强度的变化规律,提出基于偏应力极值的非线性强度准则,并与12种岩石试验强度和4种典型岩石强度准则进行对比,发现该强度准则的预测值与试验强度非常接近,相关性系数R~2均在0.98以上,平均相对误差(MAPE,E_(MAP))均小于4%(除7号岩石为6.83%);该强度准则、指数准则、H-B准则、MM-C准则和D-P准则对所有12种岩石预测E_(MAP)的平均值分别为2.32%、2.43%、5.28%、7.39%和13.74%,说明该强度准则能够很好地预测不同类型岩石的强度,其预测精度略优于指数准则(岩石力学界认为预测精度较高的强度准则),远好于其他3种强度准则。在上述所建常规三轴强度准则的基础上,通过引入中主应力参数和罗德应力参数,构建考虑中主应力效应的真三轴强度准则,并与8种岩石的真三轴试验强度进行对比,该强度准则很好地反映了大主应力随中主应力的增加呈先增大后减小的变化规律,所得R~2均在0.9以上,其中5种岩石的R~2大于0.96;除了13和14号岩石(E_(MAP)分别为7.79%和4.84%),其余6种岩石的平均相对误差E_(MAP)均小于4%,说明该强度准则能够较好地预测岩石的真三轴试验强度,很好地反映了中主应力效应,具有良好的普遍适用性。子午面和偏平面的应力空间特征也说明该强度准则很好地反映了岩石的静水压力效应和中主应力对大主应力的影响规律。     

多轴应力状态下混凝土的动态强度准则

为了解复杂应力状态下混凝土动态强度变化规律,提出了一个考虑应变率效应的八面体应力空间的多轴静动破坏准则．该准则的空间破坏包络曲面采用二次函数形式,在偏平面上的破坏包络线采用Willam-Warnke 模型在偏平面上的椭圆曲线,使用特征应力点法对拉压子午线方程进行修正以考虑偏平面上罗德角对动态强度的影响．通过对大量混凝土多轴静动强度试验成果的分析,表明此强度准则与已有的试验结果吻合较好,能很好地反映平面应力或三轴应力状态下普通混凝土的静动强度变化规律,并且形式简单,便于实际应用．     

修正的Ottosen强度破坏准则

基于从Matsuoka-Nakai,Lade-Duncan和Ottosen等强度破坏准则导出的角隅函数,提出了修正的Ottosen强度破坏准则表达式,并通过混凝土和岩石的真三轴强度破坏试验结果进行验证.修正的Ottosen强度破坏准则不仅继承了原有的Ottosen强度破坏准则的优点,而且在低应力水平特别是在拉应力水平下能更准确地预测岩土类材料的破坏强度.     

平面应变条件下基于Lade-Duncan强度准则中主应力条件的土压力及其适用性

针对实际工程中大量存在的挡土墙、基坑开挖等平面应变问题,考虑中主应力对强度的影响,将平面应变条件下Lade-Duncan强度准则的中主应力关系代入SMP、Lade-Duncan、AC-SMP和广义Mises强度准则中得到新的平面应变强度准则。据此建立基于各强度准则的主、被动土压力计算公式,进而推广至黏性土,并将主、被动土压力理论计算值与实测值进行对比分析。结果表明,Mohr-Coulomb强度准则因其未考虑中主应力的影响,致使计算结果相比实测情况偏保守;SMP强度准则、Lade-Duncan强度准则考虑到中主应力对土压力大小的影响,计算结果相比Mohr-Coulomb强度准则更接近实测情况;AC-SMP强度准则、广义Mises强度准则在一定内摩擦角范围内可以描述挡土墙的土压力大小,但超出适用范围时,二者均不再适用于描述挡土墙的土压力大小;广义Mises强度准则在适用范围内的计算结果相比SMP强度准则、Lade-Duncan强度准则更接近实测数据。     

Hoek-Brown破坏准则求解圆形硐室塑性区半径与修正的芬纳公式比较

目的 为定量确定围岩塑性区半径和给支护锚杆的深度设计提供科学依据.方法 以Hoek-Brown破坏准则为极限平衡条件,推求侧压力系数为1.0时圆形硐室理想弹塑性围岩的弹塑性应力和塑性区半径,运用Mohr-Coulomb准则直线拟合Hoek-Brown准则曲线和面积差补方法 ,求取等效的岩体Mohr-Coulomb强度参数后,建立相对塑性区半径随支护力和地质强度指标变化的二元非线性回归数学模型,并与源自于Mohr-Coulomb强度准则为屈服条件的修正的芬纳公式进行比较研究.结果 支护力每增加1.0 MPa,就可确保地质强度指标降低10～20的岩体中不会出现塑性区.在支护力较小和岩体质量较差情况下,采用Hoek-Brown破坏准则推导得出的塑性区半径和修正的芬纳公式计算得出的塑性区半径差别稍大.相对塑性区半径与地质强度指标都呈负乘幂函数关系,随着支护力的增大,塑性区半径随着岩体质量等级的升高而下降的趋势逐渐变缓.建立的相对塑性区半径随地质强度指标和支护力变化的二元非线性回归数学模型简明,使支护力连续变化,提高了工程实用性.结论 在岩体质量较差情况下,锚杆深度取1.8～3.0倍硐半径为宜.     

基于Mohr强度理论的双参数抛物线型屈服准则

从Mohr强度理论出发,对双参数强度理论进行分析,特别是对双参数抛物线型屈服准则进行研究,推导了双参数抛物线强度准则的多种表达形式,分析了该屈服准则在应力空间中的展布特征,证明了双参数抛物线准则在偏平面上分别以两种曲线形式出现,即分段抛物线和分段直线,两者在应力空间中是光滑连接的．两种曲线构成的屈服轨迹都含有角点,对角点进行了修圆处理．通过将该屈服准则嵌入有限元程序,实现了基于双参数抛物线型屈服准则的破坏计算分析．     

基于Mohr强度理论的双参数抛物线型屈服准则

从Mohr强度理论出发,对双参数强度理论进行分析,特别是对双参数抛物线型屈服准则进行研究,推导了双参数抛物线强度准则的多种表达形式,分析了该屈服准则在应力空间中的展布特征,证明了双参数抛物线准则在偏平面上分别以两种曲线形式出现,即分段抛物线和分段直线,两者在应力空间中是光滑连接的.两种曲线构成的屈服轨迹都含有角点,对角点进行了修圆处理.通过将该屈服准则嵌入有限元程序,实现了基于双参数抛物线型屈服准则的破坏计算分析.     

边坡稳定数值计算中失稳判据和岩土强度屈服准则

通过理论分析和典型算例计算,对边坡稳定数值计算中边坡的失稳判据和失稳模式进行了深入的讨论,旨在使数值计算方法更好地服务于工程实际。边坡失稳破坏的力学分析表明,排除人为主观因素的影响,在严格收敛标准下数值计算不收敛、边坡塑性区贯通和特定监测点位移突变这三类常用判据内在的力学表现是一致的,算例1的分析结果进一步证实了该观点。边坡的失稳模式与岩土体的屈服准则密切相关,为使理论计算符合工程实践,应根据岩土体实际抗拉能力对以M-C为典型代表的基于剪切破坏的强度准则进行抗拉修正。以抗拉修正后的M-C强度准则为基础,进一步提出了拉剪复合破坏的强度折减计算流程,算例2的计算结果表明该计算流程是合理的且计算结果的精度要高于现行的计算方法。     

Ultimate end bearing capacity of rock-socketed pile based on generalized nonlinear unified strength criterion

In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end bearing capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.     

Failure criterion for soft rocks considering intermediate principal stress

The significant differences between hard rocks(more brittle) and soft rocks(more ductile) may suggest the use of different failure criteria. A strength criterion for soft rocks that includes intermediate principal stress was proposed. The new criterion includes two independent parameters: the uniaxial compressive strength(rci), which can be obtained from common laboratory tests or indirectly estimated by alternative index tests in the laboratory or field; and f(joint), which is used to characterize the rock mass quality and can be easily estimated. The authors compared the predictive capabilities of the new criterion with other criteria using the database of soft rocks under two conditions: with and without triaxial data. For the estimation of triaxial and true-triaxial strengths, the new criterion generally produced a better fit. The proposed criterion is practical for an approximate first estimation of rock mass strength, even without triaxial data, as it balances accuracy(lower prediction error) and simplicity(fewer independent parameters).     

二长岩节理抗剪强度三轴试验研究

摘要：为确定岩石节理的剪切强度,在MTS815型程控伺服岩石刚性试验机上对含不规则、无充填岩石节理试件进行三轴试验。试验过程利用伺服控制系统连续获得同一试件在不同围压条件下对应的最大轴压,并根据弹性力学理论求得不同围压下节理面的正应力和剪应力。除对每一试件的试验结果按线性Mohr-Coulomb准则拟合获得摩擦角和内聚力外,利用Matlab软件的曲线拟合工具对所有试件的正应力和剪应力分别进行了线性Mohr-Coulomb准则拟合、幂函数拟合和非线性Barton公式拟合,对比它们的拟合效果可知：(1)线性Mohr-Coulomb准则拟合明显比幂函数拟合和Barton公式拟合要差,尤其是在低正应力条件下线性Mohr-Coulomb准则拟合将高估岩石节理的剪切强度。(2)幂函数拟合和Barton公式拟合的曲线几乎重合,且总体反映了岩石节理剪切强度的非线性特征。(3)在较高正应力下,线性Mohr-Coulomb准则、幂函数和非线性Barton公式对应的剪切强度均偏高。同时,为了估计拟合公式基本参数的合理性,根据试验成果对Barton公式基本参数进行了比较可靠的区间估计。估计结果表明：用Matlab软件的曲线拟合工具直接根据试件三轴试验结果进行Barton公式拟合的基本参数在某一置信水平(如99.73%)的上、下边界获得的区间估计明显脱离实际物理意义,是错误的;而通过幂函数进行对数转换后确定出参数的上、下边界,获得幂函数相应的上、下限曲线后,再用Barton公式拟合幂函数的上、下限曲线所得的基本参数的区间估计则是合理的。     

Confining stress effect on the elastoplastic ground reaction considering the Lode angle dependence

The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC~(3D). It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.     

岩石破坏过程中的损伤统计本构模型

统计损伤力学是依据岩石破坏过程中的三轴试验资料反推其本构关系的一种有效手段。假定岩石微元强度服从幂函数分布的概率分布理论,将Hoek-Brown强度准则作为岩石统计分布变量,建立了岩石损伤变量演化方程和岩石在三维应力作用下的损伤统计本构模型,并用试验资料对其进行了验证。通过将理论结果和试验结果进行对比发现：该模型能够比较好的反映岩石的本构关系和破坏过程,从而说明了模型的合理性和可行性;模型分布参数R反映了岩石的强度,m反映了岩石的强度和脆性程度,但二者不是相互独立的,而是具有内在联系的。     

岩石中间主应力效应及强度理论研究进展

综述岩石中间主应力效应试验和强度理论的研究进展,总结了岩石中间主应力效应的基本规律和现有岩石强度理论的特点与不足,最后介绍了统一强度理论及其对岩石真三轴试验的预测与在岩土工程中的应用。研究结果表明：中间主应力效应及其区间性是岩石强度的重要特性,且已是目前岩石强度准则建立所必须考虑的基本问题之一;应用统一强度理论并考虑更多复杂因素的综合影响,可得到更符合实际情况的较理想解答。     

岩石节理剪切强度研究

利用断裂力学理论分析了纯剪切应力状态和双向压应力状态作用下节理模型的断裂机制。在已有的数值模拟和实验基础上,通过引入分形维数,推导了粗糙节理的摩尔-库仑剪切强度的改进公式。该公式的分析结果显示,节理尺度相对于岩体尺寸越大,节理的抗剪强度就越低,并且节理的抗剪切强度与分形维数的关系是一种非线性增长关系。     

Nonlinear criterion for strength mobilization in brittle failure of rock and its extension to the tunnel scale

As underground excavations are getting deeper and field stresses increase, the behavior of intact rock blocks plays an increasingly important role in understanding and estimating the overall rock mass strength. To model the brittle behavior of intact rock blocks, the stress–strain curve is usually idealized considering a linear strength mobilization approach (cohesion-weakening-friction-strengthening, CWFS), however, it is well recognized that rock presents a nonlinear behavior in terms of the confining stress. This study extends the strength mobilization in brittle failure of rock using nonlinear criteria. To determine the model parameters, a standard statistical method that uses the complete laboratory stress–strain curves of the intact rock is employed. Several hypotheses of linear and nonlinear models are statistically compared for different types of rock and confining stress levels. Results demonstrate that the best approach to model the brittle failure of rock is to consider a nonlinear strength envelope, such as the Hoek-Brown criterion assuming a residual uniaxial compressive strength different from zero and a m_i parameter that increases, both with simultaneous mobilization. This model helps to recreate high-confining conditions and a more realistic transition between peak and post-peak strength. The obtained parameters are discussed and compared with literature values to verify the validity and to develop guidelines for the estimation of parameters, providing an objective mobilization criterion. Finally, the nonlinear model was applied to a finite element code and extended to a tunnel scale in the brittle rock under high-stress conditions. A reasonable fit between the simulations and the in-situ overbreak measurements was found.     

修正的抗剪强度参数可靠度分析方法

在抗剪强度参数可靠度分析中,针对摩尔库仑强度准则方程表现出的非线性,给出了修正的可靠度分析方法.首次选取泰勒级数的部分二次项,用一个距原点最近点处拟合的超低维曲面近似极限状态面.推导了修正的可靠度计算公式,较原有的可靠分析方法(JC法),计算精度得到进一步的提高.     

围压及粗骨料对超高强混凝土抗压性能的影响

为研究围压大小和粗骨料类型对超高强混凝土抗压性能的影响,对分别含不同类型粗骨料(玄武岩、石英岩、大理岩),相同配合比的超高强混凝土试样和其基体砂浆试样在六档围压(0、5、10、20、40、70 MPa)下进行常规三轴试验.试验结果表明:粗骨料类型对超高强混凝土试样的峰值应力、弹性模量影响显著;与基体砂浆试样相比,相同轴向应力下含粗骨料超高强混凝土试样的变形明显减小;超高强混凝土的峰值点轴向应变随围压呈线性增长,破坏形态在不同围压下呈现三种类型,0围压下的劈裂破坏、5～40 MPa围压下的剪切破坏、70 MPa围压下的挤压流动破坏;峰值应力的增长速率随围压的升高逐渐变慢,含粗骨料超高强混凝土的增长速率在低围压下高于其基体砂浆试样,而在40～70 MPa围压下两者基本趋于同一速率;不同骨料对裂缝的扩展呈现不同的阻挡作用,裂缝穿越大理岩的比例远大于石英岩.分别用Mohr-Coulomb准则与Ansari准则拟合试样的抗压强度数据,结果表明Ansari准则较Mohr-Coulomb准则更精确地反映混凝土强度随围压的变化趋势.