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Memory-Enhanced Plasticity Modeling of Sand Behavior under Undrained Cyclic Loading
Abstract
This work presents a critical state plasticity model for predicting the response of sands to cyclic loading. The well-known bounding surface SANISAND framework by Dafalias and Manzari is enhanced with a memory surface to capture micromechanical, fabric-related processes directly affecting cyclic sand behavior. The resulting model, SANISAND-MS, was recently proposed by Liu et al. and successfully applied to the simulation of drained sand ratcheting under thousands of loading cycles. Herein, novel ingredients are embedded into Liu et al.'s formulation to better capture the effects of fabric evolution history on sand stiffness and dilatancy. The new features enable remarkable accuracy in simulating undrained pore pressure buildup and cyclic mobility behavior in medium-dense to dense sand. The performance of the upgraded SANISAND-MS is validated against experimental test results from the literature-including undrained cyclic triaxial tests at varying cyclic loading conditions and precyclic consolidation histories. The proposed modeling platform will positively impact the study of relevant cyclic and dynamic problems, for instance, in the fields of earthquake and offshore geotechnics.
... This situation can be particularly problematic when using advanced plasticity models which have the ability to simulate soil cyclic behaviour (e.g., the multi-surface models (Liu et al., 2019;Russell and Khalili, 2004;Yang et al., 2020)). In these models, if numerical oscillations are interpreted as true cyclic loads, a spurious plastic modulus K p or secant shear modulus may be predicted upon load reversals (Barrero et al., 2020;Benz, 2006;Benz et al., 2009;Borja and Amies, 1994;Khalili et al., 2005;Liu et al., 2020Liu et al., , 2018Russell and Khalili, 2004;Taiebat et al., 2010;Yang et al., 2020). Such predictions can exacerbate numerical problems and cause unwanted termination of the analysis. ...
... This framework has been used in many studies associated with soil behaviour under cyclic and monotonic loads (c.f., Jeremić et al., 2008;Mohammadnejad and Andrade, 2015;Taiebat, 2008;Taiebat et al., 2010;Wichtmann et al., 2019;Yang et al., 2019), and has been the basis of many recent developments in various areas of geomechanics, such as unsaturated soil mechanics (Barrero et al., 2020;Dafalias and Taiebat, 2016;Ghorbani and Airey, 2021;Liu et al., 2020Liu et al., , 2019Liu et al., ,2018Loukidis and Salgado, 2009;Petalas et al., 2019;Yang et al., 2019Yang et al., , 2020, non-coaxiality of sands under rotational shear (Lashkari and Latifi, 2008), elastic-plastic coupling (Golchin and Lashkari, 2014) and sand particle breakage (Xiao et al., 2016(Xiao et al., , 2015. ...
... In addition, h 0 and c h are model parameters. It should be noted that this representation of h (see Eq. (19)) has been commonly used in many soil models based on SANISAND04 (c.f., (Barrero et al., 2020;Liu et al., 2020Liu et al., , 2018Petalas et al., 2019;Yang et al., 2020)). The potential for stress overshooting caused by the component (19) was discussed in (Dafalias and Taiebat, 2016). ...
This paper proposes a novel solution for mitigating the stress overshooting effect arising from advanced soil plasticity models. Stress overshooting is one of the main sources of numerical instability in finite element simulations of geomaterials with advanced plasticity models. Ensuring the robust performance of these models in numerical simulations is pivotal for modelling the behaviour of civil infrastructure under complex loading paths (e.g., dynamic and cyclic loads). Therefore, the paper first analyses and discusses the key limitations of some published models associated with stress overshooting effects. The remaining challenges are also highlighted. The results of the analyses show that definitions of plastic modulus and hardening laws have a significant impact on stress overshooting effects. Based on these analyses, we propose a robust overshooting solution and implement this solution using an explicit stress integration scheme with automatic sub-stepping to mitigate stress overshooting. By performing several numerical examples, we demonstrate the effectiveness and robustness of the proposed model in alleviating the stress overshooting effects.
... The model presents considerable improved accuracy compared with many other models when simulating drained ratcheting behaviour of sand. Later, Liu et al. [23] improved SANISAND-MS on aspects of hardening rule and flow rule for better simulation of undrained cyclic behaviour of sand. For this reason, the model is referred to as SANISAND-MSu in this work. ...
... Compared with SANISAND04, within which sand fabric only evolves and activates during the post-dilative stage, SANISAND-MSu simulates the effects of soil fabric in the whole plastic deformation stage. Such an improvement allows realistic simulation of sand cyclic behaviour under both drained and undrained conditions [21,23]. The model follows critical soil state theory. ...
... The memory surface tracks the evolution of soil fabric during the plastic straining. SANISAND-MSu model [23] improves the original SANISAND-MS model [21] on two aspects, namely, proper simulation of sand fabric evolution history effects and stress-ratio effects. ...
Liquefaction has been a major challenge to design of structures founded on loose silt and sand in moderate and specially highly seismic regions. While assessment of liquefaction susceptibility and potential have been largely based on empirical methods, the design of structures on liquefiable soil requires reliable numerical tools and clear performance criteria. In this paper, solutions are provided based on the well-established SANISAND model and its more recent extension, SANISAND-MSu, implemented in the open-source finite element platform OpenSEEs. Applications are presented for structures commonly encountered in offshore energy sector such as conventional subsea facilities on mudmats and offshore wind turbines founded on large-diameter monopiles. The impact of pore-water pressure, and ultimately liquefaction, on the offshore structures is assessed by performing both quasi-static cyclic loading and earthquake shaking. The general behavior of these offshore structures during liquefaction are presented from a numerical modelling perspective. The simulation results indicate that the response of these structures is considerably affected by structural features and environmental loading conditions. The results presented in this work motivates the use of SANISAND-MSu model in enhanced 3D finite element modelling in offshore structural dynamic analyses.
... The strategy showed great improvement in predicting soil drained ratcheting performance . Further, Liu et al. (2020) included the fabric evolution history and stress ratio effects in SANISAND-MS to better capture the cyclic behavior of sand under undrained response. ...
... In this work, the implicit 3D FE method was selected to study the response of offshore monopiles under undrained conditions. The bounding surface SANISAND-MS model that caters to undrained cyclic behavior of sand (Liu et al., 2020) was adopted in this study (hereafter referred to as SANISAND-MSu). Pore water pressure effects were highlighted by comparing monopile response under drained and undrained conditions. ...
... The SANISAND-MS model and SANISAND-MSu model (Liu et al., 2020) were formulated based on the framework of SANISAND2004. In these two models, some basic features of the SANISAND2004 model are preserved. ...
Monopile response under undrained conditions in sand is gaining increasing interests owing to the recent development of offshore wind farms in seismic regions. Pore pressure evolution in liquefiable soil can significantly reduce the strength and stiffness of the soil which in turn affects the structural dynamic response. Several numerical models have been developed in the last two decades to enhance understanding of the mechanism of monopile–soil interaction with the existence of pore water pressure. In this study, the effects ofgeometry and static vertical load on monopile lateral response were studied using three-dimensional finite element methods that consider the existence of lateral cyclic load-induced pore water pressure. To achieve reliable simulation results of pore pressure development and pile displacement accumulation during cyclic loading, the simple anisotropic sand model with memory surface for undrained cyclic behavior of sand was adopted. For piles with the same diameter, the accumulated pile head displacement during lateral cyclic loading decreased linearly with increasing pile embedded length but increased with increasing eccentricity. Static vertical load had minor effects on pile cyclic lateral response. The distributions of mean effective stress and pore water pressure in the soil domain were presented. The pile reaction curve (cyclic soil reaction against pile defection) of the monopile was extracted. The numerical results aim to provide reference for optimized engineering design procedures.
... From this, it is believed that adopting the 'memory surface'-enhanced implicit model in a 3D FE platform will give deeper insight into the controlling factors of the cyclic hydro-mechanical behaviour of monopile. Recently, Liu et al. (2020) further improved SANISAND-MS for better simulation of the undrained hydro-mechanical behaviour of sand. In this paper, the updated model is implemented in the 3D FE platform OpenSEES and is referred to as SANISAND-MSu (the 'u' stands for undrained) to distinguish it from the original SANISAND-MS formulations. ...
... In particular, SANISAND-MSu puts emphasis on the following aspects (Liu et al., 2020): (a) cycle-by-cycle pore pressure accumulation in the pre-liquefaction regime (i.e. before the first-time effective stress approaches nearly zero); (b) strain accumulation in the cyclic mobility (postliquefaction) regime (but without losing the capability of reproducing sand ratcheting behaviour). ...
... The relevant loci of the model are given in Fig. 1(a), which are: (a) a yield locus (f ) defines the elastic region; (b) a bounding surface (f B ) encloses the admissible stress states; (c) a dilatancy locus (f D ) distinguishes the contractive and dilative soil behaviour; and (d ) a memory surface (f M ) phenomenologically captures the effect of soil fabric during the plastic straining. A detailed SANISAND-MSu formulation has been documented in Liu et al. (2020) and will not be presented in this paper. Instead, only the features related to the memory surface are briefly introduced. ...
Optimised design is essential to reduce the cost of monopiles for offshore wind turbines. For this purpose, an in-depth understanding of the behaviour of monopile–soil interaction is required. As more wind farms are planned in seismically active areas, the undrained behaviour of sandy soils (and the possibility of soil liquefaction) and these soils’ effects on monopile cyclic response need critical evaluation. Considering the lack of well-established test programs, implicit three-dimensional (3D) finite-element (FE) methods stand out as a robust tool to identify and highlight the governing geo-mechanisms in monopile design. In this work, an implicit 3D FE implementation of SANISAND-MS for undrained soil behaviour, termed SANISAND-MSu, is deployed in OpenSees to serve these objectives. The role of pore-water pressure on monopile performance is comprehensively investigated by comparisons between drained and undrained soil behaviour. Local soil responses are studied in detail in relation to parameters in laboratory soil testing and application to monopile geotechnical design. The results of simulations are also used to evaluate numerical p–y curves as a function of the number of load cycles on the pile. The conclusions in this work contribute to ongoing research on monopile–soil interaction and support the development of lifetime analysis for monopile–soil systems.
... The model is able to predict sand cyclic behaviour including cyclic liquefaction and cyclic mobility. and Liu et al. (2020) considered the load induced anisotropy of sand and proposed a memory-enhanced SANI-SAND-MS model to be able to accurately predict sand ratcheting behaviour under various loading paths. The elastic behaviour of many elasto-plastic constitutive models is assumed to be linear isotropic or obeys a hypoelasticity law derived from empirical formulations. ...
... Recently, a memory-enhanced constitutive model for sand, SANISAND-MS, has been developed to capture the ratcheting effects in sands that occur in high-cyclic loading , Liu et al., 2020. SANISAND-MS model is an elasto-plastic model based on bounding surface theory and a critical state framework. ...
... Recently, so-called memory surface enhanced elasto-plastic models have been proposed [42,227,226,225,430], which can (in dependence of the formulation) account for the cyclic load history and are thus able to reproduce the response of soil to high-cyclic loading calculating every individual load cycle. Liu et al. [225] proposed an extended Sanisand [82] model enhanced by a memory surface which could successfully reproduce the measured accumulated deformations in the triaxial tests with up to 10 4 cycles documented in [405]. ...
... For an extension by a memory surface to allow for the simulation of several thousands of loading cycles the reader is referred to [225,226] and for an enhanced performance under cyclic loading in general to [227]. In addition, an extension by a memory surface and semifluidised states has been proposed by [35,430] and by [290] taking into account the evolving fabric anisotropy of sand. ...
This work presents contributions to the numerical modelling of the installation process and subsequent high-cyclic loading of piles, such as relevant for pile foundations for offshore wind turbines (OWTs). The developed numerical tools are implemented in the finite element code numgeo (www.numgeo.de), which is available for download.
The influence of relative acceleration between soil grains and pore fluid, neglected by the most common hydro-mechanically coupled finite element formulation (u-p formulation) but relevant for pile driving processes with high frequencies, is investigated by a novel analytical solution and various finite elements discretising the fluid displacements in addition to the fluid pressures. It is found that only for very large frequencies (> 50 Hz) with simultaneously high values of hydraulic conductivity (>10-³ m/s) the relative acceleration is of importance. Therefore, the u-p formulation is found to be applicable for the analysis of vibratory pile driving.
Constitutive models for the prediction of the mechanical response of soils to millions of load cycles (so-called high-cycle accumulation (HCA) models) are extended to be applicable for partially drained conditions by incorporation of a so-called adaptive strain amplitude, taking into account changes in soil stiffness during the high-cyclic loading. A HCA model for clay is implemented and applied to the analysis of monopiles for OWTs subjected to cyclic lateral loading with numerous load cycles.
Two different mortar contact discretisation techniques are developed and implemented in the finite element code numgeo. It is demonstrated that a segment-based mortar contact discretisation technique can be superior to an element-based technique in terms of numerical stability for vibratory pile driving in water-saturated soil. A general framework for the formulation of constitutive interface models based on constitutive continuum models is presented. Interface models based on Hypoplasticity with intergranular strain extension, the Sanisand model and the HCA model are formulated. In contrast to existing formulations, the boundary conditions are not only satisfied for the continuum but also for the interface zone, considering all stress and strain components in the interface. The simulation of large-scale cyclic interface shear tests shows that only the novel interface formulations allows to correctly consider the stress conditions in the interface zone.
The simulation of the pile installation process using a (hydro-mechanically coupled) Coupled Eulerian-Lagrangian method, which is extended to dynamic analyses, shows that for dry sand the installation-induced changes in the soil state result in a stiffer response of the pile to subsequent loading compared to simulations without consideration of the installation process. Less permanent deformation is accumulated when the pile is subjected to high-cyclic loading using the HCA model following the installation process. However, for water-saturated initially dense sand and larger pile diameters, such as encountered for foundations for OWTs, less influence of the installation process is found. The better the drainage conditions during driving, the lower the accumulation of permanent deformations during subsequent high-cyclic loading. Lower accumulation of permanent deformations occurs if ideally drained conditions during driving are assumed. In case of clay, jacked piles show less accumulation of deformations when subjected to lateral cyclic loading compared to simulations neglecting the installation process, especially for a larger number of load cycles and for initially overconsolidated soils.
... 14,15 Another approach is to introduce a fabric tensor to describe the micro fabric change behaviors and obtain the constitutive formulations based on different assumptions for the dependency of stress-strain relationship on the fabric tensor. 2,15,[16][17][18][19][20] . This approach requires the quantification of the fabric tensor and its change mechanism and has been proven to be a practical and effective manner in numerical analyses. ...
... 14,[21][22][23][24][25][26][27][28] However, most of these models did not concurrently consider the PSR effect, which may lead to the deviations of the accumulation of plastic shear stains in several undrained cyclic loading conditions. 2,18,20 The PSR refers to the change of principal stress directions with or without the change of principal stress magnitudes and it can lead to non-coaxility of soil, which can be defined as the non-coincidence between the principal strain increment directions and principal stress directions. The PSR effect was first found by Roscoe et al. 29 in 1967. ...
Cyclic loadings could induce complicated soil responses, including the fabric change and principal stress rotation, both of which would reduce the effective confining pressure and accelerate the build‐up of excess pore water pressures, thus leading to sand liquefaction in undrained conditions. The principal stress rotation, even without the change of principal stress magnitudes, would further generate the accumulative plastic shear strains. However, most of the existing studies focus on their individual effect and the combined effect was seldom considered. In this paper, a numerical approach including an elastoplastic sand constitutive model is proposed to consider the combined effect of the fabric change and principal stress rotation. In this model, the fabric change is considered with the anisotropic critical state theory and the principal stress rotation is considered by splitting the plastic strain increment into the monotonic part and rotational part. By simulating a series of cyclic shear tests, results from the numerical solutions are found showing good agreements with the existing experimental results and the importance of considering the combined effect is demonstrated. The approach can be used to predict the stress‐strain response of sand and guide the design of foundations especially in undrained cyclic loading conditions, for example, earthquake loadings conditions.
... Lashkari (2010) for an extension with anisotropic elasticity, Taiebat and Dafalias (2008) for a yield surface with closed cap and Dafalias and Taiebat (2016) for an extension without elastic range. For an extension by a memory surface to allow for the simulation of several thousands of loading cycles the reader is referred to and for an enhanced performance under cyclic loading in general to (Liu et al., 2020). In addition an extension by a memory surface and semifluidized states was proposed in (Barrero et al., 2020;Yang et al., 2020) and Petalas et al. (2020) taking into account the evolving fabric anisotropy of sand. ...
... A better performance of the simulation using Sanisand would be expected using the recently proposed extension by a memory surface as has been demonstrated in Liu et al. (2020,). ...
The performance of three advanced constitutive models has been evaluated based on element tests and on a comparative study on the simulation of vibratory pile driving tests in saturated sand. The inspected constitutive models are the Sanisand model and Hypoplasticity with Intergranular Strain (Hypo+IGS) as well as with Intergranular Strain Anisotropy (Hypo+ISA) extension. The performance of the constitutive models is first evaluated by the simulation of element tests used for the parameter calibration of the sand used in the model tests. The constitutive models are then applied for the simulation of a vibratory pile driving test. The pile penetration, the driving force, the pore water pressure development and the incremental displacement in the vicinity of the pile tip are compared to the measurements in the model tests. The strengths and weaknesses of the different constitutive models are assessed. Generally, the model predictions showed good agreement with the experimental results. Despite different constitutive formulations (hypoplastic vs. elasto-plastic), all three models were able to reproduce the main mechanisms of the driving process properly. It may be concluded that all three models allow a proper prediction of vibratory pile driving as long as a proper calibration of the material parameters is secured.
... The SANISAND family of models is formulated in the framework of critical state soil mechanics and bounding surface plasticity. Many versions of SANISAND have been proposed capturing different aspects of sand behaviour with two recent versions performing remarkably well under cyclic loading (Liu et al. 2020, Yang et al. 2022). The 2008 formulation was chosen for the present study, because there are no simulations involving cyclic loading adopting this version available in literature and it is of interest to investigate how it performs. ...
The present work examines the advantages and disadvantages of two widely known constitutive modelling approaches for cyclic loading simulations: i) multi-surface plasticity and ii) bounding surface plasticity. Two multi-surface models and one bounding surface model are implemented and calibrated and their performance at a single element level is examined. Emphasis is placed on the performance of two multi-surface models, namely a series model for cohesionless soils employing nested kinematic hardening yield surfaces, and a parallel Iwan model capable of predicting a Masing-type nonlinear hysteretic response without the need for translating surfaces. The latter, 'PIMSS' (Parallel Iwan Multi-Surface Sand), is a new effective stress model for sands and hence its formulation is briefly described. The predictive capability and ease of calibration of the two multi-surface models are discussed. These models are then compared with a commonly used version of the bounding surface model SANISAND. The model predictions are assessed for drained and undrained monotonic and cyclic undrained triaxial tests focusing on key points such as the phase transformation behaviour of denser sands, stress attractor at liquefaction state and stiffness degradation during undrained cyclic loading.
... The implicit method is an extension of classical plasticity theory in that the real load scenario, that is, every single loading cycle, is followed in the numerical model, and the cyclic deformation is computed based on the plasticity theory. A typical example of a material law applied here is the SANI-Sand model after Dafalias et al. and Liu et al. 1,2 Since the exact loading scenario is followed and computed, the implicit method is computationally costly and can normally only be applied for a low number of cycles (maximal up to several hundred), as for large cycle numbers, the numerical errors become too great and make the system difficult to converge. In practical cases, however, it is often required to compute the cyclic deformation after millions of cycles. ...
In offshore technology, especially in offshore wind energy converters, permanent deformations of the structures must be limited. For that purpose, the accumulation of permanent deformation due to cyclic loading must be predicted as accurately as possible. To account for this accumulation in non‐cohesive soils, different approaches such as semi‐empirical methods, p‐y curve methods and numerical methods are available. Among the numerical approaches, the Stiffness Degradation Method (SDM) has the advantage of practical feasibility. However, it is only compatible with a relatively simple constitutive law and does not consider the influence of un‐ and reloading stress paths in the soil. With the basic concept of SDM, a new method termed Cyclic Strain Accumulation Method (CSAM) is proposed. In CSAM, the weaknesses of SDM, especially its incompatibility with advanced constitutive laws, are overcome, while retaining the practical feasibility as the main advantage of SDM. Through numerical calculations of a monopile, it is found that the CSAM is able to reproduce SDM results if the same material law is applied. The results of SDM and CSAM for the case of a vertical loaded strip footing have been presented. The comparison shows that the CSAM results are more realistic than the SDM results. Besides, CSAM is computationally more efficient and open for further optimisation. The effects of sophisticated material law and the consideration of un‐ and reloading are investigated. Results show that CSAM is a promising new approach to account for the deformation of foundations under cyclic loading in non‐cohesive soils.
... increased attention from researchers in the last decades resulting in a significant number of published models, for e.g. 47,[63][64][65][66] . Lastly, the yield surface of this model was reduced even to zero and becomes identical to the stress point itself, and plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally non-linear 67 . ...
The design of deep dump slopes for opencast mines usually requires information about the soil resistance to liquefaction during earthquakes. This resistance depends not only on the initial stress, the initial density, and the amplitude of the cyclic loading, but also on the preshearing, that is, the deviatoric stress path applied to the soil before the cyclic loading. To explore the influence of preshearing on the subsequent soil behaviour, a set of triaxial tests with a combination of undrained
preshearing and drained stress cycles using two sample preparation methods is presented. It is shown that the preshearing as well as the preparation method have a major influence on the strain accumulation upon cyclic loading. Simulations of the experiments with four advanced constitutive models reveal that neither the long-lasting effect of preshearing nor the preparation method can adequately be captured by all of the models. This deficiency of the constitutive models can lead
to unsafe designs due to the overestimation of the cyclic resistance to liquefaction and to the underestimation of long term settlements.
... As is shown in Fig. 2, SANISAND-MS can capture the effect of the stress path polarisation angle on the cyclic ratcheting response. Furthermore, the modelboth in its first and upgraded (Liu et al., 2018(Liu et al., , 2020 versions -has been successfully applied to the 3D FE analysis of offshore monopiles under lateral cyclic loading, and has shown encouraging performance with respect to the simulation of pile tilt accumulation under different loading and drainage conditions (Liu et al., 2022a;Cheng et al., 2021;Liu and Kaynia, 2021;Liu et al., 2022b). ...
Offshore monopile foundations are exposed to misaligned wind and wave loadings, which are respectively dominated by (nearly) static and cyclic load components. While the response of these systems to unidirectional cyclic loading has been extensively investigated, only a few studies have been devoted to the realistic case of misaligned static and cyclic loads, and particularly to the effects of such misalignment on the accumulation of pile rotation under prolonged cycling. This paper presents a 3D finite-element (FE) modelling study on the relationship between load misalignment and cyclic monopile tilt under drained conditions, based on the use of the SANISAND-MS model to enable accurate simulation of cyclic sand ratcheting. After qualitatively identifying the relationship between relevant loading parameters and cyclic stress/densification mechanisms in the soil, specific parametric studies are performed to explore the impact on pile tilt accumulation. The results show that, in comparison to unidirectional loading, misaligned static-cyclic loading gives rise to lesser-known pile-soil interaction mechanisms: when the direction of cycling deviates from that of the static load, ''cyclic compression'' and ''direct cyclic shearing'' mechanisms begin to co-exist. This is quantitatively captured by a newly proposed empirical equation for monopile tilt calibrated against the 3D FE simulation results obtained in this work.
... The advantages of the memory surface formulation are not limited to the simulation of sand ratcheting under drained, singleamplitude cyclic loading. Original work, not reported for brevity, has recently been published with regard to SANISAND-MS' performance under multi-amplitude cyclic loading sequences [23], and its enhancement for tackling undrained conditions [24]. ...
The development of offshore wind farms requires advanced knowledge and technology, particularly with regard to the design and installation of foundation systems. Offshore wind turbine foundations, such as monopiles, cannot be adequately designed without in-depth analysis of soil-foundation interaction under environmental cyclic loads, such as those induced by wind and marine waves. Serviceability criteria for offshore monopiles include the estimation of long-term, permanent tilt under long-lasting cycling. In the lack of well-established analysis methods, both experimental and computational studies have been carried out in the last decade to support the fundamental understanding of cyclic monopile–soil interaction mechanisms, and in turn the conception of engineering methods for monopile tilt predictions. With regard to the case of monopiles in sandy soil, this paper summarises recent work on the 3D finite element (FE) modelling of monopile tilt based on the SANISAND-MS model proposed by Liu et al. (2019) [1], which enables realistic simulation of cyclic sand ratcheting and densification around the pile. Overall, the presented numerical results confirm the suitability of the SANISAND-MS 3D FE framework as well as, however, its high computational costs. To foster more efficient application to geotechnical design, it is shown how the same theoretical framework on which the SANISAND-MS formulation is based, can be exploited to derive 1D pile-soil interaction models for the p-y-type analysis of cyclically loaded monopiles. In this respect, the importance of preliminary 3D FE modelling and linking to site investigation data (e.g., CPT profiles) is recognised as key to the practical calibration and use of cyclic p-y models.
... 49 "Partially drained" in this paper is used to describe the situation 50 where pore pressure accumulation and dissipation occurs simulta-51 neously, which is different from the fully drained and perfectly 52 undrained conditions. 53 To account for the effect of cyclic loading in clay and sand 54 layers, NGI has developed two finite element calculation proce- (Liu et al. 2020) can also be used for this purpose. In this work, 86 the NGI-ADP model (Grimstad et Fig. 1). ...
Cyclic loading of saturated sand under partially drained conditions may lead to accumulated strains, pore pressure buildup, and 7 consequently reduced effective stress, stiffness, and shear strength. This will affect the ultimate limit state capacity of monopile foundations in 8 sand for offshore wind turbines. This paper calculates the performance of large-diameter monopile foundations, which are installed in uniform 9 dense sand, subjected to storm loading using the partially drained cyclic accumulation model (PDCAM). The simultaneous pore pressure 10 accumulation and dissipation is accounted for by fully coupled pore water flow and stress equilibrium (consolidation) finite element analyses. 11 Drainage and cyclic load effects on monopile behavior are studied by comparing the PDCAM simulation results with simulation results using 12 a hardening soil model with small strain stiffness. At the end, a simplified procedure of PDCAM, named PDCAM-S, is proposed, and the 13 results using this approach together with PLAXIS 3D and the NGI-ADP soil model are compared with the PDCAM results.
... The SaniSand family of models has attracted increased attention from researchers in the last decades resulting in a significant number of published models, for e.g. [2,[22][23][24]44]. Lastly, the yield surface of this model was reduced even to zero and becomes identical to the stress point itself, and plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally nonlinear [3]. ...
The design of massive dump slopes for opencast mines usually requires information about the soil resistance to liquefaction during earthquakes. This resistance depends not only on the initial stress, the initial density, and the amplitude of the cyclic loading, but also on the preshearing, that is, the deviatoric stress path applied to the soil before the cycling loading. To explore the influence of preshearing on the subsequent soil behaviour, a set of triaxial tests with a combination of undrained preshearing and drained stress cycles using two sample preparation methods is presented. It is shown that the preshearing as well as the preparation method have a mayor influence on the strain accumulation upon cyclic loading. Simulations of the experiments with four advanced constitutive models reveal that neither the long-lasting effect of preshearing nor the preparation method can adequately be captured by all of the models. This deficiency of the constitutive models can lead to unsafe designs due to the overestimation of the cyclic resistance to liquefaction and to the underestimation of long term settlements.
... It should be clarified that, in absence of cyclic experimental data to determine the values of parameters related to the memory surface development, the parameter μ 0 was set equal to 200 to quantitatively capture the trend of load degradation during cyclic loading. Please note that the parameter ξ has no influence in the current simulation while β is typically set to 1, following Griffiths (1985) and (Liu et al. 2020). Figure 14 presents a comparison between the experimental and the predicted behavior for the finite element analysis. ...
This paper aims to complement current knowledge about performance of deep foundations in residual soils by presenting the results of a new experimental field-testing program on steel driven piles (with hollow circular and square cross sections) subjected to cyclic lateral loading at controlled displacement amplitudes. The results show that the maximum mobilized lateral load (at the maximum applied displacement) decreases with the number of cycles to reach a constant final value maintained up to 100 cycles. The amount of load degradation is dependent on the displacement amplitude of the cyclic loading. It is also observed that the ultimate lateral load pile capacity is unaffected (if not slightly enhanced) by the application of cyclic loading. Combined 3-D finite element and pile test analysis revealed that the progressive degradation of maximum mobilized cyclic loading can be related to the progressive plastic displacement accumulation and not only to cement bonding degradation of the residual soil.
... In order to overcome this drawback, the above bounding surface − formulation is enriched with an additional 'memory locus', which can be exploited to keep track of the cyclic stress history and make the stiffness of the system evolve in agreement with relevant experimental evidence. The same approach has been recently developed for the constitutive modelling of (multiaxial) cyclic sand behaviour (Corti et al., 2016;Liu et al., 2019Liu et al., , 2020, and is here applied for the first time to 1D − modelling. The use of a memory locus (Eq. ...
The analysis of cyclically loaded piles is acquiring ever greater relevance in the field of geotechnical engineering, most recently in relation to the design of offshore monopiles. In this area, predicting the gradual accumulation of pile deflection under prolonged cycling is key to performing relevant serviceability assessments, for which simplified pile–soil interaction models that can be calibrated against common geotechnical data are strongly needed. This study proposes a new cyclic p−y model for piles in sand that takes a step further towards meeting the mentioned requirements. The model is formulated in the framework of memory-enhanced bounding surface plasticity, and extends to cyclic loading conditions the previous monotonic, CPT-based p−y formulation by Suryasentana and Lehane (2016); additionally, detailed modelling of pile–soil gapping is introduced to cope with the presence of unsaturated sand layers or, more generally, of cohesive soil behaviour. After detailed description of all model capabilities, field data from an onshore cyclic pile loading test are simulated using the proposed p−y model, with the most relevant parameters calibrated against available CPT data. Satisfactory agreement is shown between experimental and numerical results, which supports the practical applicability of the model and the need for further studies on a fully CPT-based calibration.
... The SANISAND-MS parameter for Karlsruhe sand (Liu et al. 2020, with relative density Dr = 50%, is obtained from Liu et al. (2021). The selected constitutive model has been successfully applied to a 3D FE modelling and verified the capability of reproducing the monopile-soil interaction for a smaller monopile (D = 5 m and L = 20 m) , as shown in Fig. 2. It should be noted that in this simplified case, the soil has been considered in drained conditions with an effective unit weight γ = 9.4 kN/m 3 . ...
Stress-strain response of the soil is dependent on the particular stress path imposed by the nearby geotechnical structure. This paper uses 3D numerical analyses to explore the stress paths experienced by soil elements around large diameter piles in sand subjected to cyclic lateral loading. Based on the outcome of the finite element analysis, typical stress paths for different soil elements around the pile are extracted featured with variation of normal stress and shear stress and the rotation of principal stress axis. This preliminary investigation provides recommendation for experimental campaign of tests and the Hollow Cylinder Torsional Apparatus is found enables a much better simulation, including the replication of the rotation of principal stress axes.
... Although various studies have been conducted to evaluate the response of large-diameter monopiles in sandy seabeds (Depina et al. 2015), less attention has been devoted to the influence of soft clay, which is a common geological characteristic along China's southeast coast. The geotechnical conditions of this region feature normally consolidated soft clays with varying thicknesses near the surface, followed by silty clays, loose to dense sands, or silty sands (Liu et al. 2020). Offshore monopile design must fulfill requirements regarding the capacity under loads of exceptional magnitude [ultimate limit states (ULS)]. ...
... Capturing the response after initial liquefaction has proven a challenge for constitutive models. To this extent, a variety of constitutive schemes has been proposed first by Elgamal et al. [20], then by Zhang and Wang [77], Boulanger and Ziotopoulou [8] and Tasiopoulou and Gerolymos [57], and very recently by numerous publications targeting this issue (e.g., [3,10,31,74]). In this model, the cyclic mobility response is captured with the aid of function h post-liq , primarily in Eq. (38) for the dilatancy D in dilation and secondarily in Eq. (30) for the evolution equation of the deviatoric fabric tensor f that affects the plastic modulus K p . ...
The paper describes the formulation and simulative potential of a constitutive model for monotonic and cyclic shearing of sands. It is a SANISAND-type model that does not consider a (small) yield surface and employs the last stress reversal point for defining both the elastic and the plastic strain rates. Emphasis is put on the updating of the stress reversal point to avoid stress-strain overshooting. It incorporates a fabric evolution index that scales the plastic modulus targeting strain accumulation with cycles and a post-liquefaction formulation affecting the dilatancy function. The paper includes the calibration process of the 14 model parameters. Model performance is verified against a large database of monotonic and cyclic shearing tests on Toyoura and Ottawa-F65 sands. To complement sand-specific data, empirical relations are used for validating the shear modulus at small strains, its degradation with cyclic shear strain, the corresponding increase in hysteretic damping, the evolving rates of volumetric and shear strain accumulation with cycles and the effect of relative density and stress level on liquefaction resistance. Model verification shows that a single set of sand-specific parameters may be used for both monotonic and cyclic shearing of any strain level, irrespective of stress level and relative density.
... 12 Quite recently, three-dimensional finite element (3D FE) simulations have been increasingly adopted to explore 13 the fundamental mechanisms that govern monopile tilting (Pisanò, 2019;Jostad et al., 2020;, also 14 Following the work of Corti et al. (2016), the 'memory surface' concept has been introduced into the SANISAND 64 constitutive formulation to enhance the simulation of cyclic strain accumulation, i.e., to control the development of 65 cyclic ratcheting. As is shown in Fig. 1, SANISAND-MS features four main model surfaces -namely, bounding, 66 yield, dilatancy and memory surfaces -and has been quantitatively validated against experimental data from the 67 literature -more details about model formulation and validation may be found in ; Liu and Pisanò 68 (2019); Liu et al. (2020). The applicability of the resulting 3D FE SANISAND-MS framework to the analysis of 69 cyclically loaded monopiles has been recently demonstrated by and Liu and Kaynia (2021), though 70 with exclusive reference to single-amplitude loading cycles. ...
Offshore monopiles accumulate permanent tilt under long-lasting cyclic environmental loads. Accurate prediction of monopile tilt is key to assessing their serviceability, and requires a fundamental understanding of loading history effects. While both experimental and numerical studies are shedding light on this matter, this work uses step-by-step implicit 3D FE modelling to investigate loading history effects in the response to cyclic lateral loading of monopiles in sand and to identify links between local soil behaviour and relevant features of global pile behaviour. For this purpose, the recently developed SANISAND-MS model is adopted to achieve a reliable simulation of sand’s cyclic ratcheting. In particular, the validity of an up-scaled Miner’s rule for monopile tilting under multi-amplitude cyclic loading is assessed based on the results of 3D FE parametric analyses, with emphasis on the role played by the engineering idealisation of random environmental loading. The validity of such a rule has been numerically investigated both in terms of local soil element response and global foundation behaviour — for the particular case of a large-diameter monopile. In respect, the effect of the loading history idealisation is presented, and it is concluded that Miner’s rule does not always rigorously apply to all the cases considered herein. The translation of irregular loading histories into a regular version with loading packages sorted in ascending amplitude order is shown to be a reasonable approach, at least when the possibility of cyclic pore pressure build-up is disregarded.
... Although the excessive accumulation of strain in bounding surface models is well recognized and has been sought redressed (Liu et al., 2019;Liu et al., 2020), it is arguably a result of a more fundamental shortcoming, namely a lack of memory of the stress history for more than a single cycle. The kinematic hardening multisurface framework, on the other hand, accounts for both the immediate and the remote stress history. ...
A simplified kinematic hardening plasticity framework for the constitutive modelling of soils is presented. In contrast to conventional kinematic hardening plasticity, the yield surfaces do not enter explicitly into the governing equations but are used only for the purpose of computing an effective hardening modulus. This leads to models reminiscent of conventional nonlinear elastic/perfectly plastic models, thus facilitating an efficient numerical implementation. The framework is detailed both with respect to total and effective stress analysis. Its capabilities are illustrated by the development of a simple model for undrained total stress analysis of clays.
... Such a goal is pursued through the application of SANISAND-MS, a constitutive model recently proposed by Liu et al. (2019a) to enhance the simulation of high-cyclic sand ratcheting (Wichtmann, 2005;di Prisco & Mortara, 2013), and therefore the assessment of foundation serviceability under cyclic loading. Following recent constitutive modelling work (Liu & Pisanò, 2019;Liu et al., 2019aLiu et al., , 2020, SANISAND-MS is here adopted for the first time to tackle a 3D boundary value problem. It is worth recalling that a thorough validation process should include quantitative comparison between the results of pile loading tests and corresponding 3D FE simulations, with the latter to be performed using soil parameters calibrated against soil laboratory data. ...
Serviceability criteria for offshore monopiles include the estimation of long-term, permanent tilt under repeated operational loads. In the lack of well-established analysis methods, experimental and numerical research has been carried out in the last decade to support the fundamental understanding of monopile–soil interaction mechanisms, and the conception of engineering methods for monopile tilt predictions. With a focus on the case of monopiles in sand, this work shows how step-by-step/implicit, three-dimensional (3D) finite-element (FE) modelling can be fruitfully applied to the analysis of cyclic monopile–soil interaction and related soil deformation mechanisms. To achieve adequate simulation of cyclic sand ratcheting and densification around the pile, the recently proposed SANISAND-MS model is adopted. The link between local soil behaviour and global monopile response to cyclic loading is discussed through detailed analysis of model prediction. Overall, the results of numerical parametric studies confirm that the proposed 3D FE modelling framework can reproduce relevant experimental evidence about monopile–soil interaction, and support future improvement of engineering design methods.
... Larger accumulations of rotation and displacements were observed at the early cyclic stages, followed by a progressive stiffening of the pile repose and a decrease in the rate of displacement and rotation accumulation. This response could be predicted owing to the capabilities of the employed constitutive model, which has proved to satisfactorily capture the ratcheting behaviour and the progressive soil stiffening under cyclic loading [12,24,25]. ...
Based on advanced 3D finite element modelling, this paper analyses the stress paths experienced by soil elements in the vicinity of a monopile foundation for offshore wind turbines subjected to cyclic loading with the aim of informing soil laboratory testing in support of monopile foundation design. It is shown that the soil elements in front of the laterally loaded monopile are subjected to complex stress variations, which gradually evolve towards steady stress cycles as the cyclic lateral pile loading proceeds. The amplitude, direction and average value of such steady stress cycles are dependent on the depth and radial distance from the pile of the soil element, but it also invariably involves the cyclic rotation of principal stress axes. Complementary laboratory testing using the hollow-cylinder torsional apparatus was carried out on granular soil samples imposing cyclic stress paths (with up to about 3 × 104 cycles) which resemble those determined after 3D finite element analysis. The importance of considering the cyclic rotation of principal stress axes when investigating the response of soil elements under stress conditions mimicking those around a monopile foundation subjected to cyclic lateral loading is emphasised.
The present study is devoted to the investigation of the dilatancy behaviour of a fine sand based on hollow cylinder tests. Medium and dense samples were tested at a constant average stress by applying torsional angles for shear strains 𝛾 = 1, 2, 3 and 4%. Dilatancy curves along with shear wave velocity measurements to investigate the influence of the shear strain amplitude in the shear modulus degradation curve are presented and discussed. The measured stress and strain paths were used to compare the performance of four advanced constitutive models especially in describing the dilatancy behaviour of sand. From the perspective of their constitutive equations, the differences between the simulations with various material models are examined. It may be concluded that all four models allow a proper prediction of torsional shear tests as long as a proper calibration of the material parameters is secured.
Soil deposits may be subjected to preloading episodes due to different factors such as previous earthquakes, excavations, refilling, compaction, construction of overlying structures, storms under onshore/offshore conditions, among many others. It is well-known that preloading episodes remarkably influence the subsequent soil mechanical behavior and liquefaction resistance. In order to accurately describe the influence of cyclic preloadings, advanced constitutive models which are able to realistically reproduce the soil mechanical behavior are necessary. In this work, a numerical study was carried out to investigate the influence of cyclic preloadings on the liquefaction resistance of sands. The numerical analyses were performed considering three advanced and well established constitutive models, namely: the hypoplastic model for sands by Von Wolffersdorf (1996) with the Intergranular Strain extension by Niemunis and Herle (1997), the same hypoplastic model for sands extended with Intergranular Strain Anisotropy by Fuentes et al. (2020), and the bounding surface plasticity model Sanisand by Dafalias and Manzari (2004). The simulations were performed based on the experimental databases on Zbraslav sand by Duque et al. (2023a,b). Remarks about the model capabilities and limitations on tests with different types of cyclic preloadings and their repercussion on boundary value simulations are given at the end.
In particular during storm events an accumulation of excess pore pressures may occur in
the soil around cyclically loaded offshore foundations. The excess pore pressure build-up
reduces the effective stresses in the soil and, hence, may negatively affect the structural
integrity by influencing the soil-structure interaction. Besides a loss in bearing capacity,
large plastic deformations may occur to the structure. Especially for offshore wind turbines
an accurate estimation of such deformations is of great importance. Even though the
consideration of this degradation effect on the bearing capacity is commonly demanded by
the involved certification or approval bodies, no general applicable and accepted method
for the calculative verification currently exists. Over the past decades several researchers
investigated the excess pore pressure build-up around offshore foundations due to environmental
cyclic loads. They tried to capture the loss of bearing capacity, the accumulation
of plastic rotation and the essential influence on the serviceability limit state and fatigue
design. However, even if there are some sophisticated concepts, none of them is seen as
the simple general applicable choice.
Within this thesis a new numerical method – termed Excess Pore Pressure Estimation
method (EPPE) – is presented in great detail. This method allows for the transfer of
the soil behaviour obtained in cyclic simple shear tests to the bearing behaviour of the
entire foundation. Herein, the numerical model accounts for the cyclic excess pore pressure
accumulation by respecting the element-based mean stress and stress amplitude as
well as an equivalent number of load cycles. The simulation of the excess pore pressure
build-up due to certain cyclic loading is based on undrained conditions, i.e. the excess
pore pressure build-up due to cyclic loading is derived by disregarding the simultaneous
consolidation process. The respected transfer method, in the form of contour plots, enables
the consideration of site-specific cyclic direct simple shear and triaxial test results
from laboratory devices to elements within the finite element model. Each integration
point is evaluated individually. Based on the derived excess pore pressure field, a consolidation
analysis takes place in the second step. The actual accumulated excess pore
pressure in each element at the end of the storm (or cyclic loading event) is then found
by analytically superposing the excess pore pressure decay curves from the consolidation
analysis.
For a deeper understanding of cyclic soil behaviour, the cyclic response in different laboratory
devices with different densities and under varying stress states was investigated by
the author. A contour approach based on cyclic load- and displacement-controlled test
results is derived to study the element response from the numerical point of view and
use these for the calibration of an implicit model. Moreover, different explicit approaches
are presented and compared in terms of their estimation behaviour of cyclic excess pore pressure generation, their predicted foundation capacity and their model assumptions.
The intention is hence to examine existing approaches and their applicability by means of
an elaborate comprehensive study. A simple modular explicit model is presented which
can be easily assessed with engineering judgment. If needed, the different individual
calculation steps can be exchanged with more sophisticated ones.
For a reference sandy soil, results of cyclic laboratory tests are presented and used on a
reference monopile foundation for a predefined storm event. The EPPE approach helps
to quantify the risk of capacity degradation as well as to evaluate an appropriate safety
margin. It is possible with the current methodology to evaluate the degradation potential
for different sites quite easily and fast.
Long-term cyclic loading from environmental conditions can lead to excessive permanent rotation of offshore wind turbines (OWTs) due to the ratcheting response of sand. A practical hybrid strain accumulation approach, termed the bounding surface stiffness degradation method (B-SDM), for finite element analysis (FEA)-based design of OWTs under cyclic loading is presented. This method includes a base elastoplastic constitutive model that captures the stress–strain relationship in the first load-unload cycle and a cyclic strain accumulation scheme for modelling the subsequent cycles. The presented approach allows for a versatile overlay scheme that calculates cyclic strain accumulation to be applied to a range of base elastoplastic models. The base constitutive model utilised is established based on the bounding surface concept and considers strain-hardening and plastic volume change before failure. The method has been validated by single element test data on sand and used in finitesingle-element element modelling of monopile response in cyclic loading. When the monopile response is modelled in 3D FEA, the conventional step-by-step modelling approach is used until the end of the first regular cycle. Strain accumulation in subsequent cycles is modelled using the B-SDM, in which the plastic modulus and dilatancy relationship are scaled based on a strain accumulation law.
The paper proposes a robust solution to the stress overshooting problem in bounding surface models. Stress overshooting is one of the main sources of numerical instability in finite element simulations using bounding surface models and has hindered the application of these models in solving large-scale boundary value problems. By proposing a novel framework that can be employed for the models that obey the kinematic hardening law, we provide a robust solution to the overshooting problem. The explicit integration scheme with automatic and adaptive sub-stepping is employed to increase the speed of finite element simulations. The robustness of the solution proposed is demonstrated by several numerical examples.
Sand liquefaction under static and dynamic loading can cause failure of embankments, slopes, bridges and other important infrastructure. Sand liquefaction in the seabed can also cause submarine landslides and tsunamis. Fabric anisotropy related to the internal soil structure such as particle orientation, force network and void space is found to have profound influence on sand liquefaction. A constitutive model accounting for the effect of anisotropy on sand liquefaction is proposed. Evolution of fabric anisotropy during loading is considered according to the anisotropic critical state theory for sand. The model has been validated by extensive test results on Toyoura sand with different initial densities and stress states. The effect of sample preparation method on sand liquefaction is qualitatively analysed. The model has been used to investigate the response of a sand ground under earthquake loading. It is shown that sand with horizontal bedding plane has the highest resistance to liquefaction when the sand deposit is anisotropic, which is consistent with the centrifuge test results. The initial degree of fabric anisotropy has a more significant influence on the liquefaction resistance. Sand with more anisotropic fabric that can be caused by previous loading history or compaction methods has lower liquefaction resistance.
Large-diameter thin-walled steel cylinders, which were first used in the Hong Kong-Zhuhai-Macao Bridge project as an enclosure structure for artificial islands, have been applied in many large-scale offshore projects. The thin-walled steel cylinder may fail during vibratory penetration in certain conditions such as asynchronicity of hammers and presence of corestones or sloping rockhead, which cannot be accommodated in routine wave equation analysis. This study aims to further develop the novel thin-walled offshore retaining structure. A three-dimensional (3D) finite element model is established to simulate the penetration of large-diameter thin-walled steel cylinders using a group of vibratory hammers. The dynamic response of the steel cylinder under multi-point vibrations is sensitive to penetration depth, vibration amplitude, and frequency. Failure under unsynchronized vibrations occurs first at the free part of the cylinder above the ground level. A “shearing” failure mode can develop when the asynchronous hammers cluster together and a “shearing-compressive” failure mode can develop when the asynchronous hammers are alternately distributed. Failure of the cylinder in the presence of geological obstacles occurs at the cylinder toe. “Compressive buckling” and “extrusion buckling” failure modes can develop when the steel cylinder encounters a corestone and sloping rockhead, respectively.
The offshore wind sector is skyrocketing worldwide, with a clear trend towards wind farms installed in increasingly deep waters and harsh marine environments. This is posing significant engineering challenges, including those regarding the design of support structures and foundations for offshore wind turbines (OWTs). Substantial research efforts are being devoted to the geotehnical design of monopile foundations, currently supporting about 80% of OWTs in Europe. This paper overviews recent work carried out at TU Delft on the numerical integrated modelling of soil-monopile-OWT systems, and its input to the improvement of geotechnical design approaches. The benefits of incorporating advanced soil constitutive modelling in three-dimensional finite element simulations are highlighted, with emphasis on the interplay of cyclic soil behaviour and dynamic OWT performance. Ongoing research on high-cyclic soil plasticity modelling is also presented, and related to the analysis of monopile tilt under irregular environmental loading.
Liquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress‐strain response in earthquake‐induced liquefaction and post‐liquefaction is complex and yet very important for stress‐deformation and performance‐based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre‐liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post‐liquefaction response.
The offshore wind sector is skyrocketing worldwide, with a clear trend towards wind farms installed in increasingly deep waters and harsh marine environments. This is posing significant engineering challenges, including those regarding the design of support structures and foundations for offshore wind turbines (OWTs). Substantial research efforts are being devoted to the geotehnical design of monopile foundations, currently supporting about 80% of OWTs in Europe. This paper overviews recent work carried out at TU Delft on the numerical integrated modelling of soil-monopile-OWT systems, and its input to the improvement of geotechnical design approaches. The benefits of incorporating advanced soil constitutive modelling in three-dimensional finite element simulations are highlighted, with emphasis on the interplay of cyclic soil behaviour and dynamic OWT performance. Ongoing research on high-cyclic soil plasticity modelling is also presented, and related to the analysis of monopile tilt under irregular environmental loading.
Predicting the cyclic response of soils is still challenging in many geotechnical applications. In this area, the continual efforts on the constitutive modelling of cyclic sand behaviour demand new and reliable dataset for model validation – even more so for loading conditions involving numerous loading cycles (‘high-cyclic’ loading). This paper concerns the recent memory-enhanced bounding surface formulation by Liu et al. as a suitable platform to reproduce the high-cyclic response of sands. New evidence of its suitability is provided based on the recent dataset published by Park and Santamarina, comprising the results of high-cyclic oedometer tests at varying initial/loading conditions. Model simulations show satisfactory agreement with experimental data, and prove the ability of the model to predict ‘terminal densities’ under confined cyclic compression.
SANISAND is the name of a family of bounding surface plasticity constitutive
models for sand within the framework of critical state theory, which have been
able to realistically simulate the sand behavior under conventional monotonic
and cyclic loading paths. In order to incorporate the important role of evolving
fabric anisotropy, one such model was modified within the framework of the
new anisotropic critical state theory and named SANISAND-F model. Yet the
response under continuous stress principal axes rotation requires further modification
to account for the effect of ensuing noncoaxiality on the dilatancy and
plastic modulus. This modification is simpler than what is often proposed in
the literature, since it does not incorporate an additional plastic loading mechanism
and/or multiple dilatancy and plastic modulus expressions. The new
model named SANISAND-FN is presented herein and is validated against published
data for loading that includes drained stress principal axes rotation on
Toyoura sand.
The modelling and simulation of cyclic sand ratcheting is tackled by means of a plasticity model formulated within the well-known critical state, bounding surface SANISAND framework. For this purpose, a third locus – termed the ‘memory surface’ – is cast into the constitutive formulation, so as to phenomenologically capture micro-mechanical, fabric-related processes directly relevant to the cyclic response. The predictive capability of the model under numerous loading cycles (‘high-cyclic’ loading) is explored with focus on drained loading conditions, and validated against experimental test results from the literature – including triaxial, simple shear and cyclic loading by oedometer test. The model proves capable of reproducing the transition from ratcheting to shakedown response, in combination with a single set of soil parameters for different initial, boundary and loading conditions. This work contributes to the analysis of soil–structure interaction under high-cyclic loading events, such as those induced by environmental and/or traffic loads.
In this paper the formulation of a simplified model for predicting pore water pressure build-up under seismic loading is updated and applied to different soils. The model is directly based on the results of cyclic laboratory tests and it is based on the damage parameter concept, avoiding any arbitrary equivalence criterion necessary to compare the seismic demand to the cyclic strength of liquefiable soils. The model is suitable to be implemented into non-linear coupled seismic response analyses since it operates in the time domain. The analytical formulation is fully described and the calibration and the physical meaning of the model parameters are analysed in detail. Simple applications show the practical usefulness of the model with respect to other literature approaches.
In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.
Understanding the evolution of microstructure in granular soils can provide significant insights into constitutive modeling of soil liquefaction. In this study, micromechanical perspectives of the liquefaction process are investigated using the Discrete Element simulation. It is observed that during various stages of undrained cyclic loading, the soil exhibits definitive change in the load-bearing structure, indicated by evolution of the coordination number and non-affine displacements. A new particle-void fabric, termed as “centroid distance”, is also proposed to quantify the evolution of particles and voids distribution in the granular packing. The fabric index is found to have strong correlation with cyclic mobility and post-liquefaction deformation of granular soils. Evolution of the fabric index indicates that particles and voids redistribute irreversibly before and after liquefaction. A highly anisotropic particle-void structure and loading-bearing capacity can be formed in the post liquefaction stage.
The theory of zero purely elastic range in stress space within the framework of bounding surface plasticity is applied to sand constitutive modelling. The yield surface shrinks to zero and becomes identical to the stress point itself, and plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally non-linear. The simplicity of the conceptual structure of the model is particularly attractive as it consists of only one surface, the bounding/failure surface, and the stress point itself in the stress ratio π-plane. The image stress point on the bounding surface is defined analytically in terms of the direction of the rate of the stress ratio, with the latter being inside, on, or outside the surface, so that the model can address consistently hardening, softening and critical state response. An updating scheme of the initial value of stress ratio at unloading–reloading events is proposed in order to avoid the overshooting phenomenon. The model follows the basic premises of the SANISAND family of models that unify the description for any pressure and density within critical state theory. The simulating capabilities of the model are shown to be comparable with those of classical models with very small yield surfaces, and additional simulations of unorthodox loading paths such as rotational shear are successfully compared with experimental data.
For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of
initial conditions and load characteristics are necessary. It is the purpose of these two companion papers to provide such database collected for a fine sand. Part II concentrates on the undrained triaxial tests with strain cycles, where a large range of strain amplitudes has been studied. Furthermore, oedometric and isotropic compression tests as well as drained triaxial tests with un- and reloading cycles are discussed. A combined monotonic and cyclic loading has been also studied in undrained triaxial tests. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.
A dataset of undrained cyclic triaxial tests for liquefaction with parametrically changing relative density and fines content is reviewed and interpreted in the scope of energy. It is found that the strain amplitude or pore-pressure buildup during cyclic loading is uniquely correlated not only to the energy dissipated in soil specimens, but also to strain energy given from outside. Hence, an energy-based method (EBM) is developed in which liquefaction potential can be evaluated by comparing strain energy for liquefaction in a sand layer with upcoming seismic energy without regard to the differences in seismic motions. Comparative studies in soil models demonstrate that the effect of various input motions is intrinsically included in EBM, whereas it has to be considered by choosing proper coefficients in a conventional stress-based method (SBM). Another significant difference is that liquefaction potential tends to be higher for a shallower depth in EBM, while it is vice versa in SBM in a uniform sand deposit.
Ground motions of the 2011 Tohoku earthquake recorded at Onahama port
(Iwaki, Fukushima prefecture) rank among the highest accelerations ever
observed, with the peak amplitude of the 3-D acceleration vector
approaching 2g. The response of the site was distinctively non-linear,
as indicated by the presence of horizontal acceleration spikes which
have been linked to cyclic mobility during similar observations.
Compared to records of weak ground motions, the response of the site
during the Mw 9.1 earthquake was characterized by increased
amplification at frequencies above 10 Hz and in peak ground
acceleration. This behaviour contrasts with the more common non-linear
response encountered at non-liquefiable sites, which results in
deamplification at higher frequencies. We simulate propagation of SH
waves through the dense sand deposit using a non-linear finite
difference code that is capable of modelling the development of excess
pore water pressure. Dynamic soil parameters are calibrated using a
direct search method that minimizes the difference between observed and
simulated acceleration envelopes and response spectra. The finite
difference simulations yield surface acceleration time-series that are
consistent with the observations in shape and amplitude, pointing
towards soil dilatancy as a likely explanation for the high-frequency
pulses recorded at Onahama port. The simulations also suggest that the
occurrence of high-frequency spikes coincided with a rapid increase in
pore water pressure in the upper part of the sand deposit between 145
and 170 s. This sudden increase is possibly linked to a burst of
high-frequency energy from a large slip patch below the Iwaki region.
This paper presents a theoretical framework for predicting the post-liquefaction deformation of saturated sand under undrained cyclic loading with emphasis on the mechanical laws, physical mechanism, constitutive model and numerical algorithm as well as practical applicability. The revealing mechanism behind the complex behavior in the post-liquefaction regime can be appreciated by decomposing the volumetric strain into three components with distinctive physical background. The interplay among these three components governs the post-liquefaction shear deformation and characterizes three physical states alternating in the liquefaction process. This assumption sheds some light on the intricate transition from small pre-liquefaction deformation to large post-liquefaction deformation and provides a rational explanation to the triggering of unstable flow slide and the post-liquefaction reconsolidation. Based on this assumption, a constitutive model is developed within the framework of bounding surface plasticity. This model is capable of reproducing small to large deformation in the pre- to post-liquefaction regime. The model performance is confirmed by simulating laboratory tests. The constitutive model is implemented in a finite element code together with a robust numerical algorithm to circumvent numerical instability in the vicinity of vanishing effective stress. This numerical model is validated by fully coupled numerical analyses of two well-instrumented dynamic centrifuge model tests. Finally, numerical simulation of liquefaction-related site response is performed for the Daikai subway station damaged during the 1995 Hyogoken-Nambu earthquake in Japan.
The requirement for a rational engineering approach to constructing structures using undensified hydraulic sand fill has identified several deficiencies in current technology. In particular, there is no single parameter measure of sand behaviour. This Paper presents an appropriate physical parameter, termed the state parameter, that combines the influence of void ratio and stress level with reference to an ultimate (steady) state to describe sand behaviour. Data from a triaxial testing programme on Kogyuk sand with four fines contents is presented and the significant engineering design parameters are demonstrated to be dependent on the state parameter. The concept of state is a fundamental physical concept and has wide applicability both as an empirical normalizing parameter and for constitutive modelling of soil behaviour.
Plusieurs insuffisances de la technologie habituelle ont été révélées lorsqu'on a tenté de trouver une méthode de construction rationnelle pouvant être utilisé dans le cas de structures liées à l'emploi de remblais hydrauliques sableux non-compactés. En particulier il n'y a pas de paramètre unique pour mesurer le comportement du sable. Cet article présente un paramètre physique adéquat (appelé paramètre d'état) qui combine l'influence de l'indice des vides et du niveau des contraintes dans un état final (stationnaire) pour décrire le comportement du sable. On présente des données obtenues à partir d'un programme d'essais triaxiaux sur du sable de Kogyuk avec quatre contenus différents de fines. On démontre comment les paramètres significatifs du projet dépendent du paramètre d'état. La notion d'état est une notion physique fondamentale qui a une large application comme paramètre empirique de normalisation et qui peut s'employer pour modéliser le comportement du sol.
Lateral ground displacements generated by liquefaction-induced lateral spread are a severe threat to the Navy's shore facilities. During past earthquakes, lateral spread displacements have pulled apart or sheared shallow and deep foundations of buildings, several pipelines and other structures and utilities that transect the ground displacement zone, buckle bridges or other structures constructed across the toe, and toppled retaining walls, bulkheads, etc. that lie in the path of the spreading ground. Port facilities have been particularly vulnerable to ground displacement because they are commonly sited on poorly consolidated natural deposits or fills that are particularly susceptible to liquefaction and lateral spread. This Technical Note presents methods for evaluating liquefaction susceptibility of sediments beneath level to gently sloping sites and for estimating magnitudes of potential lateral ground displacement at those sites. This design guide provides procedures including equations, tables, and charts required to evaluate liquefaction susceptibility beneath level and gently sloping sites and to estimate probable freefield lateral displacements at those sites. Free-field ground displacements are those that are not impeded by structural resistance, ground modification, or a national boundary. This Technical Note does not provide guidance, however, for estimating ground settlements as a consequence of seismic compaction of granular soils or static consolidation of cohesive soils.
The effects of initial soil fabric on the shear behaviour of granular materials are investigated by employing distinct element method (DEM) numerical analysis. Soil specimens are represented by an assembly of non-uniform sized spherical particles. DEM specimens that have different initial contact normal distributions were prepared at two different densities (loose and dense) and then isotropically consolidated triaxial tests were simulated with the following conditions: (a) different drainage conditions (undrained/drained), (b) different modes of shearing (compression/extension), and (c) different directions of shearing (vertical/horizontal). The numerical analysis results are compared qualitatively with the observed experimental data and the effects of initial soil fabric on resulting soil behaviours are discussed. The discussions include the effects of specimen reconstitution methods, effects of large preshearing, and anisotropic characteristics in drained and undrained conditions. The effects of initial soil fabric on the quasi-steady state are also investigated. The numerical analysis results can systematically explain that the observed experimental behaviours of sand are due principally to the effects of initial soil fabric. The outcome provides insights into the observed phenomena in microscopic view.
A constitutive soil model that was originally developed to model liquefaction and cyclic mobility has been updated to comply with the established guidelines on the dependence of liquefaction triggering to the number of loading cycles, effective overburden stress (Kσ), and static shear stress (Kα). The model has been improved with new flow rules to better capture contraction and dilation in sands and has been implemented as PDMY03 in different computational platforms such as OpenSees finite-element, and FLAC and FLAC3D finite-difference frameworks. This paper presents the new modified framework of analysis and describes a guideline to calibrate the input parameters of the updated model to capture liquefaction triggering and post-liquefaction cyclic mobility and the accumulation of plastic shear strain. Different sets of model input parameters are provided for sands with different relative densities. Model responses are examined under different loading conditions for a single element.
The development of the offshore wind industry is motivating substantial research efforts worldwide, where offshore wind turbines (OWTs) of increasing size are being installed in deeper water depths. Foundation design is a major factor affecting the structural performance of OWTs, with most installations founded to date on large-diameter monopiles.
This work promotes advanced 3D finite element (FE) modelling for the dynamic analysis of OWT-monopile-soil systems. A detailed FE model of a state-of-the-art 8 MW OWT is analysed by accounting for dynamic soil-monopile interaction in presence of pore pressure effects. For this purpose, the critical-state, bounding surface SANISAND model is adopted to reproduce the hydro-mechanical cyclic response of the sand deposit. The response to realistic environmental loading histories (10 min duration) are simulated, then followed by numerical rotor-stop tests for global damping estimation.
While linking to existing literature, all FE results are critically inspected to gain insight relevant to geotechnical design. The modelling tools adopted (i) support the robustness of ‘soft-stiff’ foundation design with respect to natural frequency shifts, even during severe storm events; (ii) provide values of foundation damping in line with field measurements; (iii) suggest that pore pressure effects might more likely affect soil-monopile interaction under weak-to-moderate environmental loading.
We present a theoretical model to describe the response of a one dimensional mechanical system under cyclic loading. Specifically, the model addresses the non-linear response on loading, hysteretic behaviour on unloading and reloading, and the phenomenon of ratcheting under very many cycles. The methods developed are formulated within the hyperplasticity framework. The model can be expressed in the form of general incremental relationships, can therefore be applied without modification directly to any loading history, and can be readily implemented within a time-stepping numerical code. A rigorous procedure is described to accelerate the ratcheting process, so that the effects of very large numbers of cycles can be analysed through a reduced number of cycles. A generalisation from unidirectional to multidirectional loading is described, together with a tensorial form for application to material modelling. The original motivation was for the application to design of piles under lateral loading, and an example of this application is provided. However, the model is equally applicable to many other problems involving unidirectional or bi-directional cyclic loading in which the system exhibits a similar character of hysteretic behaviour, with ratcheting under large numbers of cycles.
The prediction of the stress-strain response of granular soils under large numbers of repeated loading cycles requires subtle changes to existing models, although the basic framework of kinematic hardening/bounding surface elastoplasticity can be retained. Extending an existing model, an extra memory surface is introduced to track the stress history of the soil. The memory surface can evolve in size and position according to three rules that can be linked with physical principles of particle fabric and interaction. The memory surface changes in size and position through the experienced plastic volumetric strains, but it always encloses the current stress state and the yield surface; these simple rules permit progressive stiffening of the soil in cyclic loading, the accurate prediction of plastic strain rate accumulation during cyclic loading, and the description of slightly stiffer stress-strain response upon subsequent monotonic reloading. The implementation of the additional modeling features requires the definition of only two new constitutive soil parameters. A parametric analysis is provided to show model predictions for drained and undrained cyclic loading conditions. The model is validated against available tests on Hostun sand performed under drained triaxial cyclic loading conditions with various confining pressures, densities, average stress ratios, and cyclic amplitudes.
Liquefaction of saturated sands was studied by means of pulsating loading triaxial tests on isotropically consolidated undrained laboratory samples. An analysis indicates that this type of test can be made to simulate idealized loading conditions on elements of soil in the field during earthquakes. The test results indicate that the danger of liquefaction of a saturated sand is determined by the following factors: (1) Void ratio; the higher the void ration the more easily liquefaction will occur. (2) Confining pressure; the lower the confining pressure the more easily liquefaction will occur, and (3) magnitude of cycle stress or strain; the larger the cyclic stress or strain the fewer the number of cycles required to induce liquefaction. Data from large shaking table experiments, and from observations of liquefaction during recent earthquakes lend qualitative support to the conclusions drawn from these laboratory cyclic loading triaxial tests.
An earlier model by the authors for the seismic liquefaction of sands is revised and extended. The model, based on liquefaction case history data and the hypothesis that increase in pore water pressure is proportional to the density of seismic energy dissipation, relates pore pressure increase during an earthquake to the earthquake magnitude, epicentral distance, initial effective overburden stress and standard penetration value of the site soil. The principal assumptions of the original model are examined and a revised model proposed. This includes an allowance for constant-Q material attenuation between the earthquake source and site and a non linear relation, based on laboratory testing, between pore pressure increase and density of dissipated seismic energy in the site soil. The effect of model uncertainty on probabilistic estimates of liquefaction hazard are examined, and a factor correcting for uncertainty is obtained in closed form.
Two aspects of seismically-induced liquefaction are discussed which are of vital engineering significance: the triggering condition and the consequences of liquefaction. The triggering condition is examined with respect to liquefaction analysis, note being taken of the onset condition which is governed by cyclic strength. Consequences of liquefaction are discussed with respect to post-seismic stability analysis, in which the residual strength plays a major role. Procedures used for liquefaction analysis based on the results of in situ sounding tests are introduced, and the applicability of this method for estimating associated ground settlements is discussed.
The evaluation of residual strength requires a better understanding of undrained sand behaviour. Results of extensive laboratory rests on Japanese standard sand are examined and new index parameters are proposed to quantify undrained sand behaviour better. The results of laboratory tests on silty sands are examined in the same way. AH the results are presented in terms of whether sand behaviour is contractive or diltative. The laboratory-established criterion for contractive or diltative behaviour is expressed in terms of field parameters such as N value from the SPT or qc value from the CPT. This correlation permits in situ deposits to be classified as being either able or not able to develop flow slide.
The laboratory-established relationships between the normalized residual strength and the field parameters are presented. These correlations are shown to be consistent with many cases of flow failure observed in recent large earthquakes. The relationship between cyclic strength and residual strength is clarified.
L'article étudie deux des aspects de la liquéfaction sismiquement induite qui sont d'une importance vitale pour les ingénieurs: les conditions de déclenchement et les conséquences de la liquéfaction. Les conditions de déclenchement sont examinées au travers d'une analyse de la liquéfaction pour laquelle les toutes premières conditions, régies par la résistance cyclique, sont prises en compte. Les conséquences de la liquéfaction sont étudiées à l'aide d'une analyse de stabilité post-sismique pour laquelle la résistance résiduelle joue une rôle primordial. L'on présente les méthodes utilisées pour l'analyse de la liquéfaction fondées sur les résultats d'essais in-situ. L'applicabilité de cette méthode à l'estimation des tassements associés est également discutée. L'évaluation de la résistance résiduelle demande une meilleure compréhension du comportement des sables non-drainés. Les résultats d'essais extensifs de laboratoire sur des sables japonais standards sont étudiés et de nouveaux paramètres sont proposés pour améliorer la quantification du comportement des sables non-drainés. Les résultats obtenus pour des sables argileux sont étudiés de la même façon. Tous ces résultats sont présentés différemment selon que le comportement du sable est contractant ou dilatant. Le critère établi en laboratoire pour des comportements dilatant ou contractant peut s'exprimer en terme de paramètres de chantier tels que N valeurs issues du SPT ou qc valeurs issues du CPT. CPT. Cette corrélation permet de classer les dépôts in-situ comme étant capables ou non de développer un glissement par écoulement. L'article présente également les relations établies en laboratoire entre la résistance résiduelle normalisée et les paramètres de chantier-tels que SPT ou CPT. Ces corrélations sont en accord avec de nombreux cas de rupture par écoulement observés lors de grands séismes récents. La relation existant entre résistance cyclique et résistance résiduelle est clarifiée.
The static undrained behavior of saturated sand is shown to be dilative in triaxial compression, even in the loosest deposited state. However, the behavior in triaxial extension is contractive for relative densities of up to 60%, implying a profound anisotropy of response to undrained loading. On monotonic loading, following liquefaction, the sand always responds in a dilative manner even though it is contractive under static loading. The postliquefaction response represents continuously stiffening behavior and an approach to any residual strength is not observed, regardless of density or effective stress conditions prior to cyclic loading.
Dilatancy is often considered a unique function of the stress ratio η = q/p', in terms of the triaxial stress variables q and p'. With this assumption, the direction of plastic flow is uniquely related to η, irrespective of the material internal state. This obviously contradicts the facts. Consider two specimens of the same sand, one is in a loose state and the other in a dense state. Subjected to a loading from the same η, the loose specimen contracts and the dense one dilates. These two distinctly different responses are associated with a single η but two different values of dilatancy, one positive and the other negative. Treating the dilatancy as a unique function of η has developed into a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing). A theory is presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics. Micromechanical analysis is used to justify and motivate a simple macroscopic constitutive framework. A rudimentary model is presented, and its simulative capability shown by comparison with experimental data of the response of a sand under various initial state and loading conditions.
Within the critical state soil mechanics framework, the two-surface formulation of plasticity is coupled with the state parameter to construct a constitutive model for sands in a general stress space. The operation of the two-surface model takes place in the deviatoric stress-ratio space, and the state parameter is used to define the peak and dilatancy stress ratios of sand. The model is capable of realistically simulating stress-strain behaviour of sands under monotonic and cyclic, drained and undrained loading conditions. It includes features such as the softening of sands at states denser than critical as they dilate in drained loading and softening of sands looser than critical in undrained loading, and the pore-water pressure increase under undrained cyclic loading. Most important, all these simulations are achieved by a unique set of model constants at all densities and confining pressures of engineering relevance for a given sand. The numerical implementation of the model is particularly easy and efficient due to the very simple formulation. Calibration of model constants is done straightforwardly on the basis of triaxial experiments and measurements of well-known characteristics of sand stress-strain behaviour. Possibly the most attractive feature of the model is its simplicity and its foundation on concepts and data which are well established and understood by the geotechnical engineering community, with basic reference to critical state soil mechanics.
A simple stress-ratio controlled, critical state compatible, sand plasticity model is presented, first in the triaxial and then in generalized stress space. The model builds upon previous work of the writers, albeit the presentation here is made with extreme simplicity in mind, and three novel aspects are introduced. The first is a fabric-dilatancy related quantity, scalar valued in the triaxial and tensor valued in generalized stress space, which is instrumental in modeling macroscopically the effect of fabric changes during the dilatant phase of deformation on the subsequent contractant response upon load increment reversals, and the ensuing realistic simulation of the sand behavior under undrained cyclic loading. The second aspect is the dependence of the plastic strain rate direction on a modified Lode angle in the multiaxial generalization, a feature necessary to produce realistic stress-strain simulations in nontriaxial conditions. The third aspect is a very systematic connection between the simple triaxial and the general multiaxial formulation, in order to use correctly the model parameters of the former in the implementation of the latter. The simulative ability of the model is illustrated by comparison with data over a very wide range of pressures and densities.
A model for presentation of pore water pressures induced in sand samples during cyclic undrained testing is described. The proposed model belongs to a class of so-called ‘damage parameter models’, which correlate the pore pressure rise with a parameter based on an accumulated variable during testing. The concept of threshold strain is also incorporated in the model. The model has been verified on several series of published cyclic test data. Its parameters lie in a narrow band for a wide range of sand properties. The empirical functions that represent the common shape of individual curves for interpreted pore pressure data are also suggested. The proposed procedure has been adapted for presentation of other cyclic soil tests, and examples of interpretation of cyclic stress-controlled as well as cyclic drained tests are included.
One of the important geotechnical considerations for many engineering installations, such as pipelines and anchors, in an oceanic environment involving sand deposits is that of potential ocean floor instability due to the development of high pore pressures caused by the direct action of waves. This article presents a procedure for evaluating the magnitude and distribution of wave‐induced pore pressures in ocean floor deposits. The method takes into account the distribution of wave‐induced pore pressures in ocean floor deposits. The method takes into account the distribution of cyclic shear stresses in the soil profile as well as the important factor of pore‐pressure dissipation. The variation of properties within the soil profile can also be easily incorporated into the analytical procedure. The analysis provides the complete time history of pore‐pressure response and shows clearly that failure to include the pore‐pressure dissipation effects would lead to radically conservative design. The results also provide a basis for designing remedial measures, if required, to avert the development of high pore pressures and their deleterious effects.
The stress-strain response of overconsolidated clay depends both on its current state and on the loading history followed to reach that state, in particular the relative directions of the current and previous loading paths. A constitutive soil model is developed which predicts this behaviour by allowing elasto-plastic deformation controlled by two nested kinematic hardening surfaces inside a conventional Modified Cam-clay state boundary surface. This relatively straightforward model requires only eight parameters, each with a rational basis, and which can be determined from a small number of well-controlled stress path tests. Predistion of soil behaviour using this model are compared with data from triaxial stress path tests. The close agreement confirms that the essential features of soil behaviour are predicted by the model. The wider implications of the use of the model in geotechnical analysis are illustrated by comparing predictions made using the model (in conjunction with finite element analysis) with data from a spacially commissioned series of centrifuge tests of a circular foundation loaded on overconsolidated clay. The stress history of the soil was carefully controlled in the experiments and was replicated in the course of the analyses. The computations reproduced the main characteristics of the observed ground movement, in particular the surface profile. In contrast, conventional constitutive models of soil behaviour show very poor predictions. This demonstrates the importance of using a model that simulates the behaviour of soil over a wide range of strain increments and with changes in load path direction.
Cyclic loading can be important for the foundation design of structures, both offshore, along the coast, and on land, and for the stability of slopes. This is illustrated by several examples. The paper discusses how soil behaves under cyclic loading, both for structures and for slopes, and shows that the cyclic shear strength and the failure mode under cyclic loading depend strongly on the stress path and the combination of average and cyclic shear stresses. Diagrams with the cyclic shear strength of clay, sand, and silt that can be used in practical design are presented. Comparisons between calculations and model tests indicate that foundation capacity under cyclic loading can be determined on the basis of cyclic shear strength determined in laboratory tests.Le chargement cyclique est important pour la conception de fondations de structures, autant en mer, sur la côte et sur la terre, et pour la stabilité des pentes. Ceci est illustré à l'aide de plusieurs exemples. Cet article discute du comportement du sol soumis à un chargement cyclique, pour la structure et les pentes, et démontre que la résistance au cisaillement cyclique et le mode de défaillance sous chargement cyclique dépendent fortement du cheminement des contraintes et de la combinaison des contraintes en cisaillement moyennes et cycliques. Des diagrammes de résistance au cisaillement cyclique pour l'argile, sable et silt, qui peuvent être utilisés pour la conception, sont présentés. Des comparaisons entre les calculs et les essais modélisés indiquent que la capacité de la fondation soumise à un chargement cyclique peut être déterminée à partir de la résistance au cisaillement cyclique obtenu par des essais en laboratoire.
In this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou-Jafari-Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non-associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress–dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd.
A number of observations are made on the macroscopic behavior of materials subjected to uniaxial random cyclic loadings. These observations are then generalized to construct a model describing the material behavior for complex multiaxial loadings, in particular for cyclic loadings. This generalization introduces the concept of a bounding surface in the stress space which always encloses the loading surface. A parameter defined by the relative position of the loading and the bounding surface, and the plastic work done during the most recent loading, determine the value of the plastic modulus.Zahlreiche Beobachtungen des makroskopischen Verhaltens von Werkstoffen unter beliebiger zyklischer einachsiger Belastung werden gemacht. Diese Beobachtungen werden dann verallgemeinert, um ein Modell des Werkstoffverhaltens fr zusammengesetzte, insbesondere zyklische Belastung zu entwickeln. Diese Verallgemeinerung fhrt zum Konzept der die Belastungsflche stets einhllenden Grenzflche im Spannungsraum. Ein durch die relative Lage der Belastungsflche zur Grenzflche definierter Parameter und die plastische Arbeit whrend der letzten Belastung bestimmen den Wert des Plastizittsmoduls.
Semi-empirical procedures for evaluating the liquefaction potential of saturated cohesionless soils during earthquakes are re-examined and revised relations for use in practice are recommended. The stress reduction factor (rd), earthquake magnitude scaling factor for cyclic stress ratios (MSF), overburden correction factor for cyclic stress ratios (Kσ), and the overburden normalization factor for penetration resistances (CN) are discussed and recently modified relations are presented. These modified relations are used in re-evaluations of the SPT and CPT case history databases. Based on these re-evaluations, revised SPT- and CPT-based liquefaction correlations are recommended for use in practice. In addition, shear wave velocity based procedures are briefly discussed.
This paper presents the multiaxial formulation of a plasticity model for sand under cyclic shearing. The model adopts a kinematic hardening circular cone as the yield surface and three non-circular conical surfaces corresponding to the deviatoric stress ratios at phase transformation, peak strength and critical state. The shape of the non-circular surfaces is formulated in accordance with the experimentally established failure criteria, while their size is related to the value of the state parameter ψ. To simulate cyclic response under small and large shear strain amplitudes without a change in model parameters, it was found necessary to introduce: (a) a non-linear hysteretic (Ramberg–Osgood type) formulation for the strain rate of elastic states and (b) an empirical index of the effect of fabric evolution during shearing which scales the plastic modulus. This index is estimated in terms of a macroscopic second-order fabric tensor, which develops as a function of the plastic volumetric strain increment and the loading direction in the deviatoric plane. Comparison of simulations to pertinent data from 27 resonant column, cyclic triaxial and cyclic direct simple shear tests provide a measure for the overall accuracy of the model.
Cyclic mobility is exhibited by saturated medium to dense cohesionless soils during liquefaction, due to soil skeleton dilation at large shear strain excursions. This volume-shear coupling mechanism results in phases of significant regain in soil shear stiffness and strength, and limits the magnitude of cyclic shear deformations. Motivated by experimental observations, a plasticity model is developed for capturing the characteristics of cyclic mobility. This model extends an existing multi-surface plasticity formulation with newly developed flow and hardening rules. The new flow rule allows for reproducing cyclic shear strain accumulation, and the subsequent dilative phases observed in liquefied soil response. The new hardening rule enhances numerical robustness and efficiency. A model calibration procedure is outlined, based on monotonic and cyclic laboratory sample test data.
A simple elastic-plastic constitutive model for cohesionless soils is proposed. The model retains the extreme versatility and accuracy of the simple multi-surface J2-theory in describing observed shear nonlinear hysteretic behaviour, shear stress-induced anisotropy; and reflects the strong dilatancy dependency on the effective stress ratio. The theory is applicable to general three-dimensional stress-strain conditions, but its parameters can be derived entirely from the results of conventional laboratory soil tests. A number of examples are presented including an analysis of seismically induced liquefaction behind a retaining structure.
For simple shearing under constant pressure, the effects of fabric on liquefaction and densification potentials of saturated cohensionless granular materials are examined theoretically and experimentally. The fabric is identified with the distribution of the dilatancy angles (the angle between the sliding and the macroscopic shearing directions), and the influence of prestraining on this distribution and hence on the macroscopic sample behavior is studied. It is shown that prestraining with zero residual stress can reduce resistance to liquefaction by one or even two orders of magnitude, although the sample density and other conditions are kept the same. The micromechanical features responsible for this and related behaviors are examined in some detail. Finally, some tentative results on the effect of the inherent anisotropy that is produced during sample preparation are reported, showing that a method which yields samples more resistive in triaxial cyclic tests may provide samples less resistive in cyclic shearing.
Pore pressure model for cyclic straining of sand
- R Dobry
- W Pierce
- R Dyvik
- G Thomas
- R Ladd
Dobry, R., W. Pierce, R. Dyvik, G. Thomas, and R. Ladd. 1985. Pore
pressure model for cyclic straining of sand. Troy, NY: Rensselaer
Polytechnic Institute.