Assessing the liquefaction risk reduction of reinforced soils: A homogenization approach

In this contribution, an evaluation is given for the reduction of the liquefaction risk, which can be expected from reinforcing the soil by a periodic array of inclusions. Following a definition of the liquefaction risk reduction factor, the link is then established with the increase of longitudinal shear stiffness of the reinforced soil. Based on the homogenization theory for elastic periodic media, different geometries of the reinforcing inclusions are examined, with a particular focus on circular cylindrical (columnar) inclusions on the one hand, two mutually orthogonal arrays of trenches (cross trench configuration) on the other hand. A variational method based on minimum energy principles allows the derivation of theoretical lower and upper bounds for the reinforced soil longitudinal shear modulus. A comparison with results obtained from numerical simulations performed with a standard finite element code is then presented.