关键词:密度与压力依存特性;液化;往返活动性;本构模型;循环加载 Abstract Abstract The test shows that stress-strain relationship of saturated sand has significant dependence on density and confining pressure. The above two factors can not be ignored to describe the deformation behavior of sand under static load conditions. In addition, saturated sand also exhibits obvious stress-induced anisotropy and phase transformation behaviors under complex loading, such as cyclic loading conditions. The distance between the current stress state and its corresponding point in critical state line (CSL) can be treated as a state parameter is introduced into the proposed model to reflect the density and confining pressure dependent behaviors based on the assumption that there is a unique CSL in -- space. The influence principle to stress-strain relationship under monotonic loading condition due to density and confining pressure is accurately described by using unified hardening parameter introduced by phase changing stress ratio and peak stress ratio expressed by exponential functions of state parameter. The shear volume compression, dilatancy, strain softening and hardening are all described for sand. By using non-associated flow rule, a water drop shape yield surface and an ellipse shape plastic potential surface are adopted in -- space. The liquefaction phenomenon under monotonic loading condition are also be described. To reflect the accumulation of plastic volume strain and hysteresis loops of deviatoric plastic strain under cyclic loading condition, the state parameter can be expressed as stress ratio parameter and the rotational hardening part can be adopted to describe the stress-induced anisotropy are introduced into the hardening parameter. The attenuation of shear modulus, stiffness weaken and strength decreasing behaviors are described effectively by using the proposed model. The cyclic mobility phenomenon is predicted under undrained cyclic loading conditions. The effectiveness and applicability of the proposed constitutive model is verified by the comparison of a series of simulation and test results.
不同于黏土在 -- 空间中存在唯一的正常固结线(NCL),对于砂土而言,存在无数条压缩线,且由于砂土颗粒间调整以及破碎等 因素造成了NCL线在某一局部压力段内的下移,因而在较宽的压力段内其整体表现为斜率渐大的曲线形态, 将数据在 -- 坐标系中整理,可得到如图1所示的曲线. 显示原图|下载原图ZIP|生成PPT 图1在--空间的系列压缩线及临界状态线. -->Fig. 1Series of compression lines and critical state line in versus space -->
由图1可见,假设--坐标系中存在一条正常压密线(NCL), 正常压密线可以这样理解,在压力逐渐增大过程中, 砂土颗粒未发生由非等向压力所造成的孔隙变化等现象,如颗粒破碎以及翻滚等等. 而同样存在一条临界状态线(CSL),当临界状态线上的球应力减小为零时,则此时临界状态线与正常压密线相交于一点,坐标系上纵轴表示 在球应力为零时,此时砂土颗粒纯粹由于颗粒形状以及排列方式因素造成的初始孔隙比差异. 显然存在最密初始孔隙比,由此沿着等方向压缩路径,可得到DCL线. 在NCL线上的表示松砂的压缩线. 在压力足够大时,显然所有不同初始密度的压缩线(ICL)都将趋于同一个点. 对于正常压缩线,可将其表达为 回弹线,可表示为 临界状态线表示为 由图2所示,图中黑色方框点表示Verdugo 和 Ishihara[22]于1996年对Toyoura 砂土的试验数据,由图可见,在幂函数坐标系中,临界状态线可以用直线来表达. 由于临界状态线的唯一性,因而可以借鉴Been等的建议, 采用当前孔隙比与对应相同球应力下CSL线上的孔隙比之差 来作为状态参量. 则显然,当在CSL线以上,则剪切作用下会产生剪缩,而反之,在CSL线以下,则剪切作用下会产生剪胀. 显示原图|下载原图ZIP|生成PPT 图2在--空间Toyoura砂临界状态线. -->Fig. 2Critical state line of Toyoura sand in versus ( space -->
2 本构模型
2.1 --空间中的屈服面与塑性势面参数
如图3所示,在--坐标系中的屈服面及塑性势面为一绕原点旋转的闭合曲面,其中,屈服面形态为一水滴形闭合面,而 塑性势面为共轴的椭圆面. 显示原图|下载原图ZIP|生成PPT 图3在--空间的屈服面及塑性势面. -->Fig. 3Yielding surface and Plastic potential surface in versus space -->
新窗口打开 Verdugo和Ishihara曾针对Toyoura饱和砂土进行了一系列三轴剪切加载测试. 加载方式包括不排水常规三轴剪切以及排水常规三轴剪切. 图30为初始孔隙比为0.735时的不排水应力路径测试以及预测对比图. 在较大初始密度下,分别对应有4种初始球应力作为初始压密状态,分别为0.1, 1.0, 2.0, 3.0 MPa. 在同样密度下,随着围压的增大,砂土由剪缩到剪胀的过渡应力比即变相应力比逐渐增大,高围压下密砂表现出类似于松砂在低围压下的路径特点. 显示原图|下载原图ZIP|生成PPT 图30孔隙比0.735不排水应力路径三轴压缩预测与试验对比. -->Fig. 30Comparison between prediction and test results for stress paths under undrained triaxial compression condition with void ratio equals 0.735 -->
图31为对应图30应力路径的广义偏应力与偏应变的测试与预测对比. 由图可见,预测结果与测试结果能较好的吻合. 显示原图|下载原图ZIP|生成PPT 图31孔隙比0.735不排水应力应变关系三轴压缩预测与试验对比. -->Fig. 31Comparison between prediction and test results for stress-strain relationship under undrained triaxial compression condition with void ratio equals 0.735 -->
图32和图33分别为对应初始孔隙比为0.833时的应力路径以及应力应变关系对比图. 由图可见,在围压较小时,砂土应力路径以及应力应变关系表现出了典型的密砂特点. 显示原图|下载原图ZIP|生成PPT 图32孔隙比0.833不排水应力路径三轴压缩预测与试验对比. -->Fig. 32Comparison between prediction and test results for stress paths under undrained triaxial compression condition with void ratio equals 0.833 -->
显示原图|下载原图ZIP|生成PPT 图33孔隙比0.833不排水应力应变关系三轴压缩预测与试验对比. -->Fig. 33Comparison between prediction and test results for stress-strain relationship under undrained triaxial compression condition with void ratio equals 0.833 -->
图34和图35为对应初始孔隙比为0.907时的应力路径以及应力应变关系对比图. 由图可见,在较大围压下,砂土表现出 了强烈的松砂变形特性以及典型的应力路径. 预测结果在围压为2 MPa时过高的估计了其峰值偏应力强度. 表明所提模型在对松砂的压缩体变预估显得不足. 显示原图|下载原图ZIP|生成PPT 图34孔隙比0.907不排水应力路径三轴压缩预测与试验对比. -->Fig. 34Comparison between prediction and test results for stress paths under undrained triaxial compression condition with void ratio equals 0.907 -->
显示原图|下载原图ZIP|生成PPT 图35孔隙比0.907不排水应力应变关系三轴压缩预测与试验对比. -->Fig. 35Comparison between prediction and test results for stress-strain relationship under undrained triaxial compression condition with void ratio equals 0.907 -->
图36表示在相同的初始球应力 =1MPa而初始密度处于不同值下的广义偏应力与轴应变关系预测对比,图37 为对应的有效应力路径. 对于密砂,在孔隙比为0.725下广义偏应力强度预测值稍偏小,在松砂状态,当初始孔隙比为0.921及0.933时,预测值的峰值广义偏应力稍偏大. 由应力路径可见,在0.933时,模拟能够达到静态液化结果. 在松砂到密砂的中间密度状态,所提模型能够很好的对广义偏应力以及对应的应力路径较好的描述. 密砂的应变硬化以及松砂的应变软化特点,所提模型都能完全描述. 显示原图|下载原图ZIP|生成PPT 图36不同初始孔隙比常规三轴不排水应力应变关系预测与试验对比. -->Fig. 36Comparison between prediction and test results for stress-strain relationship under undrained triaxial compression condition with various initial value of void ratio -->
显示原图|下载原图ZIP|生成PPT 图37不同初始孔隙比常规三轴不排水应力路径关系预测与试验对比. -->Fig. 37Comparison between prediction and test results for stress paths under undrained triaxial compression condition with various initial value of void ratio -->
图38和图39为对于3种初始密度分别为0.83, 0.92, 1.0下,初始围压为0.1 MPa时的常规三轴压缩预测对比结果,对于中密砂0.83的峰值广义偏应力预测偏大. 显示原图|下载原图ZIP|生成PPT 图38 MPa排水常规三轴压缩下的广义偏应力与孔隙比关系测试与预测对比. -->Fig. 38Comparison between prediction and test results for generalized deviatoric stress versus void ratio under drained triaxial compression condition with initial value of equals 0.1 MPa -->
显示原图|下载原图ZIP|生成PPT 图39 MPa排水常规三轴压缩下的广义偏应力与大主应变 关系测试与预测对比. -->Fig. 39Comparison between prediction and test results for generalized deviatoric stress versus the principal strain under drained triaxial compression condition with initial value of equals 0.1 MPa -->
图40和图41为对于3种初始密度分别为0.81, 0.89, 0.96下,初始围压为0.5 MPa时的常规三轴压缩预测对比结果,由图可见,预测与测试结果吻合较好. 显示原图|下载原图ZIP|生成PPT 图40 MPa排水常规三轴压缩下的广义偏应力与孔隙比关系测试与预测对比. -->Fig. 40Comparison between prediction and test results for generalized deviatoric stress versus void ratio under drained triaxial compression condition with initial value of equals 0.5 MPa -->
显示原图|下载原图ZIP|生成PPT 图41 MPa排水常规三轴压缩下的广义偏应力与大主应变关系测试与预测对比. -->Fig. 41Comparison between prediction and test results for generalized deviatoric stress versus the principal strain under drained triaxial compression condition with initial value of equals 0.5 MPa -->
新窗口打开 显示原图|下载原图ZIP|生成PPT 图42Sacramento河松砂排水常规三轴压缩下的广义偏应力与大主应变关系测试与预测对比. -->Fig. 42Comparison between prediction and test results for generalized deviatoric stress versus the principal strain under drained triaxial compression condition of Sacramento river loose sand -->
显示原图|下载原图ZIP|生成PPT 图43Sacramento河松砂排水常规三轴压缩下的体应变与大主应变关系测试与预测对比. -->Fig. 43Comparison between prediction and test results for volumetric strain versus the principal strain under drained triaxial compression condition of Sacramento river loose sand -->
显示原图|下载原图ZIP|生成PPT 图44Sacramento河密砂排水常规三轴压缩下的广义偏应力与大主应变关系测试与预测对比. -->Fig. 44Comparison between prediction and test results for generalized deviatoric stress versus the principal strain under drained triaxial compression condition of Sacramento river dense sand -->
显示原图|下载原图ZIP|生成PPT 图45Sacramento河密砂排水常规三轴压缩下的体应变与大主应变关系测试与预测对比. -->Fig. 45Comparison between prediction and test results for volumetric strain versus the principal strain under drained triaxial compression condition of Sacramento river dense sand -->
为便于将所提模型应用到循环加载等复杂加载路径中,采用变换应力方法[31,32,33,34,35,36,37,38,39,40,41,42,43]将模型拓展为三维弹塑性本构模型. 为验证所提模型在循环加载下的应力应变关系的适用性,采用等方向循环压缩加载路径、双路不排水循环加载以及等 排水三轴双路循环加载分别进行了预测对比. 图46为对应松砂和密砂两种密度的Sacramento河砂土在等方向压缩加载路径下的预测对比图. 图中小方格表示为对应初始孔隙比 为0.87下的循环压缩测试结果,小圆圈表示初始孔隙比为0.61下的结果. 由对比可见,预测与试验结果吻合较好. 显示原图|下载原图ZIP|生成PPT 图46Sacramento河砂等方向压缩下的孔隙比与球应力关系测试与预测对比. -->Fig. 46Comparison between prediction and test results for void ratio versus the mean stress under isotropic compression condition of Sacramento river sand -->
新窗口打开 图47和图48为Ishihara等[44]对Niigata砂土进行的双路不排水三轴循环加载测试结果,在初始球应力为212.6 kPa,初始孔 隙比为0.737下的对比结果,测试结果应力路径表明,在5个循环周期后,在第6个循环加载过程中,产生了往返活动性现象. 预测结果为在第5个循环加载过程中,产生了往返活动性应力路径. 图48在出现往返活动性路径时,同时伴随着大主应变的剧烈增大,对比结果可较好地吻合这一规律. 由于在三轴伸长路径,未进行三轴伸长路径应力比强度的修正,造成了预测幅值偏大,这可通过将所提模型三维化来解决. 显示原图|下载原图ZIP|生成PPT 图47Niigata砂双路不排水循环加载下的应力路径测试与预测对比. -->Fig. 47Comparison between prediction and test results for stress path under two way undrained cyclic loading condition of Niigata sand -->
显示原图|下载原图ZIP|生成PPT 图48Niigata砂双路不排水循环加载下的应力应变关系测试与预测对比. -->Fig. 48Comparison between prediction and test results for stress strain relationship under two way undrained cyclic loading condition of Niigata sand -->
新窗口打开 图49和图50为Pradhan等[45]对Toyoura松砂进行的等 路径下的双路循环加载测试结果. 松砂的初始孔隙比为0.845,球 应力为98.1 kPa. 在三轴压拉循环加载作用下,应力比与偏应变出现了明显的滞回曲线特性,松砂体变在往复加载作用下出现了剪缩循环累积现象. 所提模型能较好地反映了上述循环加载下的应变响应. 显示原图|下载原图ZIP|生成PPT 图49Toyoura松砂在 kPa等三轴压缩下的应力应变关系测试与预测对比 . -->Fig. 49Comparison between prediction and test results for stress strain relationship under drained compression with constant =98.1kPa loading condition of Toyoura loose sand -->
显示原图|下载原图ZIP|生成PPT 图50Toyoura松砂在 kPa等三轴压缩下的体应变与广义偏应变关系测试与预测对比. -->Fig. 50Comparison between prediction and test results for volumetric strain versus generalized deviatoric strain under drained compression with constant kPa loading condition of Toyoura loose sand -->
图51和图52为Pradhan等对Toyoura密砂进行的等 路径下的双路循环加载测试结果. 其中,初始孔隙比为0.653,球应力 为98.1 kPa. 在密砂状态下,应力比峰值较松砂更高,同时,偏应变也较小. 而体变造成剪缩体变较小,由于密实状态,因而变相比更小,剪胀容易产生,因此,剪缩与剪胀随着加载进程而循环进行切换. 剪缩剪胀最大体变幅值都不大于0.5%,所提模型在应力比与偏应变预测对比中基本与实测相符,在体变预测中,预测的 剪缩体变值偏大,而剪胀体变值偏小,主要是循环加载过程中变相比受转轴控制,实际上密砂状态循环加载作用下变相比不 仅收到应力诱导各向异性影响,同时砂土颗粒排列以及形状等原生各向异性也会产生影响,未能考虑上述影响. 显示原图|下载原图ZIP|生成PPT 图51Toyoura密砂在=98.1kPa等三轴压缩下的应力应变关系测试与预测对比. -->Fig. 51Comparison between prediction and test results for stress strain relationship under drained compression with constant =98.1kPa loading condition of Toyoura dense sand -->
显示原图|下载原图ZIP|生成PPT 图52Toyoura密砂在 kPa等三轴压缩下的体应变与广义偏应变关系测试与预测对比. -->Fig. 52Comparison between prediction and test results for volumetric strain versus generalized deviatoric strain under drained compression with constant kPa loading condition of Toyoura dense sand -->
5 结 论
在临界状态土力学框架体系下提出了一个能考虑初始密度与围压且能反映循环加载等复杂应力路径的饱和砂土弹塑性本构模型. 该模型具备以下一些基本特点: (1) 模型通过引入状态参量来表示相同球应力下临界状态线上的孔隙比与当前孔隙比之差,并将变相应力比、潜在强度比表示为状态参量的指数函数,该指数函数能反映密砂变相应力比小、潜在应力比大,松砂变相应力比大而潜在强度比小等特征,利用过渡应力比来修正统一硬化参数,使得硬化参数能同时考虑剪切体缩、体胀规律特性以及等方向压缩的体缩特性. (2) 引入修正屈服面形状的状态参量 ,通过该参数与硬化参数配合使用能反映松砂应变软化力学特性,如静态以及循环加载液化现象. (3) 在硬化参数中引入了考虑应力诱导各向异性的旋转硬化参量部分,与各向同性硬化部分共同作用. 由于屈服面与塑性势面均引入了能反映循环加载作用特性的转轴,塑性偏应变也对屈服面的硬化过程贡献作用. 在不排水往复循环作用下,能反映塑性体应变的循环累积作用,能反映塑性偏应变的往复滞回特点,如往返活动性现象. 同时对于松砂以及密砂的循环加载作用响应结果能较好的描述. 模型表明,仅用一套参数,可以对不同初始密度、围压以及三轴不排水、三轴排水等多种状态和路径下的应力应变关系给出较好的预测结果,表明所提模型对于砂土这种密度与压力依存性材料具有较好的描述能力. The authors have declared that no competing interests exist.
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