Calculation Methods of Earth Pressure for Retaining Wall with Gentle Back Surface

There are two types of discriminant methods for retaining wall with gentle back surface: Wei-ci Gu’ discriminant method and critical angle discriminant method. Discriminant formula of the retaining wall with gentle back surface is \(\alpha > \alpha_{cr} = f(\delta ,\varphi ,\beta )\). According to theoretical deduction, it is found that Wei-ci Gu’ analytic solution which can be used to calculate the earth pressure of retaining wall with gentle back surface includes an assumed condition: \(\delta \approx \varphi\). The essence of Wei-ci Gu’ discriminant method and critical angle discriminant method \((\delta = \varphi )\) is the same; moreover, the second sliding surface location which is decided by the two methods, respectively, is the same too. Active earth pressure of retaining wall with gentle back surface under different conditions is calculated through Coulomb’ earth pressure theory and earth pressure theory of retaining wall with gentle back surface, respectively. The results show that the earth pressure increases gradually with the increase in the wall-back’ dip angle and the backfill’ dip angle, and it decreases with the increased backfill’ internal friction angle. Under any conditions, if and only if \(\alpha \approx \alpha_{cr}\), the calculation results obtained by Coulomb’ earth pressure theory and earth pressure theory of retaining wall with gentle back surface are approximately equal. The examples show that when the requirements of retaining wall with gentle back surface are met (\(\alpha > \alpha_{cr}\)), the bigger the difference between α and α _cr is, the bigger the calculation results’ difference by the two methods is. Change β the maximum error between the two calculation results is 38.77 %. In order to avoid major cost waste, it is suggested that when \(\alpha > \alpha_{cr}\), the earth pressure should be calculated through earth pressure theory of retaining wall with gentle back surface.