Impact response of a thin shallow doubly curved linear viscoelastic shell rectangular in plan

In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.

A Graphical Analysis-based Method for Undrained Cylindrical Cavity Expansion in Modified Cam Clay Soil

A novel graphical analysis-based method is proposed for analysing the responses of a cylindrical cavity expanding under undrained conditions in modified Cam Clay soil. The essence of developing such an approach is to decompose and represent the strain increment/rate of a material point graphically into the elastic and plastic components in the deviatoric strain plane. It allows the effective stress path in the deviatoric plane to be readily determined by solving a first-order differential equation with the Lode angle being the single variable. The desired limiting cavity pressure and pore pressure can be equally conveniently evaluated, through basic numerical integrations with respect to the mean effective stress. Some ambiguity is clarified between the generalized (work conjugacy-based) shear strain increments and the corresponding deviatoric invariants of incremental strains. The present graph-based approach is also applicable for the determination of the stress and pore pressure distributions around the cavity. When used for predicting the ultimate cavity/pore pressures, it is computationally advantageous over the existing semi-analytical solutions that involve solving a system of coupled governing differential equations for the effective stress components. It thus may serve potentially as a useful and accurate interpretation of the results of in-situ pressuremeter tests on clay soils.

Impact Forces and Energy of Flow-like Landslides Against Protection Barriers: a New MPM-validated Empirical Formulation

Full understanding the interaction mechanisms between flow-like landslides and the impacted protection structures is an open issue. In fact, while researchers have used several approaches, from experimental to numerical, it is true that the adequate assessment of the hydromechanical behaviour of the landslide body requires both a multiphase and large deformation approach.This paper firstly proposes a conceptual framework for a specific type of protection structure, namely a rigid barrier fixed to the base ground. Two different approaches are proposed: i) an advanced hydro-mechanical numerical model based on Material Point Method is tested in simulating the whole complex landslide-structure-interaction mechanism(s), ii) a more simplified empirical model is casted to estimate the impact force and the time evolution of kinetic energy. The calibration and validation of the empirical formulation are pursued, respectively, based on the MPM numerical results, and referring to a large dataset of field evidence for the peak impact pressure. Finally, the performance of the newly proposed empirical method is compared to the methods available in the literature and its advantages are outlined.