SOFTTOP

Scientific summary

The shallow layers in the top 20-30m below the ground surface account for about 80% of the site amplification and almost all of the permanent displacements. Research is urgently needed to improve understanding of the behaviour of the soft top layers during induced earthquakes, so that: (a) informed decisions can be taken on the amount of gas that can safely be produced; and (b) strengthening measures for buildings and infrastructures can be more effectively focussed on areas with the highest seismic risk. Currently, questions relating to the influence of soft deposits on earthquake progression and consequent soil response cannot be adequately answered. There is therefore a clear need for an integrated approach to wave propagation (leading to amplification), liquefaction (leading to damping and displacements), and cyclic degradation (leading to temporary reduction of shear strength and permanent deformation). 

This research aims to expand the current analysis toolkit with proper constitutive models for sand and clay, the dominant soil types in the deltaic shallow subsurface, quantified within a framework for multiscale heterogeneity. The project will improve our capability to model the amplification and consequences of induced earthquakes through the soft top soil, under the complex conditions of the natural soil’s non-linearity and non-homogeneity. This will enable the determination of more realistic spatial distributions of deformations and accelerations at the surface. It will be achieved via the following inter-connected stages: (a) a novel reliability-based framework to assess the influence of the shallow subsurface and its variability; (b) laboratory and field tests to derive and validate state-of-the-art constitutive models that adequately describe the cyclic behaviour of sand and clay layers; (c) the use of these techniques to assess the local site response and the displacement of the ground surface due to gas production; and (d) the development of industry guidance and prototype tools.

Description of the research

Scientific description

Overall Aim and Objectives

The dynamic characterisation of soft top layers is essential to understand the transfer of earthquake loads from deeper geological units to the ground surface and thereby towards structures and infrastructure. At the moment, there is scarce information about the dynamics of soft deltaic layers. In addition, induced earthquakes have specific characteristics which do not allow for straightforward implementation into existing models; for example, their short duration and repetitive nature have an impact on soil layers that has not been implemented in todays’ models. Currently, these aspects are only partly or implicitly incorporated in the hazard modelling, but they are not an integral part of it.

The overall aim of this research is to improve the capacity to predict earthquake loads at the surface. We will develop models that incorporate specific aspects of the behaviour of soft soil materials such as non-linearity, degradation/softening and heterogeneity.

The physical response of soft materials under dynamic loads will be investigated experimentally. A constitutive framework will be proposed to provide a tool for the comprehensive description of deltaic interbedded layers, especially focussing on laminated sands/clay, for which no model has been developed so far. Multiscale heterogeneity will be used to model the response of materials, geological units and the site, and to provide characteristic values of soil properties for pseudo-deterministic analyses. The results of this research will improve the accuracy of the description of the dynamic response of deltaic formations to extraction/storage activities in the deeper subsurface, which can be implemented in any future modelling approach that can deal with heterogeneity and non-linearity.

The key objectives are:

  • To investigate the influence of large-scale spatial variability arising from the spatial distribution of different geological units (e.g. peat, clay, sand), including possible liquefaction of sand layers and cyclic degradation of cohesive units, on the site response (including surface accelerations, ground velocities and settlements).

    The investigation will, for the first time, result in the quantification of an advanced (non-linear and heterogeneous) site response. Note that, although interaction with buildings is not part of this proposal, the analyses will quantify the influence of soil heterogeneity in the shallow subsurface on the spatial distribution and magnitudes of differential settlements at the ground surface.

  • To derive reliability-based characteristic property values for sands and organic clays that, when used in a conventional (deterministic) analysis, give the same soil layer and/or site response as a stochastic analysis accounting for spatial variability and uncertainty in the property values.

  • To investigate the influence of spatial variability of soil properties within sand layers on the potential for sand liquefaction initiation and post-liquefaction behaviour. Of particular interest is the influence of the spatial correlation scales in the three-dimensions: e.g. to identify the types of correlation structure which promote (or conversely, impede) the progression (and impact) of sand liquefaction. The controlling factors regarding the speed and extent of the propagation will be investigated.

    Previously, Hicks & Onisiphorou (2005) investigated the influence of spatial variability on the liquefaction potential of an underwater sand-fill berm, and demonstrated that it was possible for a predominantly dilative sand to liquefy, due to the presence of semi-continuous weak zones arising from deposition-induced anisotropy. However, although the investigation analysed the problem as a two-phase (effective stress) system, it did not investigate 3D or coupled transient effects, which are essential parameters for the application in this proposal. Although Fenton & Vanmarcke (1998) did consider 3D spatial variability in assessing the risk of liquefaction at a site subjected to earthquake loading, the investigation itself involved a series of 1D analyses of vertical profiles extracted from the 3D spatial property fields, with no coupling between the 1D analyses.

    Although the modelling of spatial variability in conjunction with advanced models of soil behaviour as described above is rare, such models are essential for modelling the complexity of the soil behaviours encountered in this proposal. The conceptual methodology developed for sand layers will also be validated for cohesive units, which will allow inclusion of the effects of temporary excess pore water pressures, cyclic degradation and permanent displacements on deep wave propagation models and site response.

  • To complement current experimental knowledge on the response of soft top alluvial/marine soil units at small to intermediate strains; in particular, organic clays and laminated sands, for which scarce data are available.

    The experimental investigation will provide the Dutch and international communities with a new dataset on geological units which have seldom been investigated. Information on laminated sands is crucial to evaluate the response of sands, while the role of organics on the dynamic response of clays is the key factor to understanding the build-up of excess pore pressures during cyclic loading and post-cyclic residual deformations.

  • To advance state-of-the-art material modelling capabilities, by developing a unitary constitutive modelling framework for the dynamic response of alluvial/marine soil units at the material scale, which includes the effects of heterogeneities at the small-scale. The characteristics of soft deltaic soils in the Netherlands and worldwide will be specifically addressed; namely, aging and lamination in sand and organic content in clay, as well as the specific characteristics of the induced earthquakes, such as repeated loading and a relatively low number of cycles.

    Few approaches exist which are able to include a description of the cyclic response of different soils like clays and sands. These will be advanced in two ways: (a) by including small-scale heterogeneities and upscaling the results to the mesoscale to feed models for the analysis of the field response; and (b) by extending concepts from existing model frameworks to the specific top soil units - laminated sands and organic clays - typically found in Groningen.

  • To identify those soil characteristics which dominate the material response, and provide indications on how laboratory and field data can be used in the implementation of an advanced physically based description of the site response, which effectively includes information on small-scale heterogeneity.

Scientific Approach

Figure 1 illustrates 3 interconnecting Work Packages (WP), and Figure 2 illustrates the proposed multi-scale framework. WP1 forms the basis of the proposal and is supported by two pillars (WP2 and WP3):

  • WP1 focuses on the heterogeneity of the shallow subsurface; in particular, on how it influences the meso-scale material response and macro-scale material behaviour under seismic loading, and on how the inherent uncertainties associated with heterogeneity and resulting shallow-subsurface behaviour may be quantified within a probabilistic, risk-based framework. WP1 culminates with a site response and deformation analysis for Groningen.
  • WP2 & WP3 focus on improving the physical understanding of the soft top geological unit material responses to repeated dynamic events of short duration, on how this can be described in a unitary framework, and on how sensitive the response is to small-scale heterogeneity.

Figure 1. Research components.

Figure 2. Schematic of multi-scale, multi-physics framework.

Work Package 1 (WP1)

WP1 uses the Random Finite Element Method (RFEM), which is capable of comprehensively analysing the effects of soil spatial variability (Fenton & Griffiths 2008). It links random theory for modelling the spatial variability of soil properties with finite elements for modelling geotechnical response, within a Monte Carlo simulation.

The main drawback of RFEM is that it is computationally expensive. This can be overcome by using recent developments: e.g. Hicks & Spencer (2010) showed how simple probability theory can be linked with 3D RFEM for modelling long embankments, while Li et al. (2016) and Li (2017) developed an analysis framework to demonstrate the potential benefits of conditioning simulations to in-situ data, and Vardon et al. (2016) utilised monitoring data (e.g. pore pressures, deformations) to reduce uncertainty via inverse analysis and data assimilation. Recently, Hicks & Li (2018) used High Performance (Cloud) Computing (Li et al. 2015) to analyse 3D RFEM problems with a largest dimension of 500m. Meanwhile, van den Eijnden and Hicks (2017) developed an unbiased performance-based subset simulation framework for efficiently investigating very low probability failure events using RFEM: by focussing on the weak tail of the response distribution, it narrows down the range of likely responses, so that computational resources can be focussed more strategically.

This project will integrate the above into a new RFEM framework, which includes:

  • Random field theory (Fenton & Vanmarcke 1990), to model the spatial variability at 3 scales: the macro-scale (≤500m), to model the spatial distribution of geological units (Figure 2(a)); the mesoscale (≤50m), to model the spatial variability of properties within geological units (Figure 2(b)); the small-scale (≤0.5m), to model the spatial variability of soil properties at the material (constitutive model) scale (Figure 2(c)).
  • Finite element analysis, incorporating a hydro-mechanical, transient, dynamic formulation, to model the response of the shallow subsurface during seismic loading.
  • Constitutive modelling of soils comprising the geological units (linking with WP2/WP3).

Particular challenges include:

  • The need for realistic soil models that may be characterised by numerous material parameters. (WP2 & WP3 will investigate the relative importance of parameters, to ensure the number to be calibrated is manageable (e.g. Hicks (2003)).
  • Most or all material parameters will vary spatially across the 3D problem domain. To model this, Fenton & Vanmarcke (1998) adopted a multi-variate approach, which involved generating, in each realisation of the Monte Carlo simulation, a separate random field for each material parameter and cross-correlating between random fields to account for parameter-interdependency. In contrast, Popescu et al. (1997) adopted a reduced-variate approach: they generated 2-D bi-variate, cross-correlated random fields of CPT tip resistance and soil classification index, from which several soil model parameters were inferred. Similarly, Hicks & Onisiphorou (2005) generated random fields of Been & Jefferies (1985) state parameter, from which 5 material parameters were back-figured. This required that the soil model calibration was state parameter dependent, but it simplified the analysis in two ways: (a) only one random field was needed per realisation; (b) cross-correlations between parameters did not need to be explicitly defined, as they were already implicit though the calibration. A reduced-variate approach will be used in this research.
  • The complexity of the problem in terms of soil behaviour, loading conditions and physical size leads to large computer storage and run-time requirements, requiring the new techniques referred to above, as well as consideration of issues such as mesh discretisation, domain decomposition and time-integration. To maximise the effectiveness of computer resources, WP1 will focus on 2D analyses, supplemented by carefully chosen 3D analyses for benchmarking. 

WP1 includes the following tasks:

  • The development of the RFEM Framework. The PI has vast experience in developing, validating and applying novel start-of-the-art computer codes based on a modular building-block approach (e.g. Hicks (1995a, 1995b), Smith et al. (2015)). Most of the framework components have been developed already. The task will be to develop a custom-built code that can deal (efficiently and effectively) with the site response analyses in this proposal, requiring the utilisation of new state-of-the-art methodology. Important for large 3D analyses will be the strategy for sharing individual realisations between multiple processors; if possible, each realisation will be run on a separate (single) processor for 2D analyses.
  • A generic study on the influence of spatial variability (of state parameter) on the potential for liquefaction initiation and propagation in a sand layer subjected to seismic loading. The study will consider a range of loading characteristics, and a range of point and spatial (correlation) statistics from previous field studies (Bakhtiari 2011, van den Eijnden & Hicks 2011, Hicks & Onisiphorou 2005, Lloret-Cabot et al. 2012, 2014, Onisiphorou 2000, Wong 2004).
  • An analysis of each of the geological units at Groningen, using the constitutive models from WP2 & WP3 and representative input base motions. The random fields will be generated based on statistics derived from Groningen site data (and previous experience). The outcome will be reliability-based characteristic values of material properties representing each material unit.
  • A detailed series of integrated site response analyses, investigating the influence of spatial variability in the locations of the geological units in the shallow subsurface. For this purpose, the material properties for individual geological units will be constant, reliability-based, characteristic values, as derived from the previous geological unit analyses. Hence, the only difference between realisations will be the spatial locations of the different geological units.

Work Packages 2 & 3 (WP2 & WP3)

These work packages will improve physical understanding of the dynamic response of topsoil layers, for which little information is presently available. Experimental testing, and development and validation of constitutive models will result in an efficient description of the top soil units, for WP1 to determine the site response and deformations, including guidance on the description of heterogeneity at the small material scale. The physically-based information on the distribution and cross-correlation of the most important material parameters will feed the reduced-variate approach of WP1.

WP2 & WP3 will advance state-of-the art knowledge by addressing the following gaps:

  • Induced seismicity differs from natural earthquakes in signature. Existing material models have been built on information coming from natural earthquakes and have not been validated for the typical loading histories characterising seismicity induced by extraction in the deep subsurface. Furthermore, no study is currently available that shows the effects of multiple induced earthquakes as is relevant in Groningen.
  • The dynamic response of soft deltaic deposits is only partly covered by background Dutch and international knowledge. Holocene and Pleistocene sands are present in Groningen, with a clear distinction in the origin, location, thickness and age of deposits, which affect the liquefaction potential (Boulanger & Idriss 2008, Idriss & Boulanger 2014, Hayati & Andrus 2009, Lasley et al. 2016). Laminated sands, the so-called Flaser beds (Figure 3), occur frequently and are difficult to identify and characterise. Indeed, only one study has so far been performed (Fugro 2016), but a fundamental understanding of the behaviour of laminated sands is lacking. In clays and peats, the development of high excess water pressures and cyclic degradation are expected as a consequence of dynamic loads, which may be responsible for high residual deformation. Anisotropy and heterogeneity introduced by the presence of organic matter have not been investigated extensively for dynamic loads. Peats have been recently characterised in a few experimental studies (Konstantinou et al. 2017, Kramer 2000). However the database has been interpreted for stiffness degradation and cyclic damping only (Zwanenburg et al. 2017). Organic clays have seldom been investigated.
  • Typical deltaic deposits have complex geological/geotechnical characteristics due to the highly dynamic depositional environment, sedimentation and tidal activity. These are responsible for small scale heterogeneities which have never been included in the material description.

Figure 3. Laminated soil deposits in Groningen (picture Deltares)

WP2 focuses on sands typical of Groningen. Existing data will be complemented with new experimental data from the laboratory and validated in the field. This is particularly important for sands, as the role of the original fabric on the response can hardly be assessed in the laboratory, despite care in sampling. The aim is to develop a physically-based constitutive approach for sandy layer units, accounting for the influence of low numbers of cycles and repeated loading, as well as sand lamination and ageing. 

WP2 involves strong cooperation with Deltares and the University of Canterbury (New Zealand), who will provide existing data and support most of the planned laboratory and field testing. It includes:

  • Analysing existing laboratory test data from Groningen on clean sands of different ages and laminated sands, and evaluating the performance (including limitations) of existing advanced models (e.g. Boulanger & Ziotopoulou 2015, Taiebat & Dafalias 2008) against these data. This will facilitate intermediate advice on the most appropriate existing constitutive model for WP1 and practice.
  • Performing cyclic triaxial and DSS tests to study the influence on the dynamic response of those soil characteristics that are presently missing, such as repeated loading and laminated soils.
  • Elaboration of laboratory data, aided by the RFEM approach from WP1 to analyse the small-scale response of the laminated soils.
  • Validation of results using field data from Groningen and New Zealand. This will include the quantification of excess pore pressures and displacements following liquefaction in vertical down-hole arrays installed in the field.

WP3 focuses on clays and peats under cyclic loading, and includes:

  • Setting-up an innovative 2D cyclic shear apparatus equipped with bender elements and high frequency pore pressure sensors, able to combine small and medium strains and including the effects of vertical accelerations on the material response.
  • An original experimental testing programme on reconstituted samples of organic clay. The most relevant state parameters (organic content, fibre content, anisotropy, OCR) will be varied, to evaluate the sensitivity of the corresponding natural soil to different initial conditions. The role of natural fabric will be investigated on samples of organic clay available from previous investigations. A unique data set on organic clays will be produced.
  • Development of a cyclic constitutive model for organic clays, able to account for anisotropy and organic content (e.g. Seidalinov & Taiebat 2014, Elia & Rouania 2016). Currently available models in the research group (e.g. Della Vecchia et al. 2014, Pisanò & Jeremić 2014) will be extended in the framework of bounding plasticity, and will include a specific description for small strains.
  • Adopting RFEM at the sample level, the relative importance of the state parameters will be studied, to isolate the physical characteristics which dominate the response. To the applicants’ knowledge, this will be the first time that a cyclic model for organic clays will be supported by a sensitivity analysis including heterogeneity of the state parameters (in cooperation with WP1).
  • Extending the previous conceptual modelling framework to peats, by re-elaborating an existing experimental database (Kramer 2000, Konstantinou et al. 2017) (in cooperation with WP1).

Literature references

Bahrampouri, M., Rodriguez-Marek, A. & Bommer, J.J., Mapping the uncertainty in modulus reduction and damping curves onto the uncertainty of site amplification functions, Soil Dynamics and Earthquake Engineering, doi.org/10.1016/j.soildyn.2018.02.022 (2018).

Bakhtiari, S., Stochastic finite element slope stability analysis, PhD thesis, University of Manchester (2011).

van Ballegooy S, Malan P, Lacrosse V, Jacka ME, Cubrinovski M, Bray JD, O’Rourke TD, Crawford SA, Cowan H Assessment of liquefaction-induced land damage for residential Christchurch. Earthquake Spectra 30(1):31-55. (2014).

Been, K. & Jefferies, M. G., A state parameter for sands, Géotechnique 35(2), 99–112 (1985).

Bommer, J. J., Dost, B., Edwards, B., Kruiver, P. P., Meijers, P., Ntinalexis, M., Polidoro, B., Rodriguez-Marek, A., Ruigrok, E., Spetzler, J. & Stafford, P. J. V4 Ground-Motion Model (GMM) for response spectral accelerations, peak ground velocity, and significant durations in the Groningen Field. Report to NAM, Version 2, 3 June 2017, 540 pp, (2017).

Bommer, J. J. Edwards, B., Kruiver, P., Rodriguez-Marek, A. ,Stafford, P. J. , Dost, B., Ntinalexis, M., Ruigrok, E. & Spetzler, J., V5 Ground-Motion Model (GMM) for the Groningen Field - Re-issue with Assurance Letter NAM, revision 1, 14 March, (2018).

Boulanger, R. W. & Idriss, I. M. (2014) CPT and SPT based liquefaction triggering procedures, Report No. UCD/CGM-14/01. Center for Geotechnical Modeling, Dept. of Civil and Environmental Engineering, University of California, Davis, (2014).

Boulanger, R. W., Ziotopoulou, K. PM4Sand (version 3): A sand plasticity model for earthquake engineering applications. Report No. UCD/CGM-15/01, Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California, Davis, CA, March, 112 pp, (2015).

Bradley, B. A., Strong ground motion characteristics observed in the 4 September 2010 Darfield, New Zealand earthquake, Soil Dynamics and Earthquake Engineering 42, 32-46 (2012).

Bradley, B. A., A New Zealand-specific pseudospectral acceleration ground-motion prediction equation for active shallow crustal earthquakes on foreign models, Bulletin of the Seismological Society of America, 103(3), 1801-1822 (2013).

Della Vecchia, G., Jommi, C. & Romero, E., A fully coupled elastic-plastic hydro-mechanical model for compacted soils accounting for clay activity. International Journal for Numerical and Analytical Methods in Geomechanics, 37, 503-535 (2013).

Elia, G. & Rouania, M., Investigating the cyclic behaviour of clays using a kinematic hardening soil model, Soil Dynamics and Earthquake Engineering, 88, 399–411 (2016).

Eijnden, A. P. van den & Hicks, M. A., Conditional simulation for characterising the spatial variability of sand state, Proceedings of the 2nd International Symposium on Computational Geomechanics, Dubrovnik, Croatia, 288-296, (2011).

Eijnden, A.P. van den & Hicks, M.A., Efficient subset simulation for evaluating the modes of improbable failure, Computers and Geotechnics, 88, 267-280 (2017).

Fenton, G. A. & Griffiths, D. V., Risk assessment in geotechnical engineering, New York: John Wiley & Sons, (2008).

Fenton, G. A. & Vanmarcke, E. H., Simulation of random fields via local average subdivision, J. Engng Mech., ASCE 116(8), 1733–1749 (1990).

Fenton, G. A. & Vanmarcke, E. H., Spatial variation in liquefaction risk, Géotechnique 48(6), 819–831 (1998).

Fenton, G. A., Naghibi, F. & Hicks, M. A., Effect of sampling plan and trend removal on residual uncertainty, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards , in press. (2018).

Fugro, Site investigation and cyclic laboratory testing – factual data report Delfzijl/Eemshaven Levee project Groningen The Netherlands, November 2016. 1016-0459-000. (2016).

Hayati, H. and Andrus, R.D. Updated liquefaction resistance correction factors for aged sands, Journal of Geotechnical and Geoenvironmental Engineering, ASCE,135(11), 1683-1692. (2009).

Hicks, M. A., MONICA - A computer algorithm for solving boundary value problems using the double-hardening constitutive law Monot: I. Algorithm development, Int. J. Num. Anal. Meth. Geomech., 19, 1-27 (1995a).

Hicks, M. A., MONICA - A computer algorithm for solving boundary value problems using the double-hardening constitutive law Monot: II. Algorithm validation, Int. J. Num. Anal. Meth. Geomech., 19, 29-57 (1995b).

Hicks, M. A., Experience in calibrating the double-hardening constitutive model Monot, Int. J. Num. Anal. Meth. Geomech., 27,  1123-1151 (2003).

Hicks, M. A. & Li, Y., Influence of length effect on embankment slope reliability in 3D, Int. J. Numerical Analytical Methods in Engng, in press, DOI: 10.1002/nag.2766 (2018).

Hicks, M. A. & Onisiphorou, C., Stochastic evaluation of static liquefaction in a predominantly dilative sand fill, Géotechnique, 55(2), 123-133 (2005).

Hicks, M. A. & Spencer, W. A., Influence of heterogeneity on the reliability and failure of a long 3D slope, Computers and Geotechnics, 37, 948-955 (2010).

Konstantinou, M., Zwanenburg, C. & Meijers, P., Dynamic behaviour of Groningen peat, Analysis and parameters assessment, Deltares, October (2017).

Kramer, S.L., Dynamic response of Mercer Slough peat, J. Geotech. Geoenviron. Eng,126(6), 504-510 (2000).

Kruiver, P., de Lange, G., Wiersma, A., Meijers, P., Korff, M., Peeters, J., Stafleu, J., Harting, R., Dambrink, R., Busschers ,F. & Gunnink, J., Geological schematisation of the shallow subsurface of Groningen (for site response to earthquakes for the Groningen gas field), Deltares, (2015).

Kruiver, P.P., Wiersma, A., Kloosterman, F.H., de Lange, G., Korff, M., Stafleu, J., Busscher, F., Harting, R., Gunnink, J.L., Green, R.A., van Elk, J., & Doornhof, D., Characterisation of the Groningen subsurface for seismic hazard and risk model. Netherlands Journal of Geosciences / Geologie en Mijnbouw. (2017).

Idriss, I.M. and R.W. Boulanger. Soil Liquefaction During Earthquakes. Earthquake Engineering Research Institute MNO 12. Oakland, CA: Earthquake Engineering Research Institute. (2008).

Lasley, S, Green, RA and Rodriguez-Marek, A. New Stress Reduction Coefficient Relationship for Liquefaction Triggering Analyses; J. Geotech. Geoenviron. Eng., 142(11): 06016013 (2016).

Li, Y., Reliability of long heterogeneous slopes in 3D, PhD thesis, Delft University of Technology, (2017).

Li, Y., Hicks, M. A. & Vardon, P. J., High performance computing strategies for nonlinear finite element analysis of long heterogeneous soil slopes, Proceedings of the 23rd UK Conference of the Association for Computational Mechanics in Engineering (ACME), Swansea, UK, 427–430 (2015).

Li, Y. J., Hicks, M. A. & Vardon, P. J., Uncertainty reduction and sampling efficiency in slope designs using 3D conditional random fields, Computers and Geotechnics, 79, 159-172 (2016).

Lloret-Cabot, M., Fenton, G. A. & Hicks, M. A., On the estimation of scale of fluctuation in geostatistics, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards , 8, 129-140 (2014).

Lloret-Cabot, M., Hicks, M. A. & Eijnden, A. P. van den, Investigation of the reduction in uncertainty due to soil variability when conditioning a random field using Kriging, Géotechnique Letters, 2, 123-127 (2012).

Maljers, D., Dubelaar, W, Stafleu, J., Busschers, F., Dambrink, R. and Schokker, J., Modelleerwerkwijze GeoTOP modelgebied Oostelijke Wadden en aandachtspunten GeoTOP versie 1.3, stand 11 maart 2016 (2016).

Maurer BW, Green RA, Cubrinovski M, Bradley BA . Assessment of CPT-Based Methods for Liquefaction Evaluation in a Liquefaction Potential Index (LPI) Framework. Geotechnique 65(5):328-336. (2015a).

Onisiphorou, C., Stochastic analysis of saturated soils using finite elements, PhD thesis, University of Manchester, (2000).

Pisanò, F. & Jeremić, B., Simulating stiffness degradation and damping in soils via a simple visco-elastic–plastic model, Soil Dynamics and Earthquake Engineering, 63, 98-109 (2014).

Popescu, R., Prevost, J. H. & Deodatis, G., Effects of spatial variability on soil liquefaction: some design recommendations, Géotechnique 47(5), 1019–1036 (1997).

Seidalinov, G .& Taiebat, M., Bounding surface SANICLAY plasticity model for cyclic clay behavior, Int. J. Numer. Anal. Meth. Geomech. 38, 702–724 (2014).

Smith, I. M., Griffiths, D. V. & Margetts, L., Programming the finite element method, 5th edition, John Wiley & Sons, (2015).

Spetzler, J. & Dost, B. Probabilistic Seismic Hazard Analysis for Induced Earthquakes in Groningen, Update June 2017, KNMI (2017).

Taiebat, M & Dafalias Y. F., SANISAND: Simple anisotropic sand plasticity modelInt. J. Numer. Anal. Meth. Geomech. 32, 915-948 (2008).

Vardon, P. J., Liu, K. & Hicks, M. A., Reduction of slope stability uncertainty based on hydraulic measurement via inverse analysis, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 10(3), 223-240 (2016).

Wong, S. Y., Stochastic characterization and reliability of saturated soils, PhD thesis, University of Manchester, (2004).

Zwanenburg, C. & Konstantinou, M., Assessment of dynamic properties for peat Factual Report, Deltares, October (2017).

Work plan

Contact information