Study On The Distribution Of The Earth Pressure Of Circular Pit

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.