复杂条件下软粘土地基多维固结分析
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摘要
本文基于前人的工作,从一维固结理论出发,对二维轴对称包括竖井地基,在复杂条件作用下的固结问题做了全面的分析。
首先,根据e～lgσ和e～lgk_v曲线关系,对循环荷载作用下一维小应变非线性固结问题进行了分析。用数值方法编制程序对单层地基在常见荷载(骤加恒载、三角形波载、正弦波载、矩形波载和梯形波载)作用下的非线性一维固结性状进行了讨论,并与传统Terzaghi固结理论和常见荷载作用下地基一维线性固结理论所得结果进行了比较。
然后,基于Gibson大应变固结理论,研究了循环荷载下一维大应变固结问题。通过具体算例比较研究了变荷载作用下,地基土体在一维大变形与一维小变形非线性固结时性状的异同。
继而,从一维固结问题扩展到轴对称二维地基,利用Laplace-Hankel联合变换法,得到变荷载作用下Biot固结方程频域内解析解。从各向同性地基问题出发,分别对半空间和下卧基岩两种边界条件进行了讨论分析。又由于天然地基在形成过程中具有取向关系,水平和竖直方向存在差异,呈现各向异性的现象。在水平方向可近似地看成各向同性,但在垂直方向其形态与水平方向差异较大,因此本文接着分析了考虑横观各向同性情况下地基固结的问题。
接着,采用Laplace变换的方法,求解了变荷载下能合理考虑土中三维渗流的未打穿砂井地基固结半解析解。此方法计算速度快,求解精确,更适合工程实际应用。
最后,建立竖井地基非线性固结计算模型,把土体材料非线性考虑到计算模型中,推导了缓加变荷载下的解析解。
本文工作表明:地基一维固结情况下,在渗透系数k_v与体积压缩系数,m_v呈非线性变化时,地基固结不同于传统Terzaghi固结理论所得结果。在循环荷载作用下,地基中各点的有效应力并不随时间的变化而同步变化,而是有其自身的规律——发展相对滞后;而且,有效应力变化幅度与外加荷载大小,d_c/c_k等参数密切相关。在考虑土体自重应力影响时,大变形固结在计算中特别需要考虑这一部分所引起的沉降,如果仍旧按照小变形固结来计算,其结果将远远小于实际所得。对于循环荷载下二维轴对称作用下地基固结情况,由于Biot固结方程充分考虑到地基土体水平向应力、应变和排水等影响因素,因此,孔压会出现负值,明显不同于一维固结下情况。未打穿砂井地基的固结速率随砂井长度的增大而增大,但当砂井长度超过一定值后,固结速率增长减慢;国内常用的将砂井底面作为其下土层排水面的简化计算法给出的平均固结度则偏大。对于竖井地基,当外加荷载比较大的情况下,考虑材料的非线性尤为必要。
On the basis of the work so far available, this paper makes a further study from the non-linear one-dimensional small and finite-strain consolidation theory and then analysis the two-dimensional axisymmetric consolidation theory with or without the vertical drain considering complicated surcharging loadings conditions as well.
First, based on the well-known empirical e～lgσ' and e～lgk_v relations, one-dimensional consolidation problems of soft soils under cyclic loadings are analyzed. On the basis of the solutions obtained and the computation through programming, the influence of some parameters and loading conditions on the non-linear one-dimensional consolidation behaviors under suddenly-imposed, sin, trapezoidal, triangular and rectangular cyclic loading, are investigated. And then the results are compared with Terzaghi's consolidation theory and linear consolidation theory under cyclic loadings.
Second, on the basis of Gibson consolidation theory and by the method of Laplace transform, the analytic solutions in frequency domain are obtained. According to numerical examples, some characteristics of non-linear consolidation behaviors of finite consolidated soil under cyclic loadings are compared with those of normal consolidated soil.
Third, based on Biot's governing consolidation equations for semi-infinite and also finite isotropic soil layer, general solutions are derived by applying the Laplace-Hankel transform technique. A numerical inverting procedure was used to study the consolidation behavior in the time domain for different external loading cases. Due to the real soil's original deposition in horizontal beds, the real soil is often anisotropic in that its horizontal properties are different from its vertic al properties. Thus, a more realistic solution to the consolidation problem which should account for the soil anisotropy was obtained.
Fourth, the general solution in the Laplace transform field for the consolidation of soil with partially penetrated vertical drains under complicated time-dependent loadings is derived. And the method is used here has been proved to be an efficient and accurate method, which can be widely used in practice engineering.
At last, a new computational model which can consider the non-linear material character of the soils is established. The analytical solutions for the non-linear consolidation of soft soil with vertical drains are obtained under both constant loading case and time-depending loading case.
From this study, the following conclusions may be obtained: on the assumption of permeability index k_v changes linearly with volume compression index w_v, consolidation of soil is different from Terzaghi's consolidation theory. And under cyclic loading, the effective stress in soil is not synchronously changed with loading but is developed in a delayed way; the scope of effective stress is related with the parameters of loading and with c_c/c_k; when considering the self-weight of soil, this portion of settlement must be calculated in the finite-strain consolidation, if the result is obtained according to the infinite consolidation, it will be far less than the actual result. For the two-dimensional consolidation, a negative pore water pressure is observed when the soil under cyclic loadings, which is different form one-dimensional consolidation theory. With the numerical modelling, it is shown that the rate of consolidation of the soft soil with partially penetrated vertical drain is increased with the increase of the drain length. However, it is slow down as the length exceeds some extent. And the consolidation degree is overestimated by the one commonly used in China. When the external loading is big enough, it is necessary to take the non-linear character of the soil into consideration.
首先,根据e～lgσ和e～lgk_v曲线关系,对循环荷载作用下一维小应变非线性固结问题进行了分析。用数值方法编制程序对单层地基在常见荷载(骤加恒载、三角形波载、正弦波载、矩形波载和梯形波载)作用下的非线性一维固结性状进行了讨论,并与传统Terzaghi固结理论和常见荷载作用下地基一维线性固结理论所得结果进行了比较。
然后,基于Gibson大应变固结理论,研究了循环荷载下一维大应变固结问题。通过具体算例比较研究了变荷载作用下,地基土体在一维大变形与一维小变形非线性固结时性状的异同。
继而,从一维固结问题扩展到轴对称二维地基,利用Laplace-Hankel联合变换法,得到变荷载作用下Biot固结方程频域内解析解。从各向同性地基问题出发,分别对半空间和下卧基岩两种边界条件进行了讨论分析。又由于天然地基在形成过程中具有取向关系,水平和竖直方向存在差异,呈现各向异性的现象。在水平方向可近似地看成各向同性,但在垂直方向其形态与水平方向差异较大,因此本文接着分析了考虑横观各向同性情况下地基固结的问题。
接着,采用Laplace变换的方法,求解了变荷载下能合理考虑土中三维渗流的未打穿砂井地基固结半解析解。此方法计算速度快,求解精确,更适合工程实际应用。
最后,建立竖井地基非线性固结计算模型,把土体材料非线性考虑到计算模型中,推导了缓加变荷载下的解析解。
本文工作表明:地基一维固结情况下,在渗透系数k_v与体积压缩系数,m_v呈非线性变化时,地基固结不同于传统Terzaghi固结理论所得结果。在循环荷载作用下,地基中各点的有效应力并不随时间的变化而同步变化,而是有其自身的规律——发展相对滞后;而且,有效应力变化幅度与外加荷载大小,d_c/c_k等参数密切相关。在考虑土体自重应力影响时,大变形固结在计算中特别需要考虑这一部分所引起的沉降,如果仍旧按照小变形固结来计算,其结果将远远小于实际所得。对于循环荷载下二维轴对称作用下地基固结情况,由于Biot固结方程充分考虑到地基土体水平向应力、应变和排水等影响因素,因此,孔压会出现负值,明显不同于一维固结下情况。未打穿砂井地基的固结速率随砂井长度的增大而增大,但当砂井长度超过一定值后,固结速率增长减慢;国内常用的将砂井底面作为其下土层排水面的简化计算法给出的平均固结度则偏大。对于竖井地基,当外加荷载比较大的情况下,考虑材料的非线性尤为必要。
On the basis of the work so far available, this paper makes a further study from the non-linear one-dimensional small and finite-strain consolidation theory and then analysis the two-dimensional axisymmetric consolidation theory with or without the vertical drain considering complicated surcharging loadings conditions as well.
First, based on the well-known empirical e～lgσ' and e～lgk_v relations, one-dimensional consolidation problems of soft soils under cyclic loadings are analyzed. On the basis of the solutions obtained and the computation through programming, the influence of some parameters and loading conditions on the non-linear one-dimensional consolidation behaviors under suddenly-imposed, sin, trapezoidal, triangular and rectangular cyclic loading, are investigated. And then the results are compared with Terzaghi's consolidation theory and linear consolidation theory under cyclic loadings.
Second, on the basis of Gibson consolidation theory and by the method of Laplace transform, the analytic solutions in frequency domain are obtained. According to numerical examples, some characteristics of non-linear consolidation behaviors of finite consolidated soil under cyclic loadings are compared with those of normal consolidated soil.
Third, based on Biot's governing consolidation equations for semi-infinite and also finite isotropic soil layer, general solutions are derived by applying the Laplace-Hankel transform technique. A numerical inverting procedure was used to study the consolidation behavior in the time domain for different external loading cases. Due to the real soil's original deposition in horizontal beds, the real soil is often anisotropic in that its horizontal properties are different from its vertic al properties. Thus, a more realistic solution to the consolidation problem which should account for the soil anisotropy was obtained.
Fourth, the general solution in the Laplace transform field for the consolidation of soil with partially penetrated vertical drains under complicated time-dependent loadings is derived. And the method is used here has been proved to be an efficient and accurate method, which can be widely used in practice engineering.
At last, a new computational model which can consider the non-linear material character of the soils is established. The analytical solutions for the non-linear consolidation of soft soil with vertical drains are obtained under both constant loading case and time-depending loading case.
From this study, the following conclusions may be obtained: on the assumption of permeability index k_v changes linearly with volume compression index w_v, consolidation of soil is different from Terzaghi's consolidation theory. And under cyclic loading, the effective stress in soil is not synchronously changed with loading but is developed in a delayed way; the scope of effective stress is related with the parameters of loading and with c_c/c_k; when considering the self-weight of soil, this portion of settlement must be calculated in the finite-strain consolidation, if the result is obtained according to the infinite consolidation, it will be far less than the actual result. For the two-dimensional consolidation, a negative pore water pressure is observed when the soil under cyclic loadings, which is different form one-dimensional consolidation theory. With the numerical modelling, it is shown that the rate of consolidation of the soft soil with partially penetrated vertical drain is increased with the increase of the drain length. However, it is slow down as the length exceeds some extent. And the consolidation degree is overestimated by the one commonly used in China. When the external loading is big enough, it is necessary to take the non-linear character of the soil into consideration.
引文
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