When cohesive soil behind a retaining wall is in active earth pressure state

cracks will appear behind the top of the retaining wall

which leads to a wide region of zero pressure

namely cracking depth. The problem of the cracking depth behind a retaining wall has not been solved well. In this study

an example is taken to illustrate that cracks can appear on the surface of filling

because the cracks are not taken into account in the variational method that is used to solve the active soil pressure of cohesive soil behind the retaining wall. The Mohr-Coulomb strength envelope is simplified by a broken line and the calculation formula of the cracking depth of the soil behind the wall is derived by the actual soil tensile strength. According to the stress boundary state and geometric boundary conditions of the upper points on the slip surface

the variational method to calculate the active earth pressure variation has been improved

and the uncertainly model of the active earth pressure is transformed into a deterministic issue. Also

the influence of internal friction angle

cohesion and tensile strength on the crack depth is analyzed. With the increase of internal friction angle and cohesion

the crack depth of soil increases and the soil pressure gradually decreases

and the slip surface shifts towards the wall back. With the increase of the tensile strength of the soil

the cracking depth and the soil pressure both gradually decrease. When the tensile strength is strong enough to resist the tension destruction of the soil

the cracking depth of the soil behind the wall becomes zero

and the soil pressure is no longer affected by the tensile strength.