A homogenization approach for evaluating the longitudinal shear stiffness of reinforced soils: column versus cross trench configuration
Résumé
The macroscopic linear elastic behaviour of inclusion reinforced soils, regarded as periodic composite media, is investigated by means of the homogenization theory. Special attention is given here to the determination of their longitudinal shear stiffness properties, which strongly govern the reinforced ground response under lateral loading. Combining the use of analytical, variational as well as numerical methods, three particular engineering relevant configurations are more thoroughly examined: single trench, column and cross trench reinforcements. Fairly accurate closed-form expressions are thus obtained giving the value of the reinforced soil longitudinal shear stiffness as a function of the individual components shear moduli and reinforcement volume fraction. It is shown in particular that adopting a cross trench reinforcement layout instead of the classical column configuration results in a much higher improvement of the longitudinal shear stiffness. The results are then applied to assessing the reduction of soil liquefaction risk which can be attributed to the presence of the reinforcing inclusions. Again, they clearly demonstrate the excellent performance of the cross trench configuration as compared to the complete inefficiency of the column reinforcement technique.
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