Examples of successful numerical modelling of complex geotechnical problems
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Over the last decades, numerical methods have gained increasing importance in practical geotechnical engineering and numerical methods have become a standard tool in geotechnical design, widely accepted by the geotechnical profession. The advantages of numerical analyses for solving practical problems have been recognised, and developments in software and hardware allow their application in practice with reasonable effort. However, there is still a gap between practice and research and, often unnecessary, simplifications are made in practice and therefore the full power of numerical analyses is not always utilised. One reason for this discrepancy is a lack of transfer of knowledge from research into practice but also a lack of theoretical background of numerical methods, constitutive modelling and modern soil mechanics in practice. In this paper, the application of advanced numerical models for solving practical geotechnical problems is shown, whereas the examples have been chosen in such a way that different aspects are highlighted in each case. Results from fibre-optic measurements for a pull-out test of a ground anchor in soft soil could be reproduced by employing advanced constitutive models, in particular for the grout, in the bonded length of the anchor. For this test, a class-A prediction has been made and numerical results have then been compared with in situ measurements. The back-analysis of a slow-moving landslide is presented next, where the rate of deformation is influenced by water level changes in a reservoir for a pumping power plant, creep of lacustrine sediments and environmental effects such as rainfall infiltration. Finally, some results of modelling cone penetration testing in silts are presented highlighting the effects of anisotropic permeability.
KeywordsFinite element analysis Anchor load test Slope stability CPT
Numerical methods have proven to be an important and powerful tool for solving practical geotechnical problems. This has been possible on the one hand because finite element/finite difference codes have been developed to a stage that they can be easily operated by geotechnical engineers. On the other hand, constitutive models which are able to describe important features of soil behaviour have been implemented in a robust manner in these codes, although it has to be emphasised that open questions in soil modelling remain and there is still no generally accepted constitutive model for soils available.
In geotechnics, the “construction material” is natural ground (soil and rock) and not man-made such as concrete and steel, fabricated to predefined specifications. This inevitably means that the material is inhomogeneous, its mechanical and hydraulical behaviour is not easily formulated in mathematical terms and material parameters are difficult to determine.
Even with a perfect site investigation scheme, significant uncertainties remain with respect to the soil profile and thus with the geotechnical model which forms the basis for the numerical model.
Installation processes, such as construction of piles, diaphragm walls, stone columns, mixed-in-place columns, jet grout panels, have an influence on the stress regime in the soil, which is still extremely difficult, if not impossible, to quantify numerically.
Geometric simplification has to be introduced (2D vs 3D), and the domain of the model to be analysed may not always be easily identified.
In the following, an attempt is made to show the benefits of using numerical methods in geotechnical engineering by means of practical examples, addressing an in situ anchor load test, a complex slope stability problem and cone penetration testing.
Example: anchor pull-out test
Soil conditions and test arrangement
Analysing an anchor pull-out test by means of numerical modelling provides a very useful tool not only to predict the ultimate load of the anchor but also to have a better insight into the interactions between the tendon, the grout and the soil. In this particular case, a class-A prediction of an in situ test was performed and these results were subsequently compared with the in situ performance of the tested anchor. The monitoring system not only involved the standard set-up for an anchor load test to obtain the load–displacement curve but included fibre-optic measurements in tendon and grout of the anchor. In this way, for example, cracking of the grout in the bonded length could be identified. In order to take into account cracking in the numerical model, an advanced constitutive model for the grout has been employed. The test was performed on a construction site in St. Kanzian, Austria. The anchor was vertically installed, was post-grouted and had a free length of 12 m and a fixed length of 8 m, respectively.
Parameters for “seeton”
Primary loading stiffness at ref. pressure
Oedometric stiffness at ref. pressure
Un/reloading stiffness at ref. pressure
Small strain shear modulus
Shear strain at 70% G0ref
Effective friction angle
Tendon and grout properties
Uniaxial compressive strength
Uniaxial tensile strength
Compressive fracture energy
Tensile fracture energy
Ratio residual/peak tensile strength
Maximum friction angle
Numerical model and simulation results
Example: slow-moving landslide
Numerical model and results
Example: numerical simulation of cone penetration test
Particle finite element method
In situ investigation methods, such as cone penetration testing (CPT), are frequently used to derive hydraulic and mechanical soil properties from measured tip resistance, sleeve friction and pore water pressure via empirical correlations. Experience has shown that CPT provides reasonable results for applications in sand or clay where either drained or undrained behaviour governs the penetration process. However, correlations for partial drainage, as it occurs during penetration in intermediate soils such as silts, are still an ongoing research topic. Recent advances in the numerical simulation of large deformation problems based on a Particle Finite Element Method (PFEM, see ) allow to model this kind of penetration problems where a rigid cone penetrates a fully water-saturated soil body. The simulations here are carried out using the platform G-PFEM, short for Geotechnical-PFEM [6, 7], which has been developed within the Kratos framework  at the Polytechnic University of Catalonia (UPC) and the Center for Numerical Methods in Engineering (CIMNE). In G-PFEM, the quasi-static linear momentum and mass balance equations are formulated for a solid and fluid phase adopting an updated Lagrangian description. The basic idea behind the PFEM is a continuous remeshing of critical regions of the domain, where new nodes can be added and old ones removed, in order to deal with large deformations and avoid excessive mesh distortion. This strategy results in an increased computational cost and therefore low-order elements in combination with a mixed formulation of the problem are used. In order to avoid locking effects, an additional degree of freedom, namely the determinant J of the deformation gradient, is introduced on top of the displacement and water pressure fields u and pw . Furthermore, the problem is stabilised using the Polynomial Pressure Projection. The interested reader is referred to Monforte et al.  and Monforte et al.  for a more detailed outline of the PFEM.
Numerical model for cone penetration
Input parameters for MCC model
1 × 108
2 × 10−8
2 × 10−7
Influence of anisotropic permeability
The numerical simulation of an anchor pull-out test showed that the predicted load–displacement curve (“class-A” prediction) and the one obtained in situ showed very good agreement. The ultimate pull-out load is achieved when the shear strength is mobilised along the entire interface grout–soil. The numerical simulation indicated that the strains in the tendon are highly influenced by the development of cracks in the grout of the fixed length which could be captured by applying an advanced constitutive model for the grout.
The second example, namely the back-analysis of a slow-moving landslide at a water reservoir, proved that complex mechanisms contributing to slope movement, such as water level fluctuations in the reservoir, creep phenomena in soft lacustrine deposits present at the toe of the slope and environmental effects such as rainfall infiltration can be accounted for in numerical analyses. It is acknowledged, however, that due to significant uncertainties in input parameters the solutions presented are by no means rigorous and unique but still provide a better insight into the mechanical behaviour of such slopes and will help the experienced geotechnical engineer in defining appropriate mitigating measures.
In the last example, it is shown that G-PFEM is an appropriate tool for simulating CPT. The application presented looked into the effect of considering anisotropic permeability of the soil layer. It could be shown that anisotropy influences the local pore pressure field under globally undrained conditions which may have a consequence when deriving coefficients of consolidation from dissipation tests.
Open access funding provided by Graz University of Technology.
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