Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

摘要: Based on the nonlinear failure criterion and upper bound theorem, modified tangential technique method was proposed to derive expression of supporting pressure acting shallow tunnel. Instead same stress state, different normal stresses element boundaries were used. In order investigate influence factors pressures, mechanism established. The solution pressure, with parameters, obtained by optimization theory. corresponding numerical results presented. comparison using single method, it is found that effective, good agreement shows present reliable.