Simulation of Cyclic Loading Conditions Within Fluid-Saturated Granular Media

Abstract

In civil engineering, the installation of a reliable foundation is essential for the stability of the emerging structure. Already during the foundation process, a comprehensive survey of the mutual interactions between the preliminary established construction pit and the surrounding soil is indispensable, especially, when building in an existing context. In this regard, drawing our attention to the construction site at the Potsdamer Platz in Berlin, which resides within a nearly fully saturated soil and in the immediate vicinity of existing structures, measurements have revealed significant displacements of the retaining walls during the vibratory installation of the foundation piles via a so-called vibro-injection procedure. Herein, due to the gradual plastic strain accumulation and the small pore-fluid permeability of the granular assembly, the rapid cyclic loading conditions gave rise to a gradual pore-pressure build-up, which degraded the load-bearing capacity of the surrounding soil.

Addressing the simulation of cyclic loading conditions within a fluid-saturated soil, the present contribution proceeds from a multi-phasic continuum-mechanical approach based on the Theory of Porous Media (TPM), where the solid scaffold is described as an elasto-(visco)plastic material incorporating both an isotropic and a kinematic hardening model. The properties of the proposed solid-skeleton description are extensively discussed. Moreover, the model response is compared to experimental data.

Appendices

Appendix A: Material Parameters of the IH Model

Fig. 10.

Microscopic picture of the soil grains (left) and grain size distribution (right) of the sand of the research unit FOR1136.

Following the DIN 18196 of the German Institute for Standardisation, the underlying granular material, in particular, the sand³ of the research unit FOR 1136 “GeoTech”, can be classified as closely graded sand with an average grain diameter of $d_{50}=0.55\,\mathrm{mm}$, see Fig. 10. The density of an individual soil grain, which corresponds to the realistic solid density of the overall aggregate, is $\rho ^{SR}=2\,650\,\mathrm{kg/m^{2}}$.

Fig. 11.

Comparison of the experimental data with the simulation results of the triaxial tests at different confining pressures (left) and of the isotropic loading-unloading loop (right).

Table 1. Material parameters of the solid skeleton of the sand of the research unit FOR1136.

Table 2. Material-parameter adjustments of the solid skeleton for the mixed isotropic-kinematic hardening (IKH) model.

In order to identify the solid-skeleton material parameters associated with the FOR1136 sand, the course of actions as described in [13] is followed. Herein, initially several triaxial tests on cylindrical sand specimens (height: $0.1\,\mathrm{m}$, diameter: $0.1\,\mathrm{m}$) have been carried out, from which, subsequently, the materials parameters are identified through a staggered identification scheme, In particular, at first, the elastic shear modulus $\mu _S$ is determined straightforward from triaxial loading-unloading loops and the compression-extension-ratio parameter $\overset{*}{\gamma }$ of the failure surface is found from compression and extension experiments at different confining pressures. Subsequently, several triaxial tests at different confining pressure, in particular, $\sigma _{c,1}=0.1\,\mathrm{MPa}$, $\sigma _{c,2}=0.2\,\mathrm{MPa}$ and $\sigma _{c,3}=0.3\,\mathrm{MPa}$, have been carried out, where the axial $\sigma _{a}$ and radial stresses $\sigma _{r}$, the axial strain $\varepsilon _{a}$, and the volumetric strain $\varepsilon ^{V}$ have been recorded. The material parameters are then found through a minimisation of the squared error between simulation and experiment, which is known as Least-Squares optimisation method. In particular, a gradient-based constrained optimisation is used, in which the Hessean matrix is approximated through the BGFS (Broyden, Fletcher, Goldfarb, Shannon) procedure, see e. g. [39], and the parameter constraints are considered via the sequential-quadratic-programming (SQP) technique, see [40]. The identified solid-skeleton material parameters of the research-unit sand FOR 1136 are summarised in Table 1.

A comparison between the simulation and the experiments for the triaxial experiments at different confining pressures and for the isotropic compression test are depicted in Fig. 11. As can been seen, the model responses are in a quite good agreement with the experimental observations.

Appendix B: Material Parameters of the IKH Model

Proceeding from the material constants of the pure isotropic hardening (IH) model, see Table 1, the governing parameters of the mixed isotropic-kinematic hardening (IKH) model are guessed and the adjustments according to Table 2 are made.