圆形基坑土压力分布模式研究
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摘要
土压力是作用在挡土结构上的主要外荷载之一,同时也是基坑围护结构设计分析的关键因素。目前土压力的发展仍不能满足实际工程的需要,有待于进一步的研究。圆形基坑的围护结构为筒形地下连续墙,作用在其上的水土压力相互抵消,呈现出主要受压的特性,能更好地发挥混凝土的良好抗压性能。另外,由于基坑周围土体的环向拱效应的影响,作用在筒形地连墙上的土压力与平面土压力不同。一般来说,前者与后者相比偏小,因此,圆形基坑越来越受到岩土工程师的青睐。然而,实际工程中人们还是用朗肯或库仑理论来计算圆形基坑土压力,这必然将引起较大的误差。由此可见,对圆形基坑土压力进行研究具有很强的理论和现实意义。鉴于目前对圆形基坑土压力研究比较缺乏,本文以上海世博500kV地下变电站工程为背景,以理论研究为主,并对背景工程和上海交通大学深水试验池工程进行现场监测,辅以数值模拟,系统研究圆形基坑土压力的分布模式,提出合理的计算方法,发展圆形基坑土压力理论,为圆形基坑围护结构的设计提供参考。本文的研究主要针对于筒形围护结构发生了向坑内的位移,坑外土体处于主动状态的情况,主要内容包括以下几个方面:
1.采用轴对称滑移线法分析了圆形基坑主动土压力的特性。基于前人的研究结果,认为圆形基坑主动土压力亦由土体重度、粘聚力和堆载引起,分析了土体重度、土体粘聚力、内摩擦角、堆载和基坑半径对土压力的影响。验证叠加原理的可行性,建议采用类似于平面土压力的表达式,将圆形基坑主动土压力表示为土压力系数的函数形式,并在后续章节中给出土压力系数的结果,以供设计参考。
2.将轴对称滑移线法进一步拓展以考虑不均匀甚至任意分布的堆载、墙-土间摩擦、地面的坡度、支护结构的倾角(非竖直)、土体分层和地下水渗流等因素。系统地研究以上因素对圆形基坑主动土压力的影响。堆载的分布形式决定了地面的边界条件,将影响滑动区域的应力状态和作用在围护结构上的土压力。在墙-土间摩擦、地面坡度和支护结构倾角同时存在的一般情况下,根据以上参数值,提出了两种破坏模式并给出适用范围;采用滑移线法分析了堆载分布、墙-土间摩擦角、地面坡度和支护结构倾角对滑动土体体积和主动土压力分布的影响。将墙后滑动楔体区域分为主动变形区、对数螺旋区和被动变形区,假定主动变形区和被动变形区内第一主应力方向不变,滑移线为直线,推导了一般情况下圆形基坑主动土压力的解析解。将土层分界面作为应力间断面,导出了间断面两侧第一主应力方向和平均应力的关系,提出了适用于分层土的迭代计算公式,进而将滑移线法推广用以计算双层土和任意多层土的主动土压力。分析表明上软下硬的土层分布方案优于上硬下软的方案。分析了“水土合算”、“水土分算”和“考虑渗流的水土分算方法”的差异,通过假定流线为通过墙脚的直线,计算了渗透力并提出考虑地下水稳定渗流的圆形基坑主动土压力滑移线解。分析了墙体入土深度对圆形基坑水土压力的影响。
3.采用滑移线法和简化滑移线法分析了非极限状态圆形基坑土压力的性状,并推荐设计采用。目前地下结构的设计多以变形为控制标准,支护结构的变形受到严格限制,墙后土体很难达到完全主动状态,因此实际土压力应介于静止土压力和主动土压力之间。定义环向应力系数等于环向应力和第一主应力之比,并将之引入极限平衡方程,重新推导了极限平衡微分方程并给出了迭代计算公式。分析了环向应力系数对土压力影响。提出“初始主动状态”和“完全主动状态”的概念,完全主动状态的土压力比实际土压力小,不能用于实际工程设计,“初始主动状态”土压力具有更强的参考价值。“完全主动状态”下,环向应力系数恒等于1;而在达到“完全主动状态”以前,环向应力系数并非定值,应当介于1和静止土压力系数之间,是墙体位移和空间坐标的函数。假定环向应力系数自墙-土接触面至破坏面由1线性递减至K0,给出了“初始主动状态”土压力结果。分析了土体动用内摩擦角和墙-土摩擦角随墙体位移的发展,考虑到墙后土体的应变特性,认为两者并不完全同步。整个滑动区域的土体动用内摩擦角在“完全主动状态”时完全发挥,而墙-土间摩擦角在“初始主动状态”即完全发挥。考虑了土体动用内摩擦角、墙-土间摩擦角和环向应力系数随墙体位移的变化,给出了非极限状态下圆形基坑土压力的滑移线解和简化滑移线解。滑移线解的精度较高,适用于平移模式的单一均匀土;简化滑移线解适用于任意变形模式的分层土,其精度亦与滑移线法相差不大。分析了圆形基坑土压力随墙体位移的变化。当墙体位移为0时,所得应为静止土压力。由于环向应力的外扩效应(环向拱效应),圆形基坑静止土压力系数和主动土压力系数均比朗肯结果小,并与基坑深径比有关。分析了几种典型位移模式下土压力的分析性状。搜集了国内外部分圆形基坑的实测数据,分析了实测墙体位移模式和土压力分布特性。认为实测墙体位移虽未能使得墙后土体达到“完全主动状态”,但很多已达“初始主动状态”。采用本文提出的非极限状态下圆形基坑土压力的计算方法进行计算,并与实测土压力进行比较,以验证本文方法的合理性并给出主动极限位移的合理取值。
4.首次提出圆形基坑主动土压力的极限分析上限法。极限分析方法是土压力理论分析的主要方法之一,该方法通过上限定理和下限定理分别给出极限荷载的上限和下限,进而确定真实解的范围。滑移线法是通过求解破坏区域的应力场给出土压力(极限荷载)的结果,因此可证明是属于下限解的范畴。Haar & von Karman完全刚塑性假定是摩尔-库伦屈服准则的轴对称形式,另外考虑了墙后土体环向压缩引起的内能耗散以修正完全刚塑性假定,进而提出了圆形基坑主动土压力的极限分析上限法(能量法)。采用库伦破坏模式、双三角形破坏模式和Log-sandwich破坏模式进行分析。以库伦破坏模式为例,将上限法进一步扩展以考虑地面坡度。定义环向应力系数为环向应力与平面竖向应力之比并用以计算内能耗散率。为使得滑动楔体的应变率场机动允许,达到主动状态时,环向应力应等于第一主应力,因此环向应力系数在滑动楔体内为变量,且与土体特性和基坑尺寸有关。分析了环向应力系数值对库伦破坏模式中破坏面的倾角、土压力合力和土压力系数的影响;分析了地面坡度和墙-土间摩擦对土压力结果的影响。土压力系数随基坑深径比的增大而减小,并且当土压力系数Kaq为0时土压力合力达最大值,相应的基坑深径比为“临界深径比”。分析了土体重度、粘聚力、基坑半径等对“临界深径比”的影响,并给出不同内摩擦角下临界深径比随土体粘聚力和基坑半径之比的变化,以供设计参考。为寻求合适的环向应力系数值,将上限解与滑移线解进行对比,认为环向应力系数等于静止土压力系数是足够的。
5.对本文的背景工程进行现场监测。对勘查资料进行分析,结合工程特点,制定合理的监测方案。对项目进行跟踪监测,分析实际工程墙体径向位移和坑外土压力的发展规律。以墙体实测位移为依据,采用本文提出的非极限状态土压力的简化滑移线法计算土压力的分布,并与实测数据对比,进一步验证本文推荐方法的合理性。采用ABAQUS有限元软件对本文背景工程建立考虑土体、地连墙、结构梁板和临时环形支撑共同作用的三维有限元模型,分析了墙体径向位移和土压力随基坑开挖的发展规律,比较了计算墙体位移和实测墙体位移的差异。将有限元所得土压力与理论计算结果和实测数据进行对比,结果表明三者吻合较好。本文的背景工程的监测和设计方法可为将来同类工程作借鉴。
The earth pressure is one of the most significant external loadings acting on the retaining structures, and it is one key problem in the design and analysis of the retaining structures of the excavation. The development of the earth pressure theory cannot meet the demand of the engineering practice and it needs investigated further. The retaining structure of the circular excavation is circular diaphragm wall. The water and earth pressure acting on the wall is axisymmetric and counteract, so the diaphragm wall exhibits mainly circumferential compression, which is in accordance with that the concrete has a superior compression resistance. Moreover, due to the“arching effect”of the soil behind the wall, the earth pressure acting on the wall is different from plane strain earth pressure. Generally, the former is a bit smaller than the latter. As a consequence, circular pit has been applied more frequently. However, in design practice, most used the traditional Rankine’s theory or Coulomb’s theory to calculate the the earth pressure of the circular pit, which will introduce some error undoubtedly. On the basis of the above points, it’s found that the investigation of the earth pressure has a great theoretical and practical significance. Due to the lack of the report about the earth pressure of circular pit in literature, the present paper relies on the project of the underground substation for the world expo in Shanghai, and extends the earth pressure theory. By using the site monitoring as well as the finite element software, the distribution of the earth pressure of the circular pit is analyzed in detail. From which, more reasonable methods for calculating the earth pressure are to be proposed, which will develop the theory of the earth pressure further and can be adopted in the structural design. The present study focus on the case when the wall deforms inward and the soil behind the wall is in active state. The main contributions of the present thesis are listed as follows:
1. The characteristics of the active earth pressure of circular pit have been analyzed by using the method of slip line in axisymmetric case. Based on the contribution of the previous investigators, it is considered that the active earth pressure is also due to the contribution of the self-weight, the cohesive strength of the soil and the surcharge loading. The effect of the unit-weight, the cohesive strength of the soil, the surcharge loading, as well as the radius of the pit on the earth pressure is analyzed. The theorem of superposition is verified and it is suggested to express the active earth pressure with earth pressure coefficients, as used in plane strain case. The earth pressure coefficients would have been given in the following sections, to be referred in the design.
2. The slip line method has been extended to consider the arbitrary distribution of the surcharge loading, soil-wall interface friction, ground slope, wall inclination, layered soil system and the seepage of the underground water. The effect of the above factors on the earth pressure is investigated in detail. The distribution of the surcharge loading controls the boundary condition on the ground surface, which will affect the stress field of the failure zone, as well as the earth pressure acting on the retaining structures. In the general case when the ground slope, soil-wall interface friction and wall inclination are all non-zero, two failure mechanisms are developed and the applied condition for each mechanism is given as well. By using the slip line method, the effect of the distribution of the surcharge loading, soil-wall interface friction, ground slope, wall inclination on the volume of the failure wedge and active earth pressure is analyzed. Dividing the failure wedge as active deforming zone, log-spiral deforming zone and passive deforming zone, and assuming that the direction of the major principal direction is constant in active and passive deforming zone, an analytical solution of the active earth pressure of circular pit is proposed in the general case. Considering the interfaces of the soil layers is stress discontinuous, the relation of the major principal directions as well as the mean stress on both sides of the interface is deduced, then a new iterative relation which accommodates the layered soil system is given. Finally, the slip line method is extended to accommodate two-layered and arbitrary multi-layered soil system. Results indicate that the scenario of a soft deposit lying on the hard soil is better than that a hard soil lying on a soft deposit. The calculation mechanisms of estimating water and earth pressures together and separately, as well as considering the seepage is compared. By assuming that the flow line is a straight line passing through the toe of the retaining wall, the seepage force is calculated and the contribution of the seepage flow is considered in determining the active earth pressure by the slip line method. Furthermore, the effect of the embed depth of the retaining wall is analyzed.
3. The slip line method and the simplified slip line method are sued to analyze the earth pressure of the circular pit when the soil behind the wall is non-yielding, and the results are suggested to be used in the design. Nowadays, the underground structures are designed under the control of deformation. The displacement of the retaining structures is controlled rigidly and the soil behind the wall cannot yield completely, as a result, the true earth pressure lies between the earth pressures at rest and at active state. Defining the tangential stress coefficient as the ratio of the tangential stress to the major principal stress, and introducing the coefficient into the limit equilibrium equation, the limit equilibrium differential equations are re-derived and the iterative relation is given as well. The effect of the tangential stress coefficient on the earth pressure is analyzed. The concept of the“initial active state”and“completely active state”are proposed. The earth pressure at the“completely active state”(active earth pressure) sometimes is smaller than the true value of the earth pressure and it is unsafe to be used in practice. However, the earth pressure at the“initial active state”can be used and it plays more significant role. In the“completely active state”, the tangential stress coefficient is constant and equals to a unity. However, when the“completely active state”is unreached, the tangential stress coefficient is variable, and lies between 1 and the earth pressure coefficient at rest K0, being dependent on the wall movement and the position. By assuming the tangential stress coefficient decreases from 1 to K0 linearly from the back face of the wall to the failure surface, the earth pressure at the“initial active state”is given. The development of the mobilized angle of the internal friction of the soil and the wall friction is analyzed and considering the strain of the soil mass behind the wall, it is better not to consider the angle of the soil friction and wall friction develops simultaneously. Actually, the angle of the internal friction of the entire soil wedge will be developed fully at the“completely active state”, while the wall friction will be developed fully at the“initial active state”. Considering the change of the mobilized angle of the internal friction of the soil, wall friction and the tangential stress coefficient with the wall movement, the earth pressure at non-limit state is calculated by the slip line method and the simplified slip line method. The slip line method has a good precision and applies to the horizontal translation mode and homogeneous soil, while the simplified slip line method can be applied to arbitrary mode of the wall movement. The precision of the latter is comparable to the former and the soil can be homogeneous or arbitrary layered. The variation of the earth pressure versus the wall movement is analyzed. When the wall movement is null, the earth pressure obtained represents that at rest. Because the tangential stress stretches outward, the earth pressure at rest or at active state in axisymmetric case is smaller than that obtained by Rankine’s theory in plane strain case, and being dependent on the ratio of the depth to the radius of the pit. The distribution of the earth pressure for some typical modes of the wall movement is given. Some measured data of the circular pit have been collected and the wall movement and the distribution of earth pressure are discussed. From the measured wall movement, one can find that the soil behind the wall may reach the“initial active state”, but far from reaching the“completely active state”. The earth pressure is calculated according to the measured wall movement and compared with measured results, which verifies the correctness of the proposed methods and helps to find the reasonable value of the limit active wall displacement.
4. An upper-bound method is proposed to determine the active earth pressure of the circular pit for the first time. Limit analysis method is one of the dominant methods calculating the earth pressure, which yields the upper and lower bound of the limit load on the basis of upper-bound theorem and lower-bound theorem, and then gives the range of the true result. The slip line method determines the earth pressure by considering the stress field of the failure zone, so it can be verified and classified as a lower-bound solution. Haar & von Karman’s perfectly plastic hypothesis can be considered as an extended form of Coulomb failure criterion. Besides, considering the additional dissipation of internal energy due to the tangential compression of the soil behind the wall, the upper-bound solution (energy method) is proposed to determine the axisymmetric active earth pressure. In the analysis, Coulomb failure mechanism, Two-triangle mechanism and Log-sandwich mechanism are adopted, and as an example, Coulomb failure mechanism is extended to consider the slope of the ground surface. The tangential stress coefficient is defined again as the ratio of the tangential stress to the vertical stress in plane strain case, in order to calculate the additional dissipation of the internal energy. In order to make the strain field kinematically admissible, the tangential stress should equal to the major principal stress, so the tangential stress coefficient will be a variable and dependent on the soil properties and the dimension of the pit. The effect of the tangential stress coefficient, as well as the ground slope and soil-wall interface friction, on the inclination of the failure surface, the total earth force and earth pressure coefficients is analyzed. Earth pressure coefficients are found decreases with increasing ratio of the depth to the radius of the excavation, and the total earth force attains a maximum value when the coefficient Kaq=0, where the ratio of the depth to the radius of the pit is defined as“the critical aspect ratio”. The effect of the unit-weight, cohesive strength of the soil and the radius of the pit on“the critical aspect ratio”is analyzed, and the figures representing the variation of“the critical aspect ratio”with the ratio of the cohesive strength of the soil to the radius of the pit is given to be referred. In order to give a reasonable value of the tangential stress coefficient, the upper-bound solution is compared with the slip line solution, and it’s found that the tangential stress coefficient equaling to the earth pressure at rest is adequate.
5. The site investigation has been performed for the underground substation for the world expo in Shanghai. By analyzing the materials of the field reconnaissance and the characteristics of the project, an efficient monitoring program is made and the measured results are recorded daily. The development of the displacement of the wall and the earth pressure on the wall is analyzed. On the basis of the measured wall movement, the earth pressure is calculated by using the proposed method in the present thesis and compared with measured results, which shows that the proposed method is reasonable and efficient. The finite element software ABAQUS is used to establish the model of the project of the underground substation, considering the soil, diaphragm wall, the structural slabs and the temporary circular struts. The excavation is also modeled in accordance to the construction procedure, and then the result of the wall movement and earth pressure is calculated and analyzed. The results of the wall movement are compared with measured data and the results of the earth pressure are compared with measured data and the results calculated by the proposed method. The comparison shows a good agreement. The monitoring work and the design method of the project on which the present thesis relies on can be used for reference in future.
1.采用轴对称滑移线法分析了圆形基坑主动土压力的特性。基于前人的研究结果,认为圆形基坑主动土压力亦由土体重度、粘聚力和堆载引起,分析了土体重度、土体粘聚力、内摩擦角、堆载和基坑半径对土压力的影响。验证叠加原理的可行性,建议采用类似于平面土压力的表达式,将圆形基坑主动土压力表示为土压力系数的函数形式,并在后续章节中给出土压力系数的结果,以供设计参考。
2.将轴对称滑移线法进一步拓展以考虑不均匀甚至任意分布的堆载、墙-土间摩擦、地面的坡度、支护结构的倾角(非竖直)、土体分层和地下水渗流等因素。系统地研究以上因素对圆形基坑主动土压力的影响。堆载的分布形式决定了地面的边界条件,将影响滑动区域的应力状态和作用在围护结构上的土压力。在墙-土间摩擦、地面坡度和支护结构倾角同时存在的一般情况下,根据以上参数值,提出了两种破坏模式并给出适用范围;采用滑移线法分析了堆载分布、墙-土间摩擦角、地面坡度和支护结构倾角对滑动土体体积和主动土压力分布的影响。将墙后滑动楔体区域分为主动变形区、对数螺旋区和被动变形区,假定主动变形区和被动变形区内第一主应力方向不变,滑移线为直线,推导了一般情况下圆形基坑主动土压力的解析解。将土层分界面作为应力间断面,导出了间断面两侧第一主应力方向和平均应力的关系,提出了适用于分层土的迭代计算公式,进而将滑移线法推广用以计算双层土和任意多层土的主动土压力。分析表明上软下硬的土层分布方案优于上硬下软的方案。分析了“水土合算”、“水土分算”和“考虑渗流的水土分算方法”的差异,通过假定流线为通过墙脚的直线,计算了渗透力并提出考虑地下水稳定渗流的圆形基坑主动土压力滑移线解。分析了墙体入土深度对圆形基坑水土压力的影响。
3.采用滑移线法和简化滑移线法分析了非极限状态圆形基坑土压力的性状,并推荐设计采用。目前地下结构的设计多以变形为控制标准,支护结构的变形受到严格限制,墙后土体很难达到完全主动状态,因此实际土压力应介于静止土压力和主动土压力之间。定义环向应力系数等于环向应力和第一主应力之比,并将之引入极限平衡方程,重新推导了极限平衡微分方程并给出了迭代计算公式。分析了环向应力系数对土压力影响。提出“初始主动状态”和“完全主动状态”的概念,完全主动状态的土压力比实际土压力小,不能用于实际工程设计,“初始主动状态”土压力具有更强的参考价值。“完全主动状态”下,环向应力系数恒等于1;而在达到“完全主动状态”以前,环向应力系数并非定值,应当介于1和静止土压力系数之间,是墙体位移和空间坐标的函数。假定环向应力系数自墙-土接触面至破坏面由1线性递减至K0,给出了“初始主动状态”土压力结果。分析了土体动用内摩擦角和墙-土摩擦角随墙体位移的发展,考虑到墙后土体的应变特性,认为两者并不完全同步。整个滑动区域的土体动用内摩擦角在“完全主动状态”时完全发挥,而墙-土间摩擦角在“初始主动状态”即完全发挥。考虑了土体动用内摩擦角、墙-土间摩擦角和环向应力系数随墙体位移的变化,给出了非极限状态下圆形基坑土压力的滑移线解和简化滑移线解。滑移线解的精度较高,适用于平移模式的单一均匀土;简化滑移线解适用于任意变形模式的分层土,其精度亦与滑移线法相差不大。分析了圆形基坑土压力随墙体位移的变化。当墙体位移为0时,所得应为静止土压力。由于环向应力的外扩效应(环向拱效应),圆形基坑静止土压力系数和主动土压力系数均比朗肯结果小,并与基坑深径比有关。分析了几种典型位移模式下土压力的分析性状。搜集了国内外部分圆形基坑的实测数据,分析了实测墙体位移模式和土压力分布特性。认为实测墙体位移虽未能使得墙后土体达到“完全主动状态”,但很多已达“初始主动状态”。采用本文提出的非极限状态下圆形基坑土压力的计算方法进行计算,并与实测土压力进行比较,以验证本文方法的合理性并给出主动极限位移的合理取值。
4.首次提出圆形基坑主动土压力的极限分析上限法。极限分析方法是土压力理论分析的主要方法之一,该方法通过上限定理和下限定理分别给出极限荷载的上限和下限,进而确定真实解的范围。滑移线法是通过求解破坏区域的应力场给出土压力(极限荷载)的结果,因此可证明是属于下限解的范畴。Haar & von Karman完全刚塑性假定是摩尔-库伦屈服准则的轴对称形式,另外考虑了墙后土体环向压缩引起的内能耗散以修正完全刚塑性假定,进而提出了圆形基坑主动土压力的极限分析上限法(能量法)。采用库伦破坏模式、双三角形破坏模式和Log-sandwich破坏模式进行分析。以库伦破坏模式为例,将上限法进一步扩展以考虑地面坡度。定义环向应力系数为环向应力与平面竖向应力之比并用以计算内能耗散率。为使得滑动楔体的应变率场机动允许,达到主动状态时,环向应力应等于第一主应力,因此环向应力系数在滑动楔体内为变量,且与土体特性和基坑尺寸有关。分析了环向应力系数值对库伦破坏模式中破坏面的倾角、土压力合力和土压力系数的影响;分析了地面坡度和墙-土间摩擦对土压力结果的影响。土压力系数随基坑深径比的增大而减小,并且当土压力系数Kaq为0时土压力合力达最大值,相应的基坑深径比为“临界深径比”。分析了土体重度、粘聚力、基坑半径等对“临界深径比”的影响,并给出不同内摩擦角下临界深径比随土体粘聚力和基坑半径之比的变化,以供设计参考。为寻求合适的环向应力系数值,将上限解与滑移线解进行对比,认为环向应力系数等于静止土压力系数是足够的。
5.对本文的背景工程进行现场监测。对勘查资料进行分析,结合工程特点,制定合理的监测方案。对项目进行跟踪监测,分析实际工程墙体径向位移和坑外土压力的发展规律。以墙体实测位移为依据,采用本文提出的非极限状态土压力的简化滑移线法计算土压力的分布,并与实测数据对比,进一步验证本文推荐方法的合理性。采用ABAQUS有限元软件对本文背景工程建立考虑土体、地连墙、结构梁板和临时环形支撑共同作用的三维有限元模型,分析了墙体径向位移和土压力随基坑开挖的发展规律,比较了计算墙体位移和实测墙体位移的差异。将有限元所得土压力与理论计算结果和实测数据进行对比,结果表明三者吻合较好。本文的背景工程的监测和设计方法可为将来同类工程作借鉴。
The earth pressure is one of the most significant external loadings acting on the retaining structures, and it is one key problem in the design and analysis of the retaining structures of the excavation. The development of the earth pressure theory cannot meet the demand of the engineering practice and it needs investigated further. The retaining structure of the circular excavation is circular diaphragm wall. The water and earth pressure acting on the wall is axisymmetric and counteract, so the diaphragm wall exhibits mainly circumferential compression, which is in accordance with that the concrete has a superior compression resistance. Moreover, due to the“arching effect”of the soil behind the wall, the earth pressure acting on the wall is different from plane strain earth pressure. Generally, the former is a bit smaller than the latter. As a consequence, circular pit has been applied more frequently. However, in design practice, most used the traditional Rankine’s theory or Coulomb’s theory to calculate the the earth pressure of the circular pit, which will introduce some error undoubtedly. On the basis of the above points, it’s found that the investigation of the earth pressure has a great theoretical and practical significance. Due to the lack of the report about the earth pressure of circular pit in literature, the present paper relies on the project of the underground substation for the world expo in Shanghai, and extends the earth pressure theory. By using the site monitoring as well as the finite element software, the distribution of the earth pressure of the circular pit is analyzed in detail. From which, more reasonable methods for calculating the earth pressure are to be proposed, which will develop the theory of the earth pressure further and can be adopted in the structural design. The present study focus on the case when the wall deforms inward and the soil behind the wall is in active state. The main contributions of the present thesis are listed as follows:
1. The characteristics of the active earth pressure of circular pit have been analyzed by using the method of slip line in axisymmetric case. Based on the contribution of the previous investigators, it is considered that the active earth pressure is also due to the contribution of the self-weight, the cohesive strength of the soil and the surcharge loading. The effect of the unit-weight, the cohesive strength of the soil, the surcharge loading, as well as the radius of the pit on the earth pressure is analyzed. The theorem of superposition is verified and it is suggested to express the active earth pressure with earth pressure coefficients, as used in plane strain case. The earth pressure coefficients would have been given in the following sections, to be referred in the design.
2. The slip line method has been extended to consider the arbitrary distribution of the surcharge loading, soil-wall interface friction, ground slope, wall inclination, layered soil system and the seepage of the underground water. The effect of the above factors on the earth pressure is investigated in detail. The distribution of the surcharge loading controls the boundary condition on the ground surface, which will affect the stress field of the failure zone, as well as the earth pressure acting on the retaining structures. In the general case when the ground slope, soil-wall interface friction and wall inclination are all non-zero, two failure mechanisms are developed and the applied condition for each mechanism is given as well. By using the slip line method, the effect of the distribution of the surcharge loading, soil-wall interface friction, ground slope, wall inclination on the volume of the failure wedge and active earth pressure is analyzed. Dividing the failure wedge as active deforming zone, log-spiral deforming zone and passive deforming zone, and assuming that the direction of the major principal direction is constant in active and passive deforming zone, an analytical solution of the active earth pressure of circular pit is proposed in the general case. Considering the interfaces of the soil layers is stress discontinuous, the relation of the major principal directions as well as the mean stress on both sides of the interface is deduced, then a new iterative relation which accommodates the layered soil system is given. Finally, the slip line method is extended to accommodate two-layered and arbitrary multi-layered soil system. Results indicate that the scenario of a soft deposit lying on the hard soil is better than that a hard soil lying on a soft deposit. The calculation mechanisms of estimating water and earth pressures together and separately, as well as considering the seepage is compared. By assuming that the flow line is a straight line passing through the toe of the retaining wall, the seepage force is calculated and the contribution of the seepage flow is considered in determining the active earth pressure by the slip line method. Furthermore, the effect of the embed depth of the retaining wall is analyzed.
3. The slip line method and the simplified slip line method are sued to analyze the earth pressure of the circular pit when the soil behind the wall is non-yielding, and the results are suggested to be used in the design. Nowadays, the underground structures are designed under the control of deformation. The displacement of the retaining structures is controlled rigidly and the soil behind the wall cannot yield completely, as a result, the true earth pressure lies between the earth pressures at rest and at active state. Defining the tangential stress coefficient as the ratio of the tangential stress to the major principal stress, and introducing the coefficient into the limit equilibrium equation, the limit equilibrium differential equations are re-derived and the iterative relation is given as well. The effect of the tangential stress coefficient on the earth pressure is analyzed. The concept of the“initial active state”and“completely active state”are proposed. The earth pressure at the“completely active state”(active earth pressure) sometimes is smaller than the true value of the earth pressure and it is unsafe to be used in practice. However, the earth pressure at the“initial active state”can be used and it plays more significant role. In the“completely active state”, the tangential stress coefficient is constant and equals to a unity. However, when the“completely active state”is unreached, the tangential stress coefficient is variable, and lies between 1 and the earth pressure coefficient at rest K0, being dependent on the wall movement and the position. By assuming the tangential stress coefficient decreases from 1 to K0 linearly from the back face of the wall to the failure surface, the earth pressure at the“initial active state”is given. The development of the mobilized angle of the internal friction of the soil and the wall friction is analyzed and considering the strain of the soil mass behind the wall, it is better not to consider the angle of the soil friction and wall friction develops simultaneously. Actually, the angle of the internal friction of the entire soil wedge will be developed fully at the“completely active state”, while the wall friction will be developed fully at the“initial active state”. Considering the change of the mobilized angle of the internal friction of the soil, wall friction and the tangential stress coefficient with the wall movement, the earth pressure at non-limit state is calculated by the slip line method and the simplified slip line method. The slip line method has a good precision and applies to the horizontal translation mode and homogeneous soil, while the simplified slip line method can be applied to arbitrary mode of the wall movement. The precision of the latter is comparable to the former and the soil can be homogeneous or arbitrary layered. The variation of the earth pressure versus the wall movement is analyzed. When the wall movement is null, the earth pressure obtained represents that at rest. Because the tangential stress stretches outward, the earth pressure at rest or at active state in axisymmetric case is smaller than that obtained by Rankine’s theory in plane strain case, and being dependent on the ratio of the depth to the radius of the pit. The distribution of the earth pressure for some typical modes of the wall movement is given. Some measured data of the circular pit have been collected and the wall movement and the distribution of earth pressure are discussed. From the measured wall movement, one can find that the soil behind the wall may reach the“initial active state”, but far from reaching the“completely active state”. The earth pressure is calculated according to the measured wall movement and compared with measured results, which verifies the correctness of the proposed methods and helps to find the reasonable value of the limit active wall displacement.
4. An upper-bound method is proposed to determine the active earth pressure of the circular pit for the first time. Limit analysis method is one of the dominant methods calculating the earth pressure, which yields the upper and lower bound of the limit load on the basis of upper-bound theorem and lower-bound theorem, and then gives the range of the true result. The slip line method determines the earth pressure by considering the stress field of the failure zone, so it can be verified and classified as a lower-bound solution. Haar & von Karman’s perfectly plastic hypothesis can be considered as an extended form of Coulomb failure criterion. Besides, considering the additional dissipation of internal energy due to the tangential compression of the soil behind the wall, the upper-bound solution (energy method) is proposed to determine the axisymmetric active earth pressure. In the analysis, Coulomb failure mechanism, Two-triangle mechanism and Log-sandwich mechanism are adopted, and as an example, Coulomb failure mechanism is extended to consider the slope of the ground surface. The tangential stress coefficient is defined again as the ratio of the tangential stress to the vertical stress in plane strain case, in order to calculate the additional dissipation of the internal energy. In order to make the strain field kinematically admissible, the tangential stress should equal to the major principal stress, so the tangential stress coefficient will be a variable and dependent on the soil properties and the dimension of the pit. The effect of the tangential stress coefficient, as well as the ground slope and soil-wall interface friction, on the inclination of the failure surface, the total earth force and earth pressure coefficients is analyzed. Earth pressure coefficients are found decreases with increasing ratio of the depth to the radius of the excavation, and the total earth force attains a maximum value when the coefficient Kaq=0, where the ratio of the depth to the radius of the pit is defined as“the critical aspect ratio”. The effect of the unit-weight, cohesive strength of the soil and the radius of the pit on“the critical aspect ratio”is analyzed, and the figures representing the variation of“the critical aspect ratio”with the ratio of the cohesive strength of the soil to the radius of the pit is given to be referred. In order to give a reasonable value of the tangential stress coefficient, the upper-bound solution is compared with the slip line solution, and it’s found that the tangential stress coefficient equaling to the earth pressure at rest is adequate.
5. The site investigation has been performed for the underground substation for the world expo in Shanghai. By analyzing the materials of the field reconnaissance and the characteristics of the project, an efficient monitoring program is made and the measured results are recorded daily. The development of the displacement of the wall and the earth pressure on the wall is analyzed. On the basis of the measured wall movement, the earth pressure is calculated by using the proposed method in the present thesis and compared with measured results, which shows that the proposed method is reasonable and efficient. The finite element software ABAQUS is used to establish the model of the project of the underground substation, considering the soil, diaphragm wall, the structural slabs and the temporary circular struts. The excavation is also modeled in accordance to the construction procedure, and then the result of the wall movement and earth pressure is calculated and analyzed. The results of the wall movement are compared with measured data and the results of the earth pressure are compared with measured data and the results calculated by the proposed method. The comparison shows a good agreement. The monitoring work and the design method of the project on which the present thesis relies on can be used for reference in future.
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