A simple model for stress-induced anisotropic softening of weak sandstones

Weak sandstones possess deformational behavior different from hard rocks; these phenomena include shear dilation and softening of the deformational moduli. It has been found previously that under hydrostatic loading, the bulk modulus increases as confining pressure arises; and that under shear loading, the weak sandstone may transform from its original isotropy to a stress-induced anisotropic material, and the deformational modulus can accordingly be softened as well. These phenomena contribute to the increase of crown settlements during tunnel excavations, and account for several cases of tunnel squeezing. Consequently, a model capable of simulating major deformational characteristics of weak sandstones is needed for engineering purposes. A simple yet innovative constitutive model is accordingly proposed. This proposed model is characterized during the simulation as having: (1) non-linear volumetric deformation under hydrostatic loading; (2) significant shear dilation prior to the failure state; (3) isotropic stiffening of deformational moduli under hydrostatic loading; and (4) anisotropic softening of deformational moduli under shearing condition.The proposed model was formulated based on the linear elastic model, and it accounts for the variations of moduli E and G through different loading conditions. It was found that the proposed model is able to closely simulate the actual deformational characteristics of weak sandstones. In addition, the proposed model only needs six material parameters, and all these parameters can be easily obtained from experiments. This model was then incorporated into a finite element program and was used to analyze a squeezing tunnel case.     

Deformational characteristics of weak sandstone and impact to tunnel deformation

In northern Taiwan, a tunnel under construction along a segment where weak sandstone, the Mushan sandstone, was encountered and an excess crown settlement (14–30 cm) has been reported. This paper studies the deformational characteristics of Mushan sandstone and its impact on tunnel deformation. To distinguish the volumetric and the shear deformation of the sandstone, experiments with controlled stress paths, including hydrostatic compression, pure shearing and conventional triaxial compression, were conducted. The measured deformations were then decomposed into elastic and plastic components further exploring the stress–strain behavior of weak sandstone. The results indicate that, similar to other soil-like geo-materials, this sandstone has plastic strain before the stress path reaches the failure envelope and significant shear dilation is induced, especially when approaching the failure envelope. Meanwhile, the distinct features of deformation have also been highlighted by comparing the experimental results to the prediction, derived from existing constitutive models that were originally developed for other geo-materials. These features include significant plastic volumetric strain at low levels of confining stress, suppression of plastic volumetric strain at higher levels of confining stress, and the fact that the actual amount of shear compression is less than that predicted by the model. Numerical analysis indicates that the weak rock leads to the greatest inward displacement, which results from the shear dilation prior to failure state.     

An associated elastic–viscoplastic constitutive model for sandstone involving shear-induced volumetric deformation

In contrast to hard rocks, weak rocks often have significant shear-induced volumetric contraction/dilation under short-term or long-term loadings, and this behavior necessitates the development of an unconventional constitutive model. As such, an elastic–viscoplastic constitutive model characterizing the mechanical behavior of weak rocks is proposed, and its validity is demonstrated by comparing the simulated and the actual deformational behaviors of weak sandstone under various stress paths. In order to distinguish the immediate and the time-dependent deformation, the procedures involving multi-stage loading–unloading and creep tests, together with controlled pure-shear stress path, have been undertaken to clarify the deformation behavior of sandstone. Through these experimental procedures, elastic and viscoplastic deformations can be effectively separated, and the coupling between shear stresses and volume stresses can also be identified. Consequently, it is found that the function form of yield surfaces can also be applied to plastic potentials and viscoplastic potentials so that the complexity of the constitutive model to be developed is significantly reduced. Furthermore, the parameters for the proposed constitutive model can be readily obtained by fitting experimental data. Through systematic comparisons of the predictions and the actual behaviors of the studied sandstone, it is found the proposed constitutive model is capable of describing the elastic, plastic, and viscoplastic deformational behaviors not only under pure shearing stress path that were used to calibrate parameters, but also under other stress paths.     

Time-dependent deformation behaviors of weak sandstones

Time-dependent deformation behavior of rocks has a significant impact on the stability of rock slopes or underground constructions. This paper presents systematic experimental data regarding time-dependent deformation of a typical weak sandstone, known as the Mushan sandstone. The observed deformations are further separated to distinguish elastic and viscoplastic behaviors of the weak sandstone through the use of multi-staged loading–creep-unloading–reloading tests. The stress path is designed to be a purely hydrostatic loading followed by a pure shear, so that the deformations induced by these two types of stresses can be distinguished.For elastic behavior, although the nonlinear stress–strain relations vary according to the applied hydrostatic stress, these stress–strain relations can be normalized by the applied hydrostatic stress or the bulk modulus and converted into a single consistent stress–strain curve. Inelastic behavior is then obtained by subtracting the elastic deformation from the total deformation. As a result, the characteristics of the viscoplastic deformation are that: (1) the direction of the viscoplastic flow is time independent, and (2) it has a similar direction to the conventionally defined plastic flow. As such, the viscoplastic potential has a similar shape to the plastic potential, but the size of the former changes with time, while the latter has a size that is time independent. Meanwhile, through the calculation of irreversible work, direct evidence of orthogonality between the yield surface and the plastic flow, as well as the viscoplastic flow, is observed. Thus, it is reasonable to assert that the yield surface, the plastic potential, and the viscoplastic potential all have the same geometry. Consequently, the associated flow rules are applicable to modeling the time-dependent deformational behavior of weak sandstones.     

岩石剪胀角模型与验证

Mohr-Coulomb模型和基于Mohr-Coulomb的应变软化模型均通常假设剪胀角为恒定值,然而这种假设不能正确表达岩石在破坏变形过程中的非线性体积变化行为。根据7种岩石类型在不同围压条件下的体积应变测量数据,结合塑性力学理论,采用非线性拟合方法建立能同时考虑围压和塑性剪切应变影响的剪胀角模型。分析模型的响应并结合岩石内部颗粒尺寸以及单轴抗压强度,将该模型划分为4种岩石类型:粗粒径硬岩、中粒径硬岩、中–细粒径软岩和细粒径软岩。根据FLAC应变软化模型中非关联塑性流动法则的计算原理,推导剪胀角模型中的塑性剪切应变与应变软化模型中塑性参数的关系,将剪胀角模型嵌入应变软化模型中,构建剪胀角模型模块。最后,采用建立的剪胀角模型预测Moura煤岩在三轴压缩条件下的体积应变–轴向应变关系曲线。研究结果表明,数值模拟与试验结果具有很好的一致性。     

循环荷载作用下花岗岩疲劳力学性质及其本构模型

 循环荷载作用下岩石力学性质研究对完善岩石力学基本理论和指导相关工程建设具有重要意义。通过花岗岩三轴循环荷载试验,系统研究花岗岩疲劳力学特性,提出花岗岩疲劳力学模型。研究结果表明：(1) 岩石残余应变和变形模量与循环次数之间关系与岩石体积变形状态相关;(2) 在应力–应变全空间内,花岗岩疲劳性质分为3个区域,不同区域内微观机制不同;(3) 岩石疲劳破坏门槛值应为剪缩和剪胀区域分界点对应的峰值偏应力;(4) 循环荷载作用下岩石疲劳势有别于单调加载时塑性势,循环荷载作用下岩石表现出比单调加载时更强的抵抗体积变形能力;(5) 提出基于内变量理论的岩石疲劳本构模型,试验数据与模拟预测对比显示模型较好地反映出岩石疲劳力学性质。     

Numerical modeling of tunnel excavation in weak sandstone using a time-dependent anisotropic degradation model

This paper presents a shear-induced anisotropic degradation model involving time-dependent behavior to simulate the deformational characteristics of weak sandstone. The stress–strain relationship of the proposed model was originated from the degradation of moduli K and G subjected to different loading conditions. An anisotropic factor β is introduced to indicate the tendency of shear-induced volumetric deformation. Furthermore, to incorporate time-dependent deformation behavior of sandstone, this anisotropic degradation model is further extended using a generalized Burger’s model. As a result, the proposed model is characterized by the following features: (1) being capable of describing shear-induced volumetric deformation, either compression or dilation, prior to the failure state; (2) being versatile in the time-dependent (creep) deformations; and (3) the anisotropic factor β serves as a convenient index regarding whether shear-induced volumetric deformation dilates or not. Afterward, the proposed model has been verified by comparing to experimental results. It is found that the proposed model is versatile in simulating short-term and long-term deformations of sandstone under different stress paths. Moreover, this model has been incorporated into finite element program and used to analyze a case of tunnel squeezing. Comparing with other existing models, it is found that the prediction of the proposed model is closer to reality and reveals a larger crown settlement, namely a squeezing condition, owing to larger extent of dilation zones. Overall, although the proposed model is a simple variable moduli model, it is capable of describing the key deformation behavior of weak sandstone reasonably-well, including time-dependent and shear-induced deformations.     

岩石隧道塑性位移新解

 在统一强度理论和弹脆塑性模型的基础上,考虑塑性区围岩弹性模量的变化、中间主应力效应、围岩应变软化和剪胀等影响,推导了深埋圆形岩石隧道塑性位移新解。文中的隧道位移新解具有广泛的理论意义,可根据具体工程实际情况,进行多种合理选择。经工程算例分析可知,由塑性区半径相关的弹性模量计算得到的位移处于上、下限之间,反映了隧道开挖卸荷扰动影响的距离变化,更符合隧道变形真实情况,并得出统一强度理论参数和剪胀特性参数对塑性区位移的影响规律。研究结果表明：隧道塑性区位移受中间主应力、围岩剪胀特性和塑性区弹性模量的影响显著,三者相互影响,共同作用。     

剪胀对地下工程岩体位移的影响——以加拿大Donkin-Morien隧道为例

根据建立的岩石剪胀角模型,分析岩石峰值内摩擦角和剪胀角的关系,得出岩石在零围压时的峰值剪胀角小于并近似等于峰值内摩擦角,并假设岩石和岩体的剪胀角遵循相似的变化趋势,结合Hoek-Brown强度准则和GSI岩体分级系统,实现剪胀角模型从完整岩石到岩体的转化。采用程序语言在FLAC3D中编写岩体剪胀角模型程序模块。以加拿大Donkin-Morien隧道为工程实例,研究围压和塑性剪切应变依赖的岩体剪胀对隧道渐进开挖过程中围岩位移的影响,论证恒定的剪胀角值不能准确表达隧道开挖边界附近的岩体位移,而考虑围压和塑性剪切应变为影响因素的岩体剪胀角模型能够合理描述围岩的位移分布,模拟结果与实际测量值具有很好的一致性。研究成果可为岩体非线性力学行为的研究和地下工程岩体的稳定性控制提供理论和实践基础。     

Considerations of rock dilation on modeling failure and deformation of hard rocks-a case study of the mine-by test tunnel in Canada

For the compressive stress-induced failure of tunnels at depth, rock fracturing process is often closely associated with the generation of surface parallel fractures in the initial stage, and shear failure is likely to occur in the final process during the formation of shear bands, breakouts or V-shaped notches close to the excavation boundaries. However, the perfectly elastoplastic, strain-softening and elasto-brittle-plastic models cannot reasonably describe the brittle failure of hard rock tunnels under high in-situ stress conditions. These approaches often underestimate the depth of failure and overestimate the lateral extent of failure near the excavation. Based on a practical case of the mine-by test tunnel at an underground research laboratory (URL) in Canada, the influence of rock mass dilation on the depth and extent of failure and deformation is investigated using a calibrated cohesion weakening and frictional strengthening (CWFS) model. It can be found that, when modeling brittle failure of rock masses, the calibrated CWFS model with a constant dilation angle can capture the depth and extent of stress-induced brittle failure in hard rocks at a low confinement if the stress path is correctly represented, as demonstrated by the failure shape observed in the tunnel. However, using a constant dilation angle cannot simulate the nonlinear deformation behavior near the excavation boundary accurately because the dependence of rock mass dilation on confinement and plastic shear strain is not considered. It is illustrated from the numerical simulations that the proposed plastic shear strain and confinement-dependent dilation angle model in combination with the calibrated CWFS model implemented in FLAC can reasonably reveal both rock mass failure and displacement distribution in vicinity of the excavation simultaneously. The simulation results are in good agreement with the field observations and displacement measurement data.     

深部岩体变形破坏动态本构模型

 根据深部岩体在卸荷条件下能量释放、消耗和转移的过程中,其体积变形经历弹性回弹和扩容以及剪切变形可能经历峰值前(弹性和内摩擦强化阶段)和峰值后(软化及残余破坏阶段)阶段的性状,提出深部岩体变形破坏全过程动态本构模型。该模型的特点可归纳为：(1) 引入Juamann导数,能够计算有限变形;(2) 描述卸荷过程中与时间相关的体变回弹、扩容至破裂的全过程关系;(3) 描述了卸荷过程中,深部岩体强度(长期强度、破坏强度和残余强度)被调动的演化过程,并用同轴的屈服面、破坏面与残余破坏面3个圆锥面加以描述;(4) 运用物理细观力学理论,引入宏观裂纹扩展滞后时间表征岩体不同构造水平在强化中的贡献,给出内摩擦强化阶段流变方程;(5) 运用裂纹运动散布理论,引入破裂时间表征宏观裂纹扩展贯通过程,给出破裂过程中的强度随时间的演化方程,用塑性流动理论给出软化阶段形变本构方程。最后,在LS-DYNA平台下对本构模型进行二次开发,通过深埋地下隧洞开挖变形破坏的算例,初步展示该模型在深部岩体力学理论与工程中的应用前景。     

深埋水工圆形隧洞塑性位移三剪统一解

基于三剪统一强度准则和弹脆塑性模型,考虑中间主应力、渗流、剪胀、软化和塑性区弹性模量等因素的影响,推导了含有5种因素综合影响的水工圆形隧洞塑性区位移解析解;通过算例分析,得出了各参数对隧洞塑性区位移的影响规律。结果表明:各参数取不同值时,位移解可退化为一系列解,参数值可根据具体工程进行合理选择,具有广泛的适用性;围岩剪胀特性对隧洞塑性区位移的影响显著,若不考虑其影响,将明显低估隧洞的变形以致工程设计偏于危险;考虑中间主应力的影响能发挥围岩的强度潜能,减少支护,节约工程造价;考虑渗流和软化特性对隧洞塑性区半径的影响可使塑性区范围更接近围岩真实的变形范围;塑性区弹性模量采用含有半径幂函数的表达式可充分考虑围岩受扰劣化后的应力重分布及爆破损伤等影响,更符合隧洞真实变形情况;该位移解为隧洞塑性区位移计算提供了理论依据,对工程设计有一定的参考价值。     

挠曲核部破碎带岩石力学特性的试验研究

立煤湾膝状挠曲核部破碎带横穿向家坝水电站大坝坝基,破碎带的岩石由于完整性差,孔隙率大,含水率较高,会对坝基的变形和稳定性产生影响。通过研究破碎带岩石的物理和力学特性,发现破碎带岩石的碎裂岩、碎屑岩在三轴压缩条件下呈现非线性的应力应变关系,强度低、变形大,且没有明显的强度峰值,最终因变形过大而破坏;试验过程中,还发现随着岩石的屈服和变形的发展,出现明显的体积膨胀。并且通过破碎带岩石的流变力学试验,发现岩石流变特征明显,偏应力对流变速率有较大影响。最后根据常规三轴试验的应力应变关系建立了基于双曲线模型的改进Burgers模型,并对其参数进行辨识。     

基于梯度塑性理论的岩样单轴压缩扩容分析

采用梯度塑性理论，对岩样剪应变局部化引起的扩容进行了理论分析。假设岩石的剪切本构关系为弹性-应变软化双线性，局部化启动于应力峰值强度，利用局部塑性剪应变与局部塑性体积应变的线性关系，得到了局部塑性体积应变、局部塑性体积增量及剪胀引起的剪切带总塑性体积增量的解析式，这体现了该理论在研究剪胀问题时的优越性。另外，还得到了弹性阶段及应变软化阶段的轴向应力-体积应变曲线的理论关系。塑性体积应变是专指由剪切带剪胀而引起的，因而，轴向应力．体积应变不具有尺寸效应，与局部化带的尺寸无关，但扩容角、剪切降模量及泊松比却对该曲线有重要影响。在弹性阶段及应变软化阶段轴向应力-体积应变均呈线性。在相同的应力水平下，扩容角越大则剪胀程度越大；剪切降模量越大，剪胀程度越小。在应变软化阶段，泊松比不影响塑性体积应变。     

横观各向同性岩石弹塑性本构模型与参数求解方法研究

地层中普遍存在层理状岩石,这些岩石细观结构具有显著的方向性,从而引起了其变形与强度具有横观各向同性。采用弹性力学与广义塑性力学基本理论,建立了岩石横观各向同性弹塑性本构模型:弹性部分采用广义胡克定律描述,塑性部分采用基于广义八面体剪应力的屈服准则和势函数、非关联流动法则和应变硬化准则描述。该模型屈服面为外凸的非等截距椭圆截面角锥体,在各向同性条件下可退化为米塞斯屈服准则。提出了模型参数求解方法:弹性参数采用三轴压缩和扭转试验联合求解;塑性参数采用不同层理方向试样的三轴压缩试验求解。以炭质板岩为例,验证了所提出的横观各向同性弹塑性模型和参数求解方法,验证结果表明所提模型较好地反映了岩石的横观各向同性,参数求解方法简单有效。此外,还根据试验数据分析了炭质板岩塑性势方向性和弹塑性参数耦合特征。研究成果将为丰富岩石力学基本理论和解决相关工程问题提供理论基础。     

考虑应力路径和加载速率效应砂土的弹黏塑性本构模型

 利用室内多应力路径平面应变压缩试验结果,分析和研究密实砂土变形和强度特征的应力路径和加载速率效应。试验结果表明：一方面,不可恢复体积应变和剪切应变都具有明显的应力路径相关性,因而在传统塑性理论中将其作为硬化参量存在不合理性;另一方面,砂土的应力–应变特性与加载速率的变化存在着显著的关系。加载速率效应与蠕变和应力松弛一样均是砂土黏性的外在反映,其最重要的特征之一是加载速率发生突变时,应力也发生相应的突变,并呈现出刚性很大、近似弹性的特性。对试验结果的进一步分析发现,一种修正的不可恢复应变能W ir*及相关的函数与应力路径不相关。将W ir*作为硬化参量,并在非线性三要素模型的理论框架下,提出一种基于能量的砂土弹黏塑性本构模型。该模型可以考虑应力路径、压力水平、固有各向异性、孔隙比等因素对砂土变形和强度特征的影响,以及应变局部化和加载速率变化所产生的黏性特性。将上述模型嵌入到有限元程序中,并对平面应变压缩试验进行模拟计算,验证模型的精确性。研究结果表明,与现有的砂土本构模型相比,所提出的模型能更好地模拟应力路径及加载速率变化对砂土变形和强度特征的影响。     

高孔岩石中局部变形带的理论 和形成条件研究进展

 近几年在野外和实验室都发现高孔隙岩石中局部化变形的压缩带、剪切带和膨胀带,是目前岩石力学、岩石物理和本构模型研究的热点之一。基于局部变形带在水利、石油、核废料处置、垃圾处理、环境污染的治理和地质构造、工程地质和岩土工程中的实际意义,介绍以局部化分岔理论为基础的多孔岩石的压缩带、剪切带的理论、形成条件和判别条件,以及与压缩带、剪切带和膨胀带相应的临界硬化模量。基于帽子模型,介绍椭圆形屈服帽上的压缩和剪切带,以及它们与s-e曲线之间的密切关系。在低围压下的s-e曲线上的第一个零模量点也就是应力平台对应于压缩带,即为帽子模型的体积屈服面;继续加载使s-e曲线继续上升到标本产生硬化,直到s-e曲线上出现第二个零模量点,也就是s-e曲线的峰值对应于剪切破坏,此时应力状态处于帽子模型的剪切屈服面上。同时还给出大量不同颗粒尺寸、不同孔隙度砂岩轴对称压缩试验结果,它们也可用1/4椭圆帽子模型来描述。     

基于状态参数的砂土非线性弹性模型研究

 砂土的密实度和有效围压显著地影响着它的力学变形特性。为了反映这2个因素的影响效应,对沈珠江基于初应变法提出的三参数(压缩模量K0、杨氏模量、体变系数)非线性弹性模型进行修正。首先建立一种可以有效地反映初始状态影响的K0压缩曲线描述模式。其次,为了反映密实度和有效围压对排水三轴试验中剪切曲线的影响,基于状态参数定义“虚拟峰值偏应力”这一变量,并给出一个新的剪切曲线描述模式。另外,为了描述砂土的变形特性,引入剪胀方程。该修正模型数学描述简单,仅有10个材料参数,且各参数均容易确定。最后,利用该修正模型对排水、不排水条件下的三轴试验进行模拟,模型的计算结果与实测结果吻合较好,表明该修正模型可以较准确地描述砂土的物理状态变化对其力学与变形特性的影响,初步验证模型的合理性。     

饱和砂土弹塑性动力本构模型研究

利用土体的塑性流动理论,提出了基于SMP破坏准则的土体弹塑性动力本构模型,用于描述饱和砂土的动力反应性质。土体总的变形由3个部分组成:弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。通过将应用该模型模拟计算的结果与试验结果进行对比,表明该模型能够较为准确地描述饱和砂土在循环加载条件下的反应性质,具有较少的模型参数,这些参数都可以通过常规的三轴压缩试验和静水压力试验进行确定。同时,该模型的形式比较简单,可用于数值计算中。