A New Modified Peck Formula for Predicting the Surface Settlement Based on Stochastic Medium Theory

Peck method and stochastic medium method are the two most commonly used methods to estimate surface settlement caused by tunnel excavation. However, the Peck method was not suitable for a shallow-buried tunnel, and the calculation process of the stochastic medium theory was complicated. To solve this problem, in this paper, a simple and accurate prediction approach for surface settlement was obtained by improving the Peck method based on the basic idea of stochastic medium theory. In detail, the over-excavation area of the tunnel was divided into n independent units, and the surface settlement caused by the collapse of each unit was calculated, respectively. Then, the total surface settlement can be obtained by superimposing surface settlement induced by each unit. Taking the shallow-buried section of Mulingguan tunnel entrance as a case, the surface settlement calculated by the modified Peck formula and original Peck formula was compared with the observed data, respectively. The comparison results indicated that the surface settlement calculated by the modified Peck formula is closer to the observed data than that calculated by the original Peck formula in the calculation process of surface settlement of shallow-buried tunnel. The table of recommendation for the number of units can be obtained by a discussion of reasonable n values. Finally, the difference between the original Peck formula and the modified Peck formula was analysed, and the results showed that the change rule of the surface settlement is consistent under the tunnel depth, internal friction angle, and ground loss of the tunnel. However, the calculation error of the surface settlements calculated by the original Peck formula is more significant than that calculated by modified Peck formula under the tunnel diameter ratio being less than 1.75. The modified Peck formula is more suitable for calculating the surface settlement under internal angle friction being less than 20 degrees or greater than 40 degrees. The research results expand the scope of application of the original Peck formula and enrich the calculation approach of surface settlement induced by underground excavation in tunnel construction.