Study On Calculation Method Of Active Earth Pressure Of Circular Foundation Pit

The soil around the circular foundation pit is affected by the arching effect,so that the active earth pressure of the circular foundation pit is smaller than that of the straight foundation pit.However,in the practical engineering design,due to the lack of perfect theoretical basis and the corresponding calculation method,the theory of plane strain earth pressure are used to calculate the earth pressure of the circular foundation pit,which inevitably increase the project cost.In this paper,the calculation model of the elastic-plastic problem for the circular foundation pit was improved,and the calculation formulas of the active earth pressure of circular foundation pit was deduced by using the axisymmetric slip line method and the upper-bound method of limit analysis.The influence factors of the intermediate principal stress coefficient of circular foundation pit were analyzed by numerical simulation method.The specifics are as follow:(1)In the axisymmetric problem of circular foundation pit,the tangential stress is the intermediate principal stress.In this paper,the intermediate principal stress coefficient b was introduced to describe the tangential stress of circular foundation pit,by which the relationship between three principal stresses is ?2=??=?3+b(?1-?3).The intermediate principal stress coefficient was used to improve the Haar&Karman plasticity hypothesis(?2=?1 or ?2=?3),which has been widely used in the current calculation.The introduction of the coefficient b make the computation model more consistent with the engineering practice.(2)Based on the theory of slip line field,the slip line equation of axisymmetric problem was deduced.By simplifying the slip curve into straight lines to solve the slip line equation,the formula of the earth pressure of the circular foundation pit was obtained.And the distribution model of earth pressure in circular foundation pit was analyzed.The results show that the earth pressure of the circular foundation pit is nonlinearly distributed with the increase of the depth,but it can be regarded as a linear distribution in the shallow depth.In addition,the influence of the radius of foundation pit on the earth pressure was analyzed.The results show that the earth pressure increases with the radius,and finally approaches to Rankine's earth pressure.(3)By using the upper limit method of limit analysis,and introducing the intermediate principal stress coefficient b to consider the internal energy dissipation caused by the work of the tangential stress,the calculation formula of earth pressure of circular foundation pit was deduced.The results show that the earth pressure corresponding to the intermediate principal stress coefficient b is significantly smaller than that in the case of plane strain.When the radius is large enough,the corresponding result of b tends to be the same,which is the Rankine's earth pressure value in the plane strain case.In addition,the angle of slip surface of the circular foundation pit is greatly influenced by the intermediate principal stress coefficient,and the larger the b is,the greater the angle is.The smaller the value of b,the smaller the angle is.As the excavating radius increases,the angle will decrease.When the radius is large enough,the angle will tend to 45°+?/2.(4)Through the finite element calculation,the influence factors and the variation regularity of the intermediate principal stress coefficient of circular foundation pit were analyzed The results show that the radius of the foundation pit and friction angle of soil are the main influence factors of the intermediate principal stress coefficient.The value of the cohesion has little effect on the intermediate principal stress coefficient.When the radius of the circular foundation pit is smaller and the smaller the friction angle is,the greater the intermediate principal stress coefficient.For practical engineering application,the recommended value of the intermediate principal stress coefficient in the soil of the circular foundation pit were suggested based on the results of a large number of finite element analysis.