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Abstract A lot of constitutive models，representing the properties of rock well，have not been utilized widely because of the difficulty in elastoplastic solution. So，based on the single curve and constant volume hypothesis，an analytical method that can be used more conveniently was summed up and modified firstly. Using this method，the stress of elastic and plastic zones，radius of plastic zone，equilibrium equation and superior and inferior limits of self-support geostress of surrounding rock after excavation were calculated accurately or approximately. In view of linear softening constitutive model，Lambert function was introduced to calculate the radius of plastic zone and its range in equilibrium curve of surrounding rock proved. For the Nelder nonlinear softening model，an exponential function was used to describe approximately the abscissa of inflection point and softening modulus. When the Weibull model was taken to represent the post-peak mechanical behaviour，since it is difficult to get the inverse function and limit of Whittaker function，a new idea，fitting the whole equilibrium curve with Gauss function and computing the radius of plastic zone by solving the inverse function of Gauss，was proposed. Then，comparison was taken between these results derived from six constitutive models and it is found that the superior limit of self-support geostress of surrounding rock was higher，the stress concentration factor was lower，the position that stress concentrates was in elastic zone，deviating from the interface between elastic and plastic zones，and the wedge angle in the tangential stress redistribution curve disappeared under nonlinear elastic condition，which is consistent with the practice. Therefore，for either soft or hard rock，a more perfect result from elastoplastic solution can be obtained by taking a smooth and continuous constitutive model.
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Received: 18 July 2012
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2013, Vol. 32 
