Method for calculating loosening earth pressure around tunnels based on ellipsoid theory of particle flows

Based on the ellipsoid theory of particle flows, that is, an ellipse sliding face is presented in the loosening zone at upper part of tunnels, a method is deduced to calculate the lateral earth pressure coefficient related to the inclination of sliding face. Besides, the method for calculating the loosening earth pressure is proposed in consideration of horizontal trapezium distribution of vertical loads in the loosening zone. The results show that the loosening zone behaves at the part of the limit ellipse under the ground line with the burial depth less than the height of the limit ellipse and a whole ellipse with the burial depth reaching the height of the limit ellipse, in which the earth pressure gets the maximum value. The lateral earth pressure coefficient is variable, and it has a positive correlation with sliding surface inclination, however, it has a negative correlation with friction angle. Usually, it values from 0.2 to 0.8 and ranges from the active coefficient to the Krynine coefficient. The proposed results are more close to the existing test data and model test data, and they can be used in the design and construction of tunnels.