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1.
单层不可压缩饱和多孔介质一维瞬态响应精确解   总被引:1,自引:0,他引:1  
基于Biot理论,考虑惯性、黏滞和机械耦合作用,假定固体颗粒和流体均不可压缩,得到了表面任意竖向荷载作用下单层饱和多孔介质一维瞬态响应的精确解。导出了以固体骨架位移表示的无量纲控制方程,并将边界条件齐次化。求解对应无黏滞耦合作用的特征值问题,得到一组满足齐次边界条件、关于空间坐标的正交函数基。利用变异系数法和基函数的正交性,得到一系列相互解耦的、关于时间的二阶常微分方程及相应的初始条件,并采用状态空间法求解常微分方程,得到位移分量。对整体平衡方程关于空间坐标积分,根据边界条件可确定总应力,并进而求得孔隙压力。通过算例验证所得解法的正确性  相似文献   

2.
《岩土力学》2017,(7):2071-2079
移动单元法在处理移动荷载下结构动力行为分析方面具有求解高效的优势,但目前针对饱和多孔介质动力响应的移动单元法的研究成果甚少。根据饱和多孔介质u-p格式动力控制方程,利用移动坐标系建立了饱和多孔介质瞬态及稳态动力控制方程的移动单元列式,通过编制相应的计算程序将计算结果与已有文献结果对比验证了算法的正确和有效性。基于移动单元法建立了移动荷载下饱和沥青路面-弹性基层系统计算模型,分析了移动荷载下该模型的瞬态动力响应规律,并与其稳态动力响应进行了对比分析,分析表明,其水动力特性较稳态响应呈现出明显的瞬态效应。基于稳态动力响应结果分析了荷载速度、排水边界、渗透系数对饱和沥青路面动力响应的影响规律,算例研究结果可以为分析水动力作用下沥青路面水稳定性功能损伤机制提供参考。  相似文献   

3.
陈星欣  白冰  蔡奇鹏 《岩土力学》2015,36(6):1698-1706
建立考虑吸附-解吸效应的颗粒加速迁移问题控制方程,通过Laplace变换和Fourier变换求出颗粒瞬时和周期性注入情况下点源和面源问题的解析解。同时,开展点源瞬时注入方式下颗粒迁移试验,并将试验和理论计算结果进行对比分析,两者较为吻合,从而验证了解析解的正确性。点源瞬时注入方式下颗粒迁移参数的分析进一步表明:吸附系数越大,颗粒的浓度峰值越小。解吸系数对浓度峰值左侧曲线影响较小,而对浓度峰值右侧曲线来说,解吸系数不仅影响颗粒浓度,也影响颗粒迁移时间;浓度等值线在x-y平面上的形状近似为椭圆形,解吸系数越大,相应的浓度等值线的范围越大;随着y方向弥散系数增大,浓度峰值上、下两侧的等值线梯度逐渐减小。研究成果可为地下污染物治理、地下水开采、核废料处置以及城市固体废弃物填埋等工程提供理论基础。  相似文献   

4.
程大伟  陈茜  安鹏  郭鸿  郑睿 《岩土力学》2015,36(10):2951-2954
渗流场水头分布计算是进行渗流量和渗流水力坡降计算的基础,准确、有效地求取渗流场水头分布是渗流计算的关键环节。对均质非饱和土体一维稳态流的流动方程进行分析,考虑到渗透系数是与基质吸力相关的函数,通过数学变换,给出了稳定渗流场的解析通式,并基于渗透性函数中的Gardner模型,给出了非饱和土一维稳态流水头垂直分布的解析解。该解析通式表明,均质非饱和土一维稳态流水头垂直分布主要受地表水头、深度和流动率3个因素控制。分别计算了一维稳态蒸发条件下粉土和黏土两种典型土类水头沿垂直方向的分布。计算结果表明:稳态蒸发条件下粉土层和黏土层内的水头分布表现出相似的变化规律,即自地表至地下水位处随着土层深度的增加,水头分布呈现出加速递减的趋势;在相同的蒸发条件下,对于相同深度处的黏土和粉土而言,黏土层内水头更高些;对同一种土类而言,在较大的蒸发状态下同一深度处土层内水头更高。反之,则较低。  相似文献   

5.
白冰 《岩土力学》2011,32(10):2901-2906
基于考虑热渗效应和等温热流效应的热-水-力耦合的线性热弹性固结控制方程,建立无限长空心圆柱饱和多孔介质热固结问题的一种理论求解方法。该方法先给出Laplace变换域上的解,然后,利用Stehfest法求其数值逆变换。该理论解考虑了空心圆柱体内、外透水界面随时间变化的外力和温度荷载耦合作用过程。最后,通过一算例分析了饱和多孔介质的热固结特征,给出其温度、孔压、位移和应力的演化规律  相似文献   

6.
多孔介质非饱和导水率预测的分形模型   总被引:6,自引:0,他引:6       下载免费PDF全文
多孔介质非饱和导水率是地下水污染预测与评价的重要参数。根据分形几何的基本原理和方法,推导出了与Campbell经验公式在形式上完全一致的多孔介质非饱和导水率的预测公式。公式中的幂指数为介质孔隙分维和随机行走分维的函数,分别体现了多孔介质的静态性质与动态性质对其中水分运动的影响,但静态性质的影响是主要的,即导水率主要受多孔介质的结构控制。根据文献中报道的大量数据,利用笔者推导的预测公式计算得到的幂指数的统计值与试验测定的幂指数的统计值基本一致,说明推导的理论公式预测多孔介质非饱和导水率是较为可靠的。  相似文献   

7.
以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明:大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。  相似文献   

8.
饱和土一维简谐响应解析解的求解和应用:I求解   总被引:1,自引:1,他引:1  
杨军  宋二祥  陈肇元 《岩土力学》2003,24(4):505-509
对于饱和土一维简谐响应的u-w和u-p方程,通过消元分别将二阶微分方程组变为一个四阶的微分方程。求解此微分方程则得到一维简谐响应的通解。对于特定的边值问题,通过求解描述边界条件的线性方程组得到满足边界条件的解析解。此解析解可用于饱和土动力响应研究的诸多方面。  相似文献   

9.
苏万鑫  谢康和 《岩土力学》2010,31(8):2661-2665
对采用混合可压缩流体方法分析非饱和土一维固结问题的固结方程进行了求解,在得到的解析解的基础上,对影响非饱和土一维固结的因素进行了分析。分析结果表明,在采用混合流体方法计算非饱和土一维固结的孔隙水压力时,所用公式与计算饱和土一维固结的太沙基理论公式基本相同,不同之处在于引入Bishop有效应力系数来体现孔隙气对孔隙水的影响。而在非饱和土孔隙气压的计算公式中除了体现孔隙水对孔隙气的影响参数以外,还有体现孔隙气体的可压缩性对固结影响的参数。在所有影响因素中,影响非饱和土一维固结最重要的因素是孔隙流体的渗流路径。  相似文献   

10.
土体一维冻结问题温度场半解析解   总被引:1,自引:0,他引:1  
周扬  周国庆 《岩土力学》2011,32(Z1):309-0313
针对土体的一维冻结过程,采用考虑土体冻结状态下未冻水存在的等效热容模型,建立了其温度场计算的半解析方法, 并与相关文献中的数值解进行了对比,验证了方法的正确性。对等效热容模型与显热容模型进行了对比, 计算结果表明:在瞬态阶段,显热容模型计算的冻结锋面推进速度较等效热容模型慢;而在接近稳态阶段,显热容模型计算的冻土区厚度较等效热容模型厚。在冻结诱导水流较弱的情形下,土体冻结状态下的持水特性越好,采用显热容模型进行温度场计算产生的误差越显著,并且其计算结果应用于人工冻结设计是偏于不安全的  相似文献   

11.
This paper develops a semi-analytical solution for the transient response of an unsaturated single-layer poroviscoelastic medium with two immiscible fluids by using the Laplace transformation and the state-space method. Using the elastic–viscoelastic correspondence principle, we first introduce the Kelvin–Voigt model into Zienkiewicz’s unsaturated poroelastic model. The vibrational response for unsaturated porous material can be obtained by combining these two models and assuming that the wetting and non-wetting fluids are compressible, the solid skeleton and solid particles are viscoelastic, and the inertial and mechanical couplings are taken into account. The Laplace transformation and state-space method are used to solve the basic equations with the associated initial and boundary conditions, and the analytical solution in the Laplace domain is developed. To evaluate the responses in the time domain, Durbin’s numerical inverse Laplace transform method is used to obtain the semi-analytical solution. There are three compressional waves in porous media with two immiscible fluids. Moreover, to observe the three compressional waves clearly, we assume the two immiscible fluids are water and oil. Finally, several examples are provided to show the validity of the semi-analytical solution and to assess the influences of the viscosity coefficients and dynamic permeability coefficients on the behavior of the three compressional waves.  相似文献   

12.
The one-dimensional transient response of unsaturated single-layer porous media is studied based on the theory of unsaturated porous media proposed by Zienkiewicz et al., and exact time-domain solutions are obtained for three types of nonhomogeneous boundary conditions. During the solution procedure, the nonhomogeneous boundary conditions are transformed into homogeneous boundary conditions. Then, the eigenfunction expansion method is utilised to obtain the exact solutions for these new boundary conditions. Several numerical examples are provided to investigate the propagation of compressional waves, and it is verified that three types of compressional waves exist in unsaturated porous media that contain two immiscible fluids.  相似文献   

13.
Based on the Biot theory, the exact solutions for one‐dimensional transient response of single layer of fluid‐saturated porous media and semi‐infinite media are developed, in which the fluid and solid particles are assumed to be compressible and the inertial, viscous and mechanical couplings are taken into account. First, the control equations in terms of the solid displacement u and a relative displacement w are expressed in matrix form. For problems of single layer under homogeneous boundary conditions, the eigen‐values and the eigen‐functions are obtained by means of the variable separation method, and the displacement vector u is put forward using the searching method. In the case of nonhomogeneous boundary conditions, the boundary conditions are first homogenized, and the displacement field is constructed basing upon the eigen‐functions. Making use of the orthogonality of eigen‐functions, a series of ordinary differential equations with respect to dimensionless time and their corresponding initial conditions are obtained. Those differential equations are solved by the state‐space method, and the series solutions for three typical nonhomogeneous boundary conditions are developed. For semi‐infinite media, the exact solutions in integral form for two kinds of nonhomogeneous boundary conditions are presented by applying the cosine and sine transforms to the basic equations. Finally, three examples are studied to illustrate the validity of the solutions, and to assess the influence of the dynamic permeability coefficient and the fluid inertia to the transient response of porous media. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

14.
The basic equations for fluid-saturated porous media proposed by Biot are modified by replacing the classical linear elastic model of the solid skeleton with the Kelvin–Voigt model. Thus, the new theory can take into account the viscoelastic effect of the solid skeleton. After the establishment of appropriate boundary and initial conditions, a time-domain series solution for the transient response of a fluid-saturated single-layer poroviscoelastic medium is obtained by using the finite Fourier transform and the corresponding analytical inverse transform. Several numerical examples are provided to illustrate the validity of the exact solution and to investigate the influence of the viscosity coefficient, permeability coefficient, and load frequency on the transient response of a fluid-saturated single-layer poroviscoelastic medium.  相似文献   

15.
The homogenization method is used to determine the formulation of the behaviour of both saturated and unsaturated porous media. This approach makes it possible to assess the validity of the effective stress concept as a function of the properties of the porous media at the microscopic scale. Furthermore, the influence of the morphologies of the solid and fluid phases on the macroscopic behaviour is studied. The strain induced by drying is examined as a function of the morphological properties. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

16.
Unsaturated soils are considered as porous continua, composed of porous skeleton with its pores filled by water and air. The governing partial differential equations (PDE) are derived based on the mechanics for isothermal and infinitesimal evolution of unsaturated porous media in terms of skeleton displacement vector, liquid, and gas scalar pressures. Meanwhile, isotropic linear elastic behavior and liquid retention curve are presented in terms of net stress and capillary pressure as constitutive relations. Later, an explicit 3D Laplace transform domain fundamental solution is obtained for governing PDE and then closed‐form analytical transient 3D fundamental solution is presented by means of analytical inverse Laplace transform technique. Finally, a numerical example is presented to validate the assumptions used to derive the analytical solution by comparing them with the numerically inverted ones. The transient fundamental solutions represent important features of the elastic wave propagation theory in the unsaturated soils. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

17.
The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

18.
饶登宇  白冰  陈佩佩 《岩土力学》2018,39(12):4527-4536
在考虑相变的热能平衡方程和非饱和水分迁移质量控制方程的基础上,建立温度场-水分场的耦合模型,并采用一种无网格粒子算法(SPH)进行数值求解。其中,耦合方程中考虑了水流传热以及温度势对水流的直接驱动,在不考虑相变的情况下,该耦合模型可退化为常温下的水-热耦合模型,故可用于模拟冻融循环的相关问题。从求解热能平衡方程中的含冰量出发,实现解耦并对半无限单向冻结条件下介质内非稳态温度场和体积含水率分布场进行模拟,将耦合作用下的温度场与不耦合的解析解进行对比,反映出水分迁移对温度场存在较大影响。最后,求解了路基边坡在季节性周期温度边界下,温度场、水分场分布的演变规律,并评估了边坡阴阳面受热不均对水热两场分布的影响。计算结果基本能反映土冻结相变的实际物理过程,光滑粒子算法可以用于尝试解决冻土领域的其他相关问题。  相似文献   

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