Additional stress of surrounding soil caused by propelling of shield tunneling

The formula for additional stress of surrounding soil versus angle is deduced based on the Mindlin solution, which is induced by bulkhead pressure and friction force during the propelling of shield tunneling. The distribution rules of additional stress versus angle are obtained by analyzing of the data from the Qingchun Road River-Crossing Tunnel Project using the Gauss-Legendre formula. The conclusions can be references for the control of shield tunneling and grouting. The distribution rules are as follows: the additional stress is strictly symmetric to the tunnel axis or 90°/270° axis; the maximum values of σx and σy are both obtained when the angels are 90° and 270° or at the positions of the top and bottom of the circle, and the value from the top is larger than that from the bottom; the minimum value of σx is obtained at the position of the lower-waist of the circle, but the minimum of σy is obtained when the angels are 0°and 180° or at the waist of the circle; the graphic of σy is glasses type; the maximum value of σz is obtained at the position of the higher-waist of the circle, and the minimum one is obtained when the angels are at 90° and 270° or at the positions of the top and bottom of the circle, and the graphic is “8” type; and the distribution rules of the additional stress induced by the friction is similar to that induced by the positive push, but the value of the former is much larger than that of the latter. So, the influences of the friction cannot be ignorable.