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。     

平面应变加–卸载试验中砂土的黏性特征及本构模型化

 通过丰浦砂的平面应变循环加载试验,分析砂土在加–卸载条件下相应的黏性特征。试验比较不同加载应变速率下2组砂土的应力–应变响应,进行蠕变加载,着重研究卸载过程中砂土的黏性特征。试验表明砂土的黏性特征与加载速率以及应力水平密切相关,且加载速率变化所引起的砂土黏性会随着加载的继续和应变的增大而逐渐衰减。卸载开始后,砂土垂直应变并未立即降低,而在一段时间范围内仍旧保持增大趋势。卸载过程中的蠕变试验还表明砂土具有“蠕变恢复”的特性。针对砂土的以上黏性特征,基于三要素模型的基本框架,提出瞬时黏性效应(TESRA)模型用以模拟加载和卸载阶段砂土黏性特征。根据试验所得到的砂土应力–应变关系,对第一次加载循环(初始加载–卸载)的砂土应力–应变响应和时程响应进行模拟,并证明瞬时黏性效应(TESRA)模型能够比较精确地模拟砂土在加–卸载循环中的黏性特征。     

平面应变条件下砂土局部化剪切带的有限元模拟

 根据饱和砂土的排水平面应变压缩试验的应变场,分析研究砂土的应变局部化现象以及剪切带的形成。在平面应变压缩条件下,砂土在峰值应力状态附近出现应变局部化现象,在残余状态最终形成一条V型剪切带。剪切带的形成是一个渐进过程,砂土呈现出渐进性破坏特性。这种由软化特性引起的应变局部化剪切带是砂土材料非常重要的变形和强度特性之一。基于砂土的三要素弹黏塑性本构模型和动态松弛有限元求解技术,对砂土的应变局部化现象和剪切带的形成进行有限元模拟。其中,砂土本构模型中引入应变局部化参数S来表示砂土峰值以后的软化和剪切带效果,剪切带在单元内未考虑其方向性,而是假设剪切带方向与最大剪切应变的方向一致。分析结果表明,动态松弛有限元法及砂土三要素模型能合理地模拟砂土的应变局部化现象,剪切带附近的最大剪应变值也非常接近,从而实现对砂土材料从硬化→峰值→软化→残余的全过程模拟以及对砂土应变局部化剪切带的定量化分析。     

适用于弹黏塑性本构模型的修正切面算法

针对弹黏塑性本构模型将原始切面算法进行了修正。该弹黏塑性本构模型结合了修正剑桥模型和过应力理论。首先对弹黏塑性本构模型的应力–应变关系式进行了调整,基于过应力理论给出了动态加载面硬化参数的演化方程。其次,利用切面算法对整理后应力–应变关系式进行了数值实现。在弹性试算过程中,该算法假设黏塑性应变率为常数,以此确保时间增量引起的当前应力点与动态加载面间的偏离。在塑性修正过程中,对动态加载面函数进行泰勒级数展开,依此获得黏塑性应变率增量。再次,提出了一种自动分步方法,有效地稳定了大应变步情况下算法的计算精度和收敛性。最后,对变应变率的固结试验和三轴剪切不排水试验进行了模拟,分析了修正切面算法的计算能力。     

K0固结软黏土的弹黏塑性本构模型

在修正剑桥模型基础上综合考虑了软黏土的各向异性及率相关性,建立了适用于K0固结软黏土的弹黏塑性本构模型。模型借鉴过应力理论的基本思想,定义了与动态加载面相对应的参考屈服面,应用径向映射准则将两者联系起来,流动函数通过分析一维情况下土体的体积蠕变速率得到。以黏塑性体积应变为硬化参数,将一维情况扩展到三维应力状态,直接用次固结系数描述土体黏性强弱,所有参数可通过压缩试验及三轴不排水剪切试验得到。分别计算了代表性等向和K0固结黏土的三轴不排水等应变率加载、不排水剪切蠕变及蠕变破坏过程,与试验结果进行对比,验证本文模型的有效可行性。     

基于土工格栅黏弹特性的加筋土本构模型研究

 将三参数黏弹性模型用于描述土工格栅在低应力水平下所表现出的蠕变特性,根据蠕变试验采用最优化方法确定有关模型参数,并证明三参数黏弹性模型能够较准确地反映土工格栅在低应力水平情况下的2个阶段衰减蠕变特性。然后,提出基于土工格栅黏弹特性的加筋土本构模型,得到土处于弹性和塑性阶段时加筋土的应力、应变计算公式。研究结果指出：加筋土中土工格栅应力与加筋土受力、格栅和土的特性、加筋层间距及时间有关;土体进入塑性状态后,土工格栅应力不变,主要表现出蠕变性,导致加筋土的应变随时间增加;随着时间的推移,土工格栅出现应力松弛,它与土体应力逐渐减小;土工格栅埋置于土中时的应力松弛量小于置于空气中的应力松弛量;加筋土塑性状态到达时间Tp受土工格栅的刚度系数E2、黏滞系数? 和土的内摩擦角? 的影响最大。     

基于内变量热力学的岩石蠕变与应力松弛研究

 蠕变变形和应力松弛是岩石材料固有的时效特性,与岩石工程的长期稳定性密切相关。基于Rice不可逆内变量热力学理论对岩石蠕变和松弛本质上的一致性问题进行了研究。给定余能密度函数和内变量演化方程建立基本热力学方程,通过不同约束条件构建黏弹–黏塑性蠕变和应力松弛本构方程。黏弹性本构方程具有普遍性,能包含经典元件组合模型的黏弹性本构方程;黏塑性本构方程考虑材料变形过程中的硬化效应,更加符合实际情况。蠕变和松弛是岩石材料在不同约束下的外在表现,但两者具有相同的非平衡演化规律,本质上具有一致性。蠕变与应力松弛本构方程基于相同的基本热力学方程,可以相互转化,且方程参数相同,因此可以通过蠕变方程和蠕变试验结果对材料的松弛特性进行分析。最后通过模型相似材料单轴蠕变加卸载试验和应力松弛试验对这一思想进行了验证。     

适用于弹黏塑性本构模型的修正切面算法

针对弹黏塑性本构模型将原始切面算法进行了修正。该弹黏塑性本构模型结合了修正剑桥模型和过应力理论。首先对弹黏塑性本构模型的应力-应变关系式进行了调整,基于过应力理论给出了动态加载面硬化参数的演化方程。其次,利用切面算法对整理后应力-应变关系式进行了数值实现。在弹性试算过程中,该算法假设黏塑性应变率为常数,以此确保时间增量引起的当前应力点与动态加载面间的偏离。在塑性修正过程中,对动态加载面函数进行泰勒级数展开,依此获得黏塑性应变率增量。再次,提出了一种自动分步方法,有效地稳定了大应变步情况下算法的计算精度和收敛性。最后,对变应变率的固结试验和三轴剪切不排水试验进行了模拟,分析了修正切面算法的计算能力。     

推断岩石长期强度的黏塑性应变率法研究

 首先,研究黏塑性应变率与加载应力水平之间的线性函数关系,从理论上说明只要能获得各分级加载应力水平对应的黏塑性应变率,便可推测岩石的长期强度。然后,利用低应力水平下的蠕变试验结果,拟合出岩石的黏弹性模型,并以该黏弹性模型推算较高应力水平条件下岩石的黏弹性应变增量,从而实现从总应变增量中分离出黏塑性应变增量,进一步计算黏塑性应变率,用于推断岩石的长期强度。此外,对大理岩,利用常规分级加载蠕变试验,检验所提出的方法的正确性。在此基础上,进一步利用试验论证缩短蠕变试验时间的可行性。研究结果表明,所提方法是正确合理的;在缩短分级加载蠕变试验时间的情况下,所推测的岩石长期强度正确合理,表明可以通过缩短试验时间快速推断岩石长期强度。所提出的推断长期强度的方法,具有快速蠕变试验、计算机程序化推断及排除人为因素的特点,且对于试验过程中的测值波动具有很好的适应能力,因此具有良好的工程应用前景。     

砂土的双硬化特性与弹塑性本构模型

 基于高精度的丰浦砂三轴等向加卸载试验与多应力路径平面应变压缩试验结果,提出平面应变条件下的修正塑性功体积硬化函数,得到双硬化框架下的修正塑性功剪切硬化函数,建立应力路径不相关的丰浦砂修正塑性功剪切–体积双硬化函数。在该双硬化函数基础上,推导基于修正塑性功的增量型剪切–体积双硬化弹塑性刚度矩阵,构建可以考虑多种变形强度影响因素的丰浦砂本构模型。数值计算与室内试验结果的比较表明,该砂土双硬化弹塑性本构模型可以合理地模拟砂土材料的变形强度特性。     

Time-Dependent Shear Deformation Characteristics of Sand and their Constitutive Modelling

Time-dependent (viscous) characteristics of the shear stress and shear strain behaviour of water-saturated or air- dried specimens of clean sands (Hostun and Toyoura sands) observed in a series of drained plane strain compression tests are presented. The overall shear stress-shear strain relationships were very similar in a set of monotonic loading tests performed at constant axial strain rates that were different by a factor of up to 500. Despite the above, significant viscous effects on the stress-strain behaviour were observed, a) when the strain rate was changed stepwise or at a constant rate, b) at creep and stress relaxation stages, and c) immediately after loading was restarted at a constant strain rate following a creep stage. One type of constitutive model was developed in the framework of the general three-component model to simulate these behaviours. According to this model, the strain is decomposed into elastic and irreversible components, while the stress is decomposed into time-independent and dependent components. This model was developed to simulate such experimental results in that the time-dependent stress component changes not only when the irreversible shear strain rate changes but also when loading continues at a certain constant irreversible shear strain rate, while these viscous effects decay with an increase in the irreversible shear strain. The rationales for the structure of the proposed model obtained from the experiment are presented. It is shown that this model can simulate well the experimental observations described above, although they were obtained under certain limited test conditions.     

Rate-Dependent Load-Strain Behaviour of Geogrid Arranged in Sand Under Plane Strain Compression

A number of previous experimental studies showed that polymer geogrid reinforcement as well as sand exhibit significantly rate-dependent behaviour. The viscous properties of polymer geogrids and Toyoura sand were independently evaluated by changing stepwise the strain rate as well as performing sustained loading and load/stress relaxation tests during otherwise monotonic loading in, respectively, tensile loading tests and drained plane strain compression (PSC) tests. The viscous properties of the two types of material were separately formulated in the same framework of non-linear three-component rheology model. The viscous response of geogrid-reinforced sand in PSC is significant, controlled by viscous properties of geogrid and sand. Local strain distributions in the reinforced sand specimen were evaluated by photogrametric analysis and used to determine the time history of the tensile strain in the geogrid. The time history of tensile load activated in the geogrid during sustained loading of reinforced sand specimen was deduced by analysing the measured time history of geogrid strain by the non-linear three-component model. It was found that the tensile load in the geogrid reinforcement arranged in a sand specimen subjected to fixed boundary loads could decrease with time. In that case, the possibility of creep rupture of geogrid is very low.     

Fem Simulation of the Viscous Effects on the Stress-Strain Behaviour of Sand in Plane Strain Compression

A stress-strain model called TESRA (Temporary Effects of Strain Rate and Acceleration), described in a non-linear three-component framework, has been proposed to simulate the effects of viscous property on the stress-strain behaviour observed in drained plane strain compression (PSC) tests on clean sands. According to the TESRA model, the current viscous stress component is obtained by integrating for a given history of irreversible strain increments of viscous stress component that developed by respective instantaneous irrecoverable strain increment and its rate and have decayed with an increase in the irreversible strain until the present. The TESRA model was implemented into a generalized elasto-plastic isotropic strain-hardening non-linear FE code. The integration scheme to obtain the viscous and inviscid stress components according to the TESRA model in FEM analysis needs some specific considerations including the relevant choice of the suitable rate parameter. The shear stress—shear (or axial) strain—time relations from five drained PSC tests on saturated Toyoura sand and air-dried Hostun sand were successfully simulated by the FE code embedded with the TESRA model. It is shown that the FE code can simulate the time-dependent stress-strain behaviour of sand accurately without spending any significant extra computational time or storage. The results of simulation using one element and multi-element are essentially the same.     

单轴试验条件下粘土的粘塑性与模拟计算

利用饱和、湿润、风干以及烘干的藤森粘土的单轴排水固结试验进行了粘土粘塑性研究。试验过程中采用计算机应变控制的控制式三轴仪来实现加载速率，可在不同加载阶段实现不同的恒应变率加载试验。试验结果表明：各种不同饱和度藤森粘土的粘塑性都表现为等时特性；经过一定时间的蠕变后，粘土弹性模量会有较大的提高，且藤森粘土所表现出的粘塑性与粘土含水量的大小无关。研究结果表明，粘土的粘塑性应力-应变特性可以采用非线性三要素模型进行较好的描述。     

Effects of Viscous Property and Wetting on 1-D Compression of Clay and Model Simulation

A series of one-dimensional (1D) compression tests on compacted kaolin powder were performed to evaluate the combined effects of the viscous property and wetting on the elasto-viscoplastic deformation of soil. In the tests, both creep deformation and collapse deformation due to wetting were allowed to take place at various fixed stress states during otherwise monotonic loading at a fixed strain rate. Combined effects of the viscous property and wetting on the stress-strain behaviour observed during 1-D compression were described by incorporating the wetting effects into a non-linear three-component elasto-viscoplastic model (a 3C model). Based on the experimental results, the effects of wetting on the inviscid stress and the irreversible strain relation of the plastic component of the 3C model and the property of the viscous component, having an Isotach property, are formulated as a function of the degree of saturation. Complicated rate- and time-dependent stress-strain behaviour observed during saturation at a fixed stress state and subsequent monotonic loading at a constant strain rate were successfully simulated.     

A Simple Pneumatic Loading System Controlling Stress and Strain Rates for One-Dimensional Compression of Clay

A simple but automated pneumatic loading system that can control the stress and strain rates for one-dimensional (1D) compression of clay was developed. The rate-dependency of stress-strain behaviour due to the viscous property of clay was investigated by 1D compression tests on standard-size specimens by various loading methods: 1) Standard Consolidation Tests (SCTs), stepwise increasing the axial stress two times every one day; 2) ordinary Constant-Rate-of-Strain (CRS) tests at different strain rates; 3) special CRS tests including unloading and reloading cycles with different stress amplitudes at strain rates of which the absolute value was either kept constant throughout respective tests or changed at the start of reloading; and 4) special CRS tests including a number of sustained loading (SL) during otherwise primary loading or unloading or reloading at constant strain rate. Sufficiently low strain rates were employed to ensure essentially fully drained condition. The followings were found. Despite that the newly developed pneumatic loading system is rather simple, 1D compression tests following such various loading histories as above can be performed on four types of clay rather accurately. The stress-strain behaviour of clay is significantly rate-dependent, exhibiting significant creep strains at SL stages. The creep strain rate is significantly different whether SL starts during otherwise primary loading or unloading or reloading, controlled by the magnitude and sign of the initial strain rate at the start of SL. The whole observed trends of rate-dependent stress-strain behaviour can be qualitatively explained by the non-linear three-component elasto-viscoplastic model extended to cyclic loading conditions.     

Residual Deformation of Geosynthetic-Reinforced Sand in Plane Strain Compression Affected by Viscous Properties of Geosynthetic Reinforcement

A series of plane strain compression (PSC) tests were performed on large sand specimens unreinforced or reinforced with prototype geosynthetic reinforcements, either of two geogrid types and one geocomposite type. Local tensile strains in the reinforcement were measured by using two types of strain gauges. Sustained loading (SL) under fixed boundary stress conditions and cyclic loading (CL) tests were performed during otherwise monotonic loading at a constant strain rate to evaluate the development of creep deformation by SL and residual deformation by CL of geosynthetic-reinforced sand and also residual strains in the reinforcement by these loading histories. It is shown that the creep deformation of geosynthetic-reinforced sand develops due to the viscous properties of both sand and geosynthetic reinforcement, while the residual deformation of geosynthetic-reinforced sand during CL (defined at the peak stress state during CL) consists of two components: i) the one by the viscous properties of sand and reinforcement; and ii) the other by rate-independent cyclic loading effects with sand. The development of residual deformation of geosynthetic-reinforced sand by SL and CL histories had no negative effects on the subsequent stress-strain behaviour and the compressive strength was maintained as the original value or even became larger by such SL and CL histories. The local tensile strains in the geosynthetic reinforcement arranged in the sand specimen subjected to SL decreased noticeably with time, due mainly to lateral compressive creep strains in sand during SL of geosynthetic-reinforced sand. This result indicates that, with geosynthetic-reinforced soil structures designed to have a sufficiently high safety factor under static loading conditions because of seismic design, it is overly conservative to assume that the tensile load in the geosynthetic reinforcement is maintained constant for long life time. Moreover, during CL of geosynthetic-reinforced sand, the residual tensile strains in the geosynthetic reinforcement did not increase like global strains in the geosynthetic-reinforced sand that increased significantly during CL. These different trends of behaviour were also due to the creep compressive strains in the lateral direction of sand that developed during CL of geosynthetic-reinforced sand.     

Viscous Behaviour of Geogrids; Experiment and Simulation

The viscous properties of three types of geogrid polymer were evaluated by sustained loading tests lasting for 30 days at a load level about a half of its nominal rupture strength. The sustained loading tests were performed during otherwise monotonic loading (ML) at constant strain or load rate, unlike the conventional creep tests, in which the strain rate immediately before the start of sustained loading, which controls the creep strain rate, is not controlled or even not recorded. The following are presented in this study. The tensile rupture strength measured by ML that was started following a 30 day-long sustained loading was essentially the same as the one at the same strain rate at rupture obtained by continuous ML without any intermission of sustained loading. This fact indicates that creep is not a degrading phenomenon. Then, if free from chemical and mechanical degrading effects, the strength of a geosynthetic reinforcement (for a given strain rate at rupture) can be maintained until late in its service life. A non-linear three-component model is used to simulate the experimental results from the previous and present studies. The model can simulate very well not only the load-strain behaviour during ML with and without step changes in the strain rate and the one after sustained loading, but also the time histories of creep strain during sustained loading for short (one hour) and long (30 days) periods.