On hypoelasticity and plasticity approaches to constitutive modelling of inelastic behaviour of soils

A comparative discussion of constitutive rate equations generated by using the hypoelasticity and plasticity theories is presented. If is shown that these two approaches are equivalent for the loading process but differ essentially in defining the unloading (or reverse loading) paths. The multisurface plasticity formulation proves to be more convenient in incorporating memory rules of particular loading events, whereas loading-unloading criteria used in hypoelasticity may result in an unrealistic prediction of material response for some loading paths, and in particular, for cyclic loading. The violation of the continuity condition between loading–unloading domains in proposed constitutive relations^3,4 limits their applicability to some particular classes of loading paths.     

泥炭质土K0固结不同开挖路径应力-应变关系研究

基坑开挖过程中不同部位的土体会因不同的卸荷力学行为而表现出动态的破坏特性。为研究基坑土体开挖过程中复杂的卸荷应力路径,利用TSZ-1S应力控制式三轴仪分别对湖相沉积的泥炭质土进行固结不排水及K₀固结下的加、卸荷试验,并按侧向、轴向、轴侧向同时卸荷等不同卸荷条件制定试验方案,模拟基坑开挖过程中不同部位土体卸荷路径下的应力-应变曲线、卸荷剪切破坏时的强度及初始切线模量等的变化规律。试验结果表明：土体的应力-应变特性与应力路径密切相关,各路径下应力-应变曲线都近似呈双曲线型;卸荷剪切破坏时强度明显低于加荷破坏。对不同卸荷路径下初始切线模量(E_i)的研究发现,E_i受侧向卸荷影响较大,卸荷后E_i有所提高,轴向卸荷对其影响较小。对各应力-应变曲线进行归一化处理,构建了考虑不同归一化因子的归一化方程,以该方程为基础对不同应力路径下的泥炭质土进行归一化处理,并对结果进行了验证,效果良好。本研究可为泥炭质土场地上基坑在不同卸荷路径下的变形参数和本构关系的研究提供参考。     

k0固结条件下淤泥土排水蠕变特性研究

利用室内试验研究土体蠕变特性时,因受试验条件限制较少开展土体的排水蠕变特性试验研究。对于先还原土体的先期固结条件,然后再开展土体的三轴排水蠕变特性试验的研究更少。为此,以淤泥土为研究对象,通过 固结三轴排水蠕变试验探讨了饱和淤泥土在轴向加载和侧向减载条件下的排水蠕变特性。由试验数据可知：排水条件下,两种应力路径的轴向蠕变规律基本一致,体积应变明显小于轴向应变,且随时间的延长呈现一定程度的剪缩与剪胀交替性。首次利用三单元力学模型推测出淤泥土的蠕变起始时间为施加偏应力荷载后的100～200 min之间。提出淤泥土蠕变系数的概念并总结其变化规律,得知淤泥土的蠕变系数与偏应力水平密切相关,即不论围压及加载方式如何,蠕变系数均随应力水平增大而增大,且基本呈直线关系,而与前期固结围压大小、蠕变荷载施加方式关系不大。最后提出了淤泥土蠕变本构模型建立的思路,即用南水双屈服面模型描述瞬时变形量和用蠕变经验公式描述蠕变变形量相结合的方式来建立蠕变本构模型。     

高应力卸荷条件下砂岩扩容特征及其剪胀角函数

为研究高应力水平条件下岩石卸荷扩容特性及其剪胀角变化规律,开展了若干不同初始围压水平的三轴峰前卸围压试验,同时进行了相应围压水平的常规三轴压缩试验。基于试验成果分析了卸荷应力路径对砂岩扩容的影响效应,总结了卸荷应力路径下剪胀角变化规律,进而提出了基于卸荷应力路径的剪胀角函数,并给出了其数值实现方法,最后通过对三轴峰前卸围压试验的数值模拟,验证了所提出的剪涨角函数的可行性与合理性。研究表明：（1）加载路径时,不同围压水平下峰前扩容体积应变值相差不大,而卸荷应力路径时,随着围压水平的增加,峰前扩容体积应变从最小值3.15×10?3增加到最大值9.65×10?3,卸荷路径下的峰前扩容体积应变约为加载路径的1.1～4.0倍;（2）卸荷应力路径下偏应力峰值对应的体积应变基本为0或接近于0,而加载应力路径下偏应力峰值对应的体积应变均为负值;（3）卸荷应力路径条件下峰前扩容体积应变在总扩容体积应变中所占比例显著大于加载路径;（4）两种应力路径下,剪胀角随塑性剪切应变增加均经历了先增加后减小的过程,并且低围压工况下偏应力峰值对应的剪胀角和最大剪胀角均大于高围压工况;（5）与加载路径相比,卸荷路径下的剪胀角更快达到剪胀角最大值,并且其偏应力峰值对应的剪胀角和最大剪胀角更大;（6）基于砂岩三轴卸荷试验成果,采用线性拟合方法得出了以围压和峰后塑性剪切应变增量为自变量的剪胀角函数,基于该函数与应变软化本构模型的砂岩三轴峰前卸围压试验的数值模拟结果与试验结果吻合较好,表明该函数能较好地描述三轴峰前卸围压条件下砂岩的扩容特性。以上结论可为深部地下工程变形预测、稳定性分析与支护设计提供理论基础。     

A hierarchical approach for constitutive modelling of geologic materials

A hierarchical concept is proposed for the development of constitutive models to account for various factors that influence behaviour of (geologic) materials. It permits evolution of models of progressively higher grades from the basic model representing isotropic hardening with associative behaviour. Factors such as non-associativeness and induced anisotropy due to friction and cyclic loading, and softening are introduced as corrections or perturbations to the basic model. The influence of these factors is captured through non-associativeness manifested by deviation from normality of the plastic strain increments to the yield surface, F. Details of four models: isotropic hardening with associative behaviour, isotropic hardening with non-associative behavioural anisotropic hardening and strain-softening with a damage variable are presented. They are verified with respect to laboratory multiaxial test data under various paths of loading, unloading and reloading for typical soils, rock and concrete. The proposed concept is general, yet sufficiently simplified in terms of physical understanding, number of constants and their physical meanings, determination of the constants and implementation.     

Material stability analysis of rock joints

For prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second‐order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and τ‐constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd.     

The effects of unloading on drained cyclic behaviour of Sydney sand

New excavation or tunnelling affects the stress state of soils in ground. The change of stress state due to excavation may affect the cyclic behaviour of soils. Cyclic loading, such as traffic and earthquake loading, induced ground deformation may be greater than expected if such effect is not considered. A series of cyclic triaxial tests were performed on Sydney sand with different relative densities. The effect of unloading sequence on deformation of the sand under cyclic loading was simulated by reducing lateral stress in steps between loading cycles. The dependence of strain accumulation on the magnitude of confining pressure reduction and on unloading stress paths was studied. The results indicate that the sand has a memory of stress history and the stress history of such unloading enlarges the strain accumulation during the subsequent cycles, and the greater the reduction of lateral stress, the greater the accumulated strain. Under cyclic loading, the accumulated axial strain could increase nonlinearly or linearly with the ratio of unloading magnitude to initial mean effective stress, depending on the stress state before cyclic loading. The unloading stress paths have limited effects on the final accumulated strain if the initial and final stress states are the same. The variation of strain accumulation direction attributes to the change of average stress ratio resulting from lateral stress reduction, but hardly depends on relative density and unloading stress paths. The strain accumulation direction after unloading roughly agrees with the modified Cam Clay flow rule.

     

锦屏二级水电站大理岩复杂加卸载应力路径力学特性研究

地下洞室开挖围岩经历典型径向卸载、环向加载应力路径,由此引起的岩体强度、变形特征和破坏机制也不尽相同。针对锦屏二级水电站高地应力赋存环境,对施工排水洞大理岩开展常规单轴全应变、三轴压缩、卸围压、卸围压-加载轴压等4种不同应力路径力学试验,得到应力-应变全过程曲线、变形破坏特征和极限储能变化规律。试验研究结果表明, （1）锦屏二级水电站大理岩破坏时轴向应变一般较小,为硬脆性材料,卸荷应力路径下该脆性特征更为明显;（2）卸围压同时加载轴压试验峰值强度对应轴向应变、环向应变及体积应变值一般高于单纯的卸围压值,而对应峰值强度则一般低于卸围压值;（3）卸荷速率较大时,变形模量越大,大理岩峰值强度越低。加载速率越大,变形模量越小,峰值强度越高。初始围压越高,变形模量值越低,峰值强度越高;（4）无侧限作用时试件主要为张拉破坏,低侧限作用时为剪切破坏为主,局部存在张拉破坏,较高侧限时,剪切面为典型X或Y型;（5）岩石试件具有极限储能值,该值受多种因素的影响。一般情况下试件破坏对应围压越高,极限储能值越高,卸载速率越大,极限储能值越小。研究结果对于岩爆孕育发生机制解释以及工程实际问题的解决均有参考价值。     

开挖卸荷对砂岩力学特性影响试验研究

卸荷作用广泛存在于人类的工程活动和地质作用过程中,岩体在卸荷条件下的力学特性研究一直是工程界探讨的热点问题之一。根据实际边坡工程开挖后应力变化状态确定试验方案,进行了砂岩三轴卸荷破坏试验,研究了卸荷状态下岩体的应力应变特征、破坏特征及力学参数变化规律,并与加载破坏试验数据进行了对比分析。试验结果表明,卸荷破坏时岩样变形模量随着卸荷量的增加可降低5%～42%左右,二者之间的关系可用指数函数拟合;卸荷破坏时岩体的峰值应变随围压线性增长,残余应变与围压无明显关系;相比于加载破坏,卸荷破坏时岩体凝聚力c值降低了4%左右,内摩擦角? 增加了12%左右;卸荷速率对岩样强度和变形参数有较大影响;卸荷条件下岩体破坏具有沿卸荷方向强烈扩容特征,主要表现为张剪破坏,并伴随有环向裂纹,初始围压越高,卸荷程度越强烈,岩体的破碎程度越高。     

杭州湾浅层储气砂土应力路径试验研究

利用GDS非饱和三轴试验系统开展了杭州湾储气砂土主动压缩、被动压缩、主动伸长与被动伸长等4种应力路径试验研究,以论证应力路径对非饱和砂土的变形性状与强度特性影响。结果表明,在卸荷应力路径被动压缩与被动伸长下非饱和砂土的应力-应变曲线呈明显的应变软化性状,而加荷应力路径主动压缩与主动伸长则分别表现为轻度应变软化及显著应变硬化变形特征;非饱和砂土的强度参数在卸荷与加荷应力路径中也存在差异,前者的有效凝聚力高于后者,而内摩擦角则相反;但其表观凝聚力与基质吸力关系在不同应力路径下均可用乘幂函数 有效描述,而试验参数a、b值不同,公式 可合理地用于表述非饱和砂土的强度特性。     

卸荷条件下岩石变形特征及本构模型研究

基于岩石试件的卸荷试验,研究了卸荷条件下岩石的应力—应变全过程曲线和破裂特征,研究表明：卸荷过程中岩石向卸荷方向回弹变形强烈、扩容显著、脆性破坏特征明显;卸荷条件下岩石破坏具有较强的张性破裂特征,各种级别的张裂隙发育,其剪性破裂面追随张拉裂隙发展。基于试验认识,将卸荷条件下岩石的本构模型分为4段：弹性段、卸荷屈服段、峰后脆性段及残余理想塑性段;通过体积应变εv将Griffith和Mohr Coulomb屈服准则结合起来,建立卸荷条件下岩石的屈服准则,并在应变空间建立相应的卸荷非线性屈服段本构方程;运用应变软化理论,建立卸荷岩石峰后脆性段本构方程。     

Numerical study on stress states and fabric anisotropies in soilbags using the DEM

Wrapping granular soils in geosynthetic containers, such as soilbags, results in a considerable increase in the bearing capacity due to the effective restraint on the dilatancy of the soil. This paper numerically investigates the stress states and fabric anisotropies in the wrapped soil using the discrete element method, providing a novel perspective for new insights into the reinforcement mechanisms and the development of constitutive relations for soilbags. The two most anticipated loading conditions, namely, unconfined compression and simple shear, are considered, and numerical predictions are compared to experimental results. During unconfined compression, both global and local p–q stress paths evolve linearly, having the same slope until the global failure of the wrapping geosynthetic. Under simple shear, the global stress path approaches the critical state line first and then turns to the compression line of the wrapped soil. Some local loading–unloading stress paths are observed, which may account for the high damping of soilbags during cyclic shear. The reduced fabric anisotropies of the normal and tangential force chains suggest greater confinement from the lateral sides of the geosynthetic container in either loading course. The performance and mechanisms of the soilbag earth reinforcement method, i.e., confinement and interlocking, can be better understood based on these new findings on the stress states and fabric anisotropies.     

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na₂SO₄ contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.

     

黏土的应力路径本构模型

根据黏土应力-应变曲线的特点及其应力路径的相关特性,将作者所建立的砂土应力路径本构模型扩展用于黏土,建立了黏土的应力路径本构模型,利用变换应力方法将SMP准则用于黏土的应力路径本构模型,使模型得到了合理的三维化。黏土的应力路径模型与修正剑桥模型相比,在双向加载A区和卸载D区二者完全相同;在单向加载B区和F区,两种模型均可计算塑性应变;特别是在C区和E区,黏土的应力路径模型可计算塑性应变,而修正剑桥模型的塑性应变为0。通过与修正剑桥模型比较和对藤森黏土试验结果的预测,反映了黏土应力路径本构模型描述黏土在不同应力路径条件下应力-应变特性的优越性。     

天津市区第一海相层粉质黏土卸荷路径下强度特性的试验研究

土的强度特性与土体中应力变化过程、固结状态有关,常规的三轴试验并不能真实地反映土体经历的应力路径对其强度特性的影响。采用自制的应力-应变联合控制式三轴试验仪,对天津市区地层中第一海相层的粉质黏土原状饱和试样进行一系列特殊三轴试验,研究了排水卸荷条件对其强度特性的影响。试验结果表明：经历排水卸荷路径的土体的加荷剪切总应力强度指标大于常规试验结果,也大于前人在不排水卸荷路径下的试验结果,但几种应力路径下土体的有效应力强度指标基本相等。研究成果对天津市区基坑开挖及支护结构设计计算、软土隧道施工研究及其他相关岩土工程问题的研究均有较大的实用价值。     

盐岩循环加卸载过程中的速率效应试验研究

作为一种典型软岩,盐岩力学特性的时间相关性显著,准确预测和评估盐穴储气库加卸载过程中的变形损伤能力,关系到能源储备库的长期安全稳定运行。为研究盐岩的速率效应,进行了不同加卸载速率的疲劳试验。基于现有蠕变本构模型,构建了速率效应方程,区分了加卸载过程中的蠕变塑性变形与加载塑性变形。研究结果表明：（1）盐岩的整体疲劳寿命、稳定变形阶段（即第2阶段）疲劳寿命占比基本随加卸载速率的增大而增大。（2）减速变形阶段（即第1阶段）疲劳寿命占比、稳定变形阶段平均残余应变基本随加卸载速率增大而减小。（3）速率耦合疲劳试验中,加卸载速率越大,残余应变越小,蠕变塑性变形随加卸载速率的增大而减小,当加卸载速率由0.04 kN/s增加至5 kN/s时,蠕变塑性变形在循环中的占比由85%下降至36%,呈现出负指数的关系。（4）整个循环加卸载过程中,加载塑性变形、蠕变塑性变形均呈现U型发展趋势,与盐岩疲劳过程的三阶段相对应。该研究结果可以为进一步分析盐岩蠕变塑性与加载塑性奠定基础。     

岩土材料不同应力路径下脆性变化的二元介质模拟

试验研究表明,岩土材料在加卸荷时表现出不同的变形破坏特性,卸荷时脆性增加。建议了一个可以描述材料脆性变化的脆性指数 ,并验证了B指标能较好地描述岩土材料在加卸荷时的脆性变化。应用二元介质模型,对岩样在卸载周围应力过程中的应力-应变关系进行了模拟,表明这一模型不但可以模拟岩样在低围压下的应变软化到高围压下的应变硬化现象,而且可以模拟岩样在卸载周围应力过程中的变形破坏过程,特别是对于表现为应变软化的岩样,可以反映出应力峰值前后卸围压时的变形破坏过程的差别。     

基于达维坚科夫骨架曲线的软土非线性动力本构模型研究

试验研究表明,上海地区软土的动力变形特性符合“应变软化”规律,可用达维坚科夫（Давидеков）模型描述。首先以达维坚科夫骨架曲线为基础,采用Masing法则,构造了土体加载、再卸载的动应力-应变关系滞回曲线,推导了达维坚科夫骨架曲线和卸载、再加载滞回曲线的增量剪切模量表达式。随后将土体动应力-应变关系曲线从一维推广到三维应变空间,基于FLAC3D提供的二次开发平台,编制了基于达维坚科夫骨架曲线和符合广义Masing法则的土体非线性动力本构模型计算程序,并且通过复杂加载路径验证了编制程序的正确性和合理性。以相关文献中的土体动剪切模量比 随剪应变幅值 变化,以及阻尼比 随剪应变幅值 变化的试验结果为依据,运用编制程序计算了不同剪应变幅值下的 - 和 - 曲线,并与文献试验结果进行了对比。研究结果表明,相比于工程上广泛应用的Hardin-Drnevich模型,基于达维坚科夫骨架曲线构造的本构模型所得到的软土 - 和 - 曲线能与试验结果更符合,进而验证了所建立的本构模型的合理性与实用性,其结果可用于上海地区软土场地的动力计算反应分析。     

软岩三轴加-卸载试验的破坏特征及抗压强度取值方法研究

软岩三轴加、卸载试验中的抗压强度参数取值是一个非常关键的问题,目前还没有比较确定的方法,通常根据经验或工程要求确定。基于此,结合一组砂质泥岩的三轴加、卸载试验进行了详细研究,试验结果表明:(1)当围压大于10 MPa时,不论是三轴加载试验还是卸载试验,砂质泥岩均表现出明显的应变硬化特性;(2)砂质泥岩在三轴压缩和三轴卸荷两种应力路径的力学响应差别明显,在卸荷条件下通常只存在一条完整的剪切破坏面,而压缩条件下岩样没有明显的控制破裂面,并且剪胀效应明显;(3)将半对数法引入到软岩三轴加、卸载试验数据分析中,可以比较方便地确定软岩三轴加、卸载试验的抗压强度;(4)基于三轴加、卸载试验过程中的应力、应变增量分析,将软岩变形破坏过程分为3个阶段:平滑阶段、规则跳跃阶段和急剧跳跃阶段,各阶段划分的意义明确,可以作为抗压强度确定时的重要参考,因此,在软岩三轴试验数据分析时,可以综合采用这两种方法。研究提出的抗压强度确定方法可操作性强,在其他软岩三轴试验数据分析中值得参考借鉴。     

动态扰动对应力松弛岩石变形行为影响的试验研究

利用自主研发的岩石松弛-扰动试验装置,测试了岩石加载、松弛、动态扰动和扰动后4个阶段的轴向应力、轴向应变和声发射响应,观察到了岩石试样在动态扰动后应变增加、应力降低的现象,砂岩试样的这种特征比花岗岩明显。初步分析认为,产生该现象的原因一方面由于松弛-扰动过程导致岩石内部出现不可逆的损伤,另一方面则是扰动去除后试样的残余变形。在初始压密和弹性阶段,砂岩试样的声发射撞击数少;在接近应变峰值阶段,撞击数骤增;在应力松弛阶段撞击数骤减;在动态扰动阶段,撞击数骤增。声发射是由于岩石损伤引起的,声发射数据反映了岩石的损伤是引起松弛试样在动态扰动后应变增加、应力降低的一个原因。另外,基于砂岩和花岗岩的准静态循环加、卸载试验,对砂岩、花岗岩在不同应变等级下的残余应变进行了定量化;砂岩的残余应变远高于花岗岩,这与砂岩试样在历经松弛-动态扰动后应变增加、应力降低较为明显的趋势相对应。同时,无论是松弛-动态扰动试验还是准静态循环加、卸载试验,岩石的残余变形都会随着卸荷初始应变的提高而增加。岩石的损伤与残余变形是密切相关的,两者的综合作用引起了动态扰动后岩石试样的应变增加、应力降低现象。