# Seitendruckbeanspruchung von Pfählen in weichen bindigen Böden

**Introduction**

As soft soil moves relatively to piles, for example by creeping slopes or construction of an adjacent embankment, passive time-dependent lateral thrust may be applied to the pile shaft. When piles are loaded by lateral soil movement, these piles are referred to the as passive piles. Thereby, a pile shaft can be stressed by shear forces and bending moments which may lead to deformations of the pile foundation and of the superstructure. Common design methods cannot capture the complex time-dependent interaction between the lateral moving soil and a single pile or pile group, both qualitatively and quantitatively. Figure 1 shows three typical design situations.

Figure 1. Passive loaded piles: a) surcharge loads; b) deep excavations; c) piled slopes (dowels).

Determining the magnitude of the passive lateral thrust requires knowledge of the the stress field developing around a pile. For predicting these stresses the highly nonlinear stress-strain behaviour of the soil, as well the large soil displacements and contact processes between the pile and the horizontally moving ground have to be taken into account. Wenz (1963) was one of the first to treat the problem of passive loads on piles in soft soils in detail. Based on plasticity theory and model experiments he determined the limiting lateral pressure on a single pile to be between 7c_{u} and 10c_{u}, where cu is the undrained shear strength of the soil. Broms (1964) proposed a limiting pressure of 9cu. His solution was largely empirical and had no theoretical background. Close to the ground surface this value was reduced to allow a different mode of deformation. Based on a mathematical expression of viscous clay Winter (1979) suggested that limiting pressure on a single pile is between 2c_{u} and 5c_{u}. In the analysis by Randolph & Houlsby (1984), it was found that the values of ultimate soil pressure ranges roughly from 9c_{u} to 12c_{u}. However, in the back-analysis of piles in unstable slopes conducted by Vigiani (1982), the ultimate soil resistance was found to be somewhat lower; i.e., between 2.8c_{u} and 4c_{u}. Poulos (1995) indicated that the limiting lateral soil pressure increases linearly from 2c_{u} at the ground level to 9c_{u} at a depth of about 3.5 times the diameter of the pile and remains constant below that depth. Based on two-dimensional numerical analyses by Bransby & Springman (1999), it was found that the ultimate soil resistance was equal to 11.75c_{u} and thus slightly smaller than the value of 12.5c_{u} that is suggested by Goldscheider & Gudehus (1974).

The calculation methods listed in the literature are generally highly simplified and give a wide range for the value of the passive lateral thrust on a pile. Relevant factors such as the surface roughness, the cross-sectional shape and time-dependent factors such as the soil viscosity are often not considered, which does not allow a reliable pile design for lateral thrust.

**Numerical simulation**

In recent years, advanced numerical modelling techniques such as the Arbitrary Lagrangian-Eulerian (ALE) method, the Coupled Eulerian-Lagrangian (CEL) method and the Material Point Method (MPM) have been developed to overcome numerical problems with large deformations and/or large displacements for geomechanical problems. In principle, all these methods are capable of modelling quasi-static large deformation problems; e.g. the progressive creep flow of soil around a pile (Moormann & Aschrafi, 2014). Among others, the basic visco-hypoplastic model proposed by Niemunis (2003) has been applied to describe creep, relaxation and rate dependency of the soft soils. However, this model does not account for anisotropy of the undrained strength, which often has significant influence on the soil-pile interaction. To overcome this limitation, an anisotropic extension of the model (Grandas-Tavera, 2013) has been applied in the simulations.

**Analysis of pile rows and pile groups**

The 3D model of a 1m thick horizontal slice of soil is shown in Figure 2. The slice is vertically loaded with a stress σ_{initial}. Soil displacement is applied at the left and the right boundary of the model.

Figure 2. Boundary conditions and mesh of a 1m thick 3D horizontal slice of a pile row: soil displacements u_{x} on left and right boundary of the model: a) plan view; b) side view.

The influence of the surface roughness was investigated for a round pile (Fig. 3, left) and a rough pile (Fig. 3, right). All other boundary conditions were maintained. While there was an increase of the lateral load of up to 40% for a round pile, there was only 6% increase for a square pile from a smooth to a rough surface. As a basic principle, it can be maintained that the surface roughness has a more significant influence for round than for square piles.

Figure 3. Influence of the surface roughness of a single pile on the normalized passive lateral thrust (v_{x}=0.1mm/min; μ=0.5; depth: 1.0m). Left: round pile; right: square pile.

In Figure 4 the results of a variation of different velocities of the moving ground are shown. In general, a variation of 10 times the strain rate can produce a change of about 10% of the shear strength (Gudehus & Leinenkugel, 1978).

Figure 4. Influence of the velocity v_{x} of the moving ground (μ=0.5; depth: 1.0m). Left: round pile; right: square pile.

**Outlook**

Although a significant influence of individual parameters was shown on passive lateral thrust, these parameters are not or only rarely taken into account in the calculation methods currently available. In this currently ongoing research project, the influence of different pile arrangements (pile group, pile row) as well as geotechnical and geomechanical boundary conditions are investigated. Furthermore, time-dependent factors will be considered in an optimized approach to determine the passive lateral thrust on a pile.

contact: Johannes Aschrafi