A simple dynamic approach for the numerical modelling of soil as a two‐phase material

Abstract

In many geotechnical problems, the presence of water and air in the voids of a soil skeleton has an influence on the behaviour of the soil. Effects such as time‐dependent deformations, temporary reduction in the shear strength of the soil or even liquefaction of loosely layered sands can occur. To account for these effects in a geotechnical analysis, the soil has to be considered as a multiphase material with interaction between the single phases. A simple dynamic approach for the numerical modelling of a fully saturated soil with the finite element method using an explicit time integration rule is presented here. The governing equations describing the soil as a two‐phase material are implemented within the framework of a user subroutine working as a constitutive model in the analysis. Simple problems considering different boundary conditions, static and dynamic loading conditions and non‐linear material behaviour are investigated to verify the implemented approach. The results are compared with analytical solutions and with solutions obtained by the finite element method using an implicit equation solver. Compared with implicit integration methods, the approach presented has the advantage that – for dynamic analyses especially. An explicit integration method is often computationally more efficient for the analysis of large models with relatively short dynamic response times and for the analysis of extremely discontinuous processes such as dynamic pile driving.Einfacher dynamischer Ansatz zur numerischen Modellierung des Bodens als 2‐Phasen‐Material. Bei vielen geotechnischen Fragestellungen wird das Bodenverhalten durch das Porenwasser und die Porenluft beeinflusst. Effekte, wie zeitabhängige Verformungen, eine temporäre Reduktion der Scherfestigkeit oder sogar eine Verflüssigung von locker gelagerten Sanden können die Folge sein. Um diese Effekte in einer geotechnischen Berechnung zu berücksichtigen, muss der Boden als Mehrphasengemisch mit einer Interaktion der einzelnen Phasen untereinander betrachtet werden. Es wird ein einfacher dynamischer Ansatz zur numerischen Modellierung von wassergesättigten Böden mittels der Finite‐Elemente‐Methode unter Verwendung einer expliziten Zeitintegration vorgestellt. Die den Boden als 2‐Phasengemisch beschreibenden Gleichungen werden auf Basis einer User‐Routine für Stoffmodelle implementiert. An einfachen Beispielen wird der Ansatz für verschiedene Randbedingungen, statische und dynamische Belastung sowie für nicht‐lineares Materialverhalten untersucht. Das Ergebnis wird mit analytischen Lösungen oder Ergebnissen verglichen, welche mit einem impliziten Gleichungslöser berechnet wurden. Im Vergleich zur impliziten Formulierung besitzt der vorgestellte Ansatz den Vorteil, dass eine explizite Formulierung für dynamische Berechnungen häufig effizienter hinsichtlich der Rechenzeit ist, insbesondere für große Finite‐Elemente‐Modelle mit kurzen Simulationsdauern und Berechnungen mit extrem diskontinuierlichen Prozessen, wie beispielsweise bei der Rammung von Pfählen.

Application of a Coupled Eulerian–Lagrangian approach on pile installation problems under partially drained conditions

“…The main disadvantage is the neglection of the acceleration of the solid skeleton within Darcy's flow law. But as shown in Hamann and Grabe [8] this simplification has marginal influence on the solution, if quasi-static or slow processes are modeled.…”

“…To adopt this explicit analysis procedure to a dynamic fully coupled pore fluid diffusion and stress analysis for the special case of fully saturated conditions, the analysis procedure can be extended [8]. A u-p-formulation is used where the principle variables are the pore pressure p w and the displacement of the solid phase u s [35].…”

Numerical simulation of the penetration process of ship anchors in sand

“…The comparison of drained and undrained analyses with field test data suggests that two-phase material models should be employed in the future, so that the effects of excess pore pressure, partial drainage and local liquefaction etc. can be precisely modelled [11]. The parametric studies show that the anchor's penetration depth and holding power depend on the density of the sand.…”

Numerical investigation of the influence of the driving frequency during pile installation of tubular piles

“…To model this appropriately, an approach for fully coupled deformation-seepage analyses for saturated soils with a direct explicit time integration scheme is used [5], [6]. Due to the explicit approach used in the procedure explained in [5], [6], it is possible to simulate the pile driving process with finite soil deformation and finite relative motion between the pile and the subsoil. Within the formulation compressive stress is negative, and negative pore pressure is suction.…”

“…A u-p-formulation is used where the principal variables are the pore water pressure field p and the displacement field of the solid phase u. The equation of motion is solved for the mixture of the solid and the fluid phase; see details in Hamann and Grabe [5], [6].…”