竖井地基轴对称固结解析理论研究
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摘要
排水固结法是一种经济有效的软土地基加固方法,获得了广泛的应用,在地基中设置竖井是加快固结的重要手段。经过几十年的发展,竖井地基固结理论研究已经取得了非常丰富的成果,但仍然有很多不完善的地方,与工程实际仍有一定的差距。为了进一步完善竖井地基固结理论,在前人研究成果基础上,本文对未打穿砂井地基,成层砂井地基,变荷载下的砂井地基,还有真空联合堆载预压竖井地基以及非线性砂井地基固结问题进行了一些有用的研究。主要具体工作和成果如下：
(1)就单面排水和双面排水情况下,考虑了涂抹区土体水平渗透系数不变、呈线性变化和呈抛物线变化3种模式,并采用虚拟井法考虑了下卧层土体的三维渗流,给出了未打穿砂井地基固结解析解,编制了计算程序,分析了地基的固结性状。结果表明,考虑扰动区水平渗透系数呈抛物线变化时固结最快,呈线性变化时次之,不变时固结最慢；并且扰动范围越大,扰动区土体受扰动程度越大,砂井打入地基深度越大,不同模式对固结度的影响越大；
(2)对成层砂井地基,就单面排水和双面排水情况下,考虑了涂抹区土体水平渗透系数3种模式,分别给出了解析解,编制了计算程序,分析了双层砂井地基的固结性状。结果表明,只有在各层土的压缩模量相同时,成层砂井地基按孔压定义的固结度才等于按变形定义的固结度,否则前者大于后者；当涂抹区水平渗透系数呈抛物线变化时地基固结最快,呈线性变化时次之,不变时最慢；增大任何一层土的压缩系数,均可加快整个地基中的孔压消散。
(3)研究了随时间任意变化荷载作用下砂井地基固结问题。首先推导出考虑涂抹效应、井阻作用、土体内径竖向组合渗流、变荷载以及涂抹区水平渗透系数线性连续变化等因素的解析解。然后将上部荷载进行傅里叶变换转化为三角级数的形式,即将复杂荷载分解为很多简单的正余弦函数之和,通过简单荷载作用下响应的叠加得到原复杂荷载作用下的响应,由此得到了一种便于工程应用的简单方法。编制了计算程序,与传统解析解进行了对比,验证了该方法的合理性。分析了几种荷载模式下砂井地基的固结性状,包括多级线性加载、三角形循环荷载、矩形循环荷载等一般模式,并通过用多段直线段逼近曲线的方法,分析了抛物线形循环荷载作用下地基的固结特性。
(4)通过引入土体孔隙比和有效应力以及孔隙比和渗透系数的对数关系,考虑了土体固结过程中压缩模量随孔隙比的减小而增大和渗透系数随孔隙比的减小而减小的特点,并考虑地基的径竖向组合渗流及水平渗透系数的3种模式,给出了一种竖井地基非线性固结解析解,并对竖井地基的非线性固结性状进行了分析。结果表明：考虑横竖向组合渗流比仅考虑径向渗流时固结快,井径比越小,水平渗透系数与竖向渗透系数之比越小,二者差距越大；考虑非线性时按应力和按变形定义的两种固结度不相等,并且按应力定义的固结度一般小于按变形定义的固结度；当压缩指数大于渗透指数时,不考虑土体的非线性得到的固结度比真实值大,当压缩指数小于渗透指数时,不考虑土体的非线性得到的固结度会比真实值小。
(5)考虑真空度沿竖井的发展是一个深度的函数,同时考虑堆载所引起的附加应力既随时间变化也随深度变化,还考虑了地基的径竖向渗流以及扰动区土体水平渗透系数的3种变化模式,推导了真空联合堆载预压下竖井地基固结度的一个较普遍的解析解。并分析了在真空度沿竖井线性下降,堆载线性施加和附加应力沿深度梯形分布等情况下的地基固结性状。结果表明,在荷载瞬时施加时,无论是否采用真空预压,真空度或大或小,其沿深度的衰减速度或快或慢,固结度始终不变。而荷载逐渐施加时,采用真空联合堆载预压比只采用堆载预压固结要快,真空度越大,沿深度衰减越慢,固结越快。在地基井径比和水平渗透系数与竖向渗透系数之比较小时,地基的竖向渗流对地基的固结度有较大的影响。
Drainage preloading has been found a economical and efficient method for ground improvement and widely used. Vertical drains are usually used to accelerate the consolidation process of soft clay. After several years of development, great deals of findings have been made to the consolidation theory of vertical drains foundation, but still there are many imperfections, and there is still a gap with the actually engineering. In order to further improve the consolidation theory of vertical drains foundation, based on the results of previous research, some useful studies are made on the consolidation of partially penetrated vertical drains foundation, multi-layered vertical drains foundation, vertical drains foundation under general time-dependent loading, vertical drains foundation with the non-linear soil and vacuum preloading vertical drains foundation. The main specific work and achievements are as follows:
1. The consolidation of soft soil with partially penetrated vertical drains under single-drainage condition and double-drainage condition was studied. Vertical and radial seepage of soils under sand drains was considered through setting suppositional sand drains. Meanwhile, in order to consider the fact that the larger the distance from sand drain is, the lighter the disturbance of construction is, the horizontal permeability of soils was expressed in unified way through introducing a function. Three types of variation patterns of the horizontal permeability of soil in the disturbed soil zone were considered, including the constant distribution pattern, the linear distribution pattern and the parabolic distribution pattern, and an analytical solution was obtained. Corresponding computer program was developed and several problems that should pay attention to during the process of programming were expatiated, then the consolidation behavior of partially penetrated sand drains foundation was investigated. The results show that consolidation is the fastest if the parabolic distribution pattern was considered, the consolidation is slower if the linear distribution pattern was considered, the slowest if the constant distribution was considered; and that the larger the disturbance zone is, the slower the consolidation is, the greater the disturbance is, the slower the consolidation is; the deeper the sand drains penetrated, the faster the consolidation is; the larger the permeability coefficient of sand drains is, the faster the consolidation is.
2. The consolidation of multi-layered sand drains foundation under single-drainage condition and double-drainage condition was analyzed. Three types of variation patterns of the horizontal permeability of soil in the smear zone were considered, and an analytical solution was obtained. Corresponding computer program was developed and the consolidation behavior of double-layered sand drains foundation was investigated. The results show that the overall average degrees of consolidation of foundation in terms of pore pressure is equal to that in terms of strain only if compression modulus of every layer is equal to each other, otherwise the former is always larger than the later; the consolidation rate is at its maximum for the parabolic distribution pattern and is at its minimum for the constant distribution pattern whereas the one for the linear distribution pattern is in the middle. Increasing compression modulus of any layer could accelerate the dissipation of pore pressure.
3. The consolidation behavior of soils with vertical drains subjected to a general time-dependent loading was studied in this paper. Firstly, an analytical solution was obtained accounting for the effects of soil smear, drain hydraulic resistance, coupled flows in the radial and vertical directions within the surrounding soil, time-dependent loading and the linear distribution of the horizontal permeability of soils in the disturbed soils zone. Then, the time-dependent loading was transferred to trigonometric series by the technique of Fourier Transform. By this method, the complex loading can be transformed into the sum of a series of sine and cosine function. Then the response of the complex loading was obtained by superimposing the responses of these relatively simple ones. A simple-to-use method was proposed according to this method. Consequently, a calculation computer program was developed and a comparison with a theoretical method is shown to assess the accuracy of the proposed method. Finally, the consolidation behavior of sand drains foundation under several conventional types of time-dependent loading was investigated, including multi-ramp loading, triangular cyclic loading and trapezium cyclic loading. Moreover, the consolidation behavior of sand drains foundation under parabolic cyclic loading was investigated by means of piecewise-linear approximation method.
4. The characteristics of the nonlinear increase in the soil's compressive modulus and the non-linear decrease in the soil's permeability during consolidation are considered. Based on the non-linear characteristics of soil, an analytical solution for the consolidation of composite ground is developed. Then the non-linear consolidation behavior of vertical drains ground is analyzed and the results show that ADC in terms of stress is not equal to that in terms of deformation and furthermore the latter is always greater than the former. When the soil's compressive indices is less than the permeability indices, ignoring the soil's non-linearity will under-estimate the consolidation rate; however, when the soil's compressive indices is greater than the permeability indices, the reverse is true:ignoring the non-linearity will over-estimate the consolidation rate.
5. A general analytical solution is obtained for the consolidation of vertical sand foundation under vacuum preloading considering simultaneously the variation of vacuum degree, the coupled variation of stress increment with depth and time together, both horizontal and vertical drainage, and the variation of horizontal permeability coefficient of soil. Furthermore, detailed solutions are obtained for excess pore water pressure and average degree of consolidation under the particular situation that the vacuum degree is linearly changed along the vertical drain depth, the stress increment is linearly changed along the column depth and the loading is applied in a single-stage way. Finally, the consolidation behavior of vertical drain foundation is analyzed. The results show that:If the loading is applied instantaneously, consolidation degrees of foundation have nothing to do with vacuum degree. If the loading is applied gradually, the larger the vacuum is, the faster the consolidation is, the slower the reducing of vacuum is, the faster the consolidation. Ignoring the vertical flow within the soil will under-estimate the consolidation rate. Furthermore, the less the radius ratio is, and the less the ratio of horizontal permeability to vertical permeability is, the greater the under-estimated value is.
(1)就单面排水和双面排水情况下,考虑了涂抹区土体水平渗透系数不变、呈线性变化和呈抛物线变化3种模式,并采用虚拟井法考虑了下卧层土体的三维渗流,给出了未打穿砂井地基固结解析解,编制了计算程序,分析了地基的固结性状。结果表明,考虑扰动区水平渗透系数呈抛物线变化时固结最快,呈线性变化时次之,不变时固结最慢；并且扰动范围越大,扰动区土体受扰动程度越大,砂井打入地基深度越大,不同模式对固结度的影响越大；
(2)对成层砂井地基,就单面排水和双面排水情况下,考虑了涂抹区土体水平渗透系数3种模式,分别给出了解析解,编制了计算程序,分析了双层砂井地基的固结性状。结果表明,只有在各层土的压缩模量相同时,成层砂井地基按孔压定义的固结度才等于按变形定义的固结度,否则前者大于后者；当涂抹区水平渗透系数呈抛物线变化时地基固结最快,呈线性变化时次之,不变时最慢；增大任何一层土的压缩系数,均可加快整个地基中的孔压消散。
(3)研究了随时间任意变化荷载作用下砂井地基固结问题。首先推导出考虑涂抹效应、井阻作用、土体内径竖向组合渗流、变荷载以及涂抹区水平渗透系数线性连续变化等因素的解析解。然后将上部荷载进行傅里叶变换转化为三角级数的形式,即将复杂荷载分解为很多简单的正余弦函数之和,通过简单荷载作用下响应的叠加得到原复杂荷载作用下的响应,由此得到了一种便于工程应用的简单方法。编制了计算程序,与传统解析解进行了对比,验证了该方法的合理性。分析了几种荷载模式下砂井地基的固结性状,包括多级线性加载、三角形循环荷载、矩形循环荷载等一般模式,并通过用多段直线段逼近曲线的方法,分析了抛物线形循环荷载作用下地基的固结特性。
(4)通过引入土体孔隙比和有效应力以及孔隙比和渗透系数的对数关系,考虑了土体固结过程中压缩模量随孔隙比的减小而增大和渗透系数随孔隙比的减小而减小的特点,并考虑地基的径竖向组合渗流及水平渗透系数的3种模式,给出了一种竖井地基非线性固结解析解,并对竖井地基的非线性固结性状进行了分析。结果表明：考虑横竖向组合渗流比仅考虑径向渗流时固结快,井径比越小,水平渗透系数与竖向渗透系数之比越小,二者差距越大；考虑非线性时按应力和按变形定义的两种固结度不相等,并且按应力定义的固结度一般小于按变形定义的固结度；当压缩指数大于渗透指数时,不考虑土体的非线性得到的固结度比真实值大,当压缩指数小于渗透指数时,不考虑土体的非线性得到的固结度会比真实值小。
(5)考虑真空度沿竖井的发展是一个深度的函数,同时考虑堆载所引起的附加应力既随时间变化也随深度变化,还考虑了地基的径竖向渗流以及扰动区土体水平渗透系数的3种变化模式,推导了真空联合堆载预压下竖井地基固结度的一个较普遍的解析解。并分析了在真空度沿竖井线性下降,堆载线性施加和附加应力沿深度梯形分布等情况下的地基固结性状。结果表明,在荷载瞬时施加时,无论是否采用真空预压,真空度或大或小,其沿深度的衰减速度或快或慢,固结度始终不变。而荷载逐渐施加时,采用真空联合堆载预压比只采用堆载预压固结要快,真空度越大,沿深度衰减越慢,固结越快。在地基井径比和水平渗透系数与竖向渗透系数之比较小时,地基的竖向渗流对地基的固结度有较大的影响。
Drainage preloading has been found a economical and efficient method for ground improvement and widely used. Vertical drains are usually used to accelerate the consolidation process of soft clay. After several years of development, great deals of findings have been made to the consolidation theory of vertical drains foundation, but still there are many imperfections, and there is still a gap with the actually engineering. In order to further improve the consolidation theory of vertical drains foundation, based on the results of previous research, some useful studies are made on the consolidation of partially penetrated vertical drains foundation, multi-layered vertical drains foundation, vertical drains foundation under general time-dependent loading, vertical drains foundation with the non-linear soil and vacuum preloading vertical drains foundation. The main specific work and achievements are as follows:
1. The consolidation of soft soil with partially penetrated vertical drains under single-drainage condition and double-drainage condition was studied. Vertical and radial seepage of soils under sand drains was considered through setting suppositional sand drains. Meanwhile, in order to consider the fact that the larger the distance from sand drain is, the lighter the disturbance of construction is, the horizontal permeability of soils was expressed in unified way through introducing a function. Three types of variation patterns of the horizontal permeability of soil in the disturbed soil zone were considered, including the constant distribution pattern, the linear distribution pattern and the parabolic distribution pattern, and an analytical solution was obtained. Corresponding computer program was developed and several problems that should pay attention to during the process of programming were expatiated, then the consolidation behavior of partially penetrated sand drains foundation was investigated. The results show that consolidation is the fastest if the parabolic distribution pattern was considered, the consolidation is slower if the linear distribution pattern was considered, the slowest if the constant distribution was considered; and that the larger the disturbance zone is, the slower the consolidation is, the greater the disturbance is, the slower the consolidation is; the deeper the sand drains penetrated, the faster the consolidation is; the larger the permeability coefficient of sand drains is, the faster the consolidation is.
2. The consolidation of multi-layered sand drains foundation under single-drainage condition and double-drainage condition was analyzed. Three types of variation patterns of the horizontal permeability of soil in the smear zone were considered, and an analytical solution was obtained. Corresponding computer program was developed and the consolidation behavior of double-layered sand drains foundation was investigated. The results show that the overall average degrees of consolidation of foundation in terms of pore pressure is equal to that in terms of strain only if compression modulus of every layer is equal to each other, otherwise the former is always larger than the later; the consolidation rate is at its maximum for the parabolic distribution pattern and is at its minimum for the constant distribution pattern whereas the one for the linear distribution pattern is in the middle. Increasing compression modulus of any layer could accelerate the dissipation of pore pressure.
3. The consolidation behavior of soils with vertical drains subjected to a general time-dependent loading was studied in this paper. Firstly, an analytical solution was obtained accounting for the effects of soil smear, drain hydraulic resistance, coupled flows in the radial and vertical directions within the surrounding soil, time-dependent loading and the linear distribution of the horizontal permeability of soils in the disturbed soils zone. Then, the time-dependent loading was transferred to trigonometric series by the technique of Fourier Transform. By this method, the complex loading can be transformed into the sum of a series of sine and cosine function. Then the response of the complex loading was obtained by superimposing the responses of these relatively simple ones. A simple-to-use method was proposed according to this method. Consequently, a calculation computer program was developed and a comparison with a theoretical method is shown to assess the accuracy of the proposed method. Finally, the consolidation behavior of sand drains foundation under several conventional types of time-dependent loading was investigated, including multi-ramp loading, triangular cyclic loading and trapezium cyclic loading. Moreover, the consolidation behavior of sand drains foundation under parabolic cyclic loading was investigated by means of piecewise-linear approximation method.
4. The characteristics of the nonlinear increase in the soil's compressive modulus and the non-linear decrease in the soil's permeability during consolidation are considered. Based on the non-linear characteristics of soil, an analytical solution for the consolidation of composite ground is developed. Then the non-linear consolidation behavior of vertical drains ground is analyzed and the results show that ADC in terms of stress is not equal to that in terms of deformation and furthermore the latter is always greater than the former. When the soil's compressive indices is less than the permeability indices, ignoring the soil's non-linearity will under-estimate the consolidation rate; however, when the soil's compressive indices is greater than the permeability indices, the reverse is true:ignoring the non-linearity will over-estimate the consolidation rate.
5. A general analytical solution is obtained for the consolidation of vertical sand foundation under vacuum preloading considering simultaneously the variation of vacuum degree, the coupled variation of stress increment with depth and time together, both horizontal and vertical drainage, and the variation of horizontal permeability coefficient of soil. Furthermore, detailed solutions are obtained for excess pore water pressure and average degree of consolidation under the particular situation that the vacuum degree is linearly changed along the vertical drain depth, the stress increment is linearly changed along the column depth and the loading is applied in a single-stage way. Finally, the consolidation behavior of vertical drain foundation is analyzed. The results show that:If the loading is applied instantaneously, consolidation degrees of foundation have nothing to do with vacuum degree. If the loading is applied gradually, the larger the vacuum is, the faster the consolidation is, the slower the reducing of vacuum is, the faster the consolidation. Ignoring the vertical flow within the soil will under-estimate the consolidation rate. Furthermore, the less the radius ratio is, and the less the ratio of horizontal permeability to vertical permeability is, the greater the under-estimated value is.
引文
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