Numerical investigations on liquefaction potential of saturated silty sands
Introduction
Liquefaction is one of the most interesting and complicated phenomena exhibited by granular materials. It is the phenomena by which loose saturated granular material loses strength and stiffness during cyclic or static loading due to the generation of excess pore water pressure (EPWP). Since the widespread liquefaction and liquefaction induced destruction of infrastructures during the 1964 earthquakes in Alaska and Japan, it has been extensively investigated. Based on the investigations of sites that liquefied and sites that did not during the earthquake in China, Wang [1] observed that the liquefiable soils tend to have fines content less than 15%, liquid limit less than 35%, and water content greater than 90% of the liquid limit. These observations were formalized into one of the first liquefaction screening criteria, popularly known as Chinese Criteria.
Despite these findings by Wang [1], liquefaction of silty and clayey soils containing much higher fines content was observed during various subsequent earthquake events. Following 1994 Chichi earthquake, the 1994 Northridge earthquake, 1999 Kocaeli earthquake, etc. many cases of liquefaction of silty and clayey soils, having significant amount of fines, were identified. It does not conform to the classical wisdom that liquefaction is the singular phenomenon manifested by sand. Bray et al. [2] conducted comprehensive geotechnical investigations of liquefied sites after the 1999 Kocaeli earthquake, which included cone penetration tests (CPT), standard penetration tests (SPT), and soil index tests. It was found that most of the structures that had suffered liquefaction induced damages were built on shallow low plastic silts, which would have been deemed non-liquefiable by the Chinese criteria. It was concluded that the fraction of clay sized particles is not a reliable liquefaction screening criterion but low liquid limit and high water content are generally good indicators of liquefiable strata during an earthquake.
Although large number of laboratory studies have been reported on the liquefaction potential of silty sands, their conclusions appear to be mutually contradictory. According to some studies, the presence of fines increases the liquefaction potential of sands [[3], [4], [5]], while others suggest that the presence of fines increases the liquefaction resistance [6]. In cyclic triaxial tests on mixtures of silica sand and non-plastic silt, Papadopoulou and Tika [7] concluded that at the same void ratio, cyclic resistance ratio (CRR) decreases with increasing fines content up to threshold fines content, whereas, at the constant intergranular void ratio, the cyclic resistance ratio increases with addition of fines up to threshold fines content. Monkul and Yamamuro [8], on the other hand, suggested that the effect of fines on the liquefaction potential of silty sand depends on the ratio of mean grain diameter of the host sand to that of the fines. It is worth noting that the classical density indices used for comparison of liquefaction potential, such as void ratio and relative density, are indifferent to grain characteristics of the mixture. Furthermore, Kim et al. [9] found that the liquefaction resistance of loose sand-clay mixtures, which were prepared at low compaction energy, increases with the addition of clay, whereas for dense mixtures, which were prepared at high compaction energy, it decreases with the addition of fines. However, a unique relation between cyclic resistance ratio and the equivalent granular void ratio was obtained. Yang et al. [10] concluded that different conclusions may be drawn if different density indexes were used for evaluating the cyclic response of silty sand.
One of the things that were evident since the early studies on liquefaction potential was the fact that the liquefaction potential of sand is inversely correlated with its density. As early as 1930's, Casagrande [11] observed that the tendency of soil to contract during shearing and thereby the generation of EPWP is related to its density, which formed the foundation of liquefaction research in subsequent studies. Based on cyclic loading tests on Sacramento River sand, Seed and Idriss [12] concluded that the number of loading cycles required to trigger liquefaction is directly proportional to the relative density of sand and proposed an empirical relationship between cyclic shear stress required to trigger liquefaction at 10 cycles of loading and the initial density of sand. Seed and Idriss [13] extended this methodology and proposed a framework for evaluating liquefaction potential of sand using SPT tests considering the relationship between relative density and SPT value. Since this seminal work, several adjustments or improvements have been made to the original simplified procedure in light of newer findings [[14], [15], [16]]. However, the basic approach for developing liquefaction potential evaluation procedures has not been changed: (a) performing SPT or CPT tests on sites, (b) calculating the cyclic shear stress experienced during the earthquake, and (c) plotting SPT blow count or cone tip resistance against earthquake induced cyclic shear stress for both liquefied and non-liquefied sites. This results in a boundary curve separating liquefiable and non-liquefiable sites, based on the type of field test. However, the limitation of this approach is that the database contains more liquefiable sites than non-liquefiable sites since liquefiable sites tend to get more interests and attentions. Furthermore, the supposition that relative density is the indicator of liquefaction potential lies at the heart of all these approaches but using relative density for studying the effect of fines on liquefaction resistance of silty sand has been found to give contradictory results in several studies. For example, at the same relative density, Carraro et al. [17] found that the cyclic resistance of silty sand first increases with the addition of fines and then starts to decrease, whereas, Singh [4] found that the cyclic resistance of silty sand first decreases with the addition of fines.
Recent studies show that inter-grain contact indices are suitable for unifying the mechanical behaviour of sand-silt mixtures. Although the critical state line in e-p' is highly dependent on the fines content, several studies have revealed that a unique critical state line was obtained for a given host sand and fine mixture in terms of various inter-grain contact indices [18,19]. Yin et al. [20] successfully modelled the evolution of minimum and maximum void ratios of various sand-silt mixtures with fines content in terms of inter-grain and inter-fine void ratios. Rahman et al. [21] showed that a unique relationship between equivalent granular void ratio and shear modulus parameter of a sand-silt mixture can be established. Thus, a wide range of mechanical responses of sand-silt mixtures can be unified using a micro-mechanical approach. Therefore, it can be argued that the liquefaction potential of silty sands can, in principle, be explained better in terms of micro-mechanical interaction of grains and is pertinent to look beyond the usual void ratio-based approach.
Based on the mechanisms responsible for liquefaction induced settlements of a structure, total settlement can be broken down into volumetric induced, shear induced, and ejecta induced settlements [22]. The shear induced settlement primarily occurs during the strong motion due to soil-structure-interaction induced ratcheting effects and bearing capacity failure. The ejecta induced settlement entails mechanisms that physically transport materials supporting the structure to the ground surface. Similarly, the volumetric induced settlement refers to consolidation and sedimentation induced settlement, which predominantly occurs after strong motion. The current state-of-art procedures for estimating liquefaction induced building settlement were developed to predict the post liquefaction 1-D consolidation settlement of free field. These semi-empirical procedures cannot estimate settlement due to other mechanisms that are primarily responsible for structural settlement due to liquefaction. Furthermore, during various earthquakes in urban settings, liquefaction has been found to be more severe under a structure, indicated by the presence of sediment ejecta around them but not away from them [2,23].
Numerical nonlinear dynamic effective stress analyses using properly calibrated constitutive models have shown promising results in capturing the dynamic responses of sand [[24], [25], [26]] and replicating settlements of structures observed in field case histories and experiments [27,28]. For example, Luque and Bray [29] successfully back-analyzed the settlement of structures during the 2011 Canterbury earthquake sequences in Christchurch. Therefore, there is high degree of confidence in ability of properly calibrated constitutive models to capture shear and consolidation induced settlement during liquefaction. They provide a unique opportunity to study the effects of a wide range of parameters on the liquefaction potential of sands and the performance of structures built on liquefiable soils, which may not be feasible to be investigated in experimental setup or from case histories.
This study explores the data published in literature regarding liquefaction potential of silty sands. The contradictory results reported by different authors are discussed and the results are re-evaluated in terms of different parameters for characterizing the liquefaction potential. Numerical studies with an advanced constitutive model for modelling cyclic behaviour of sands are conducted and the model parameters are calibrated. A correlation between equivalent granular void ratio and cyclic liquefaction resistance is proposed. Furthermore, nonlinear dynamic effective stress analysis is conducted to simulate a centrifuge experiment, and the seismic induced settlement is investigated and compared with the measurement.
Section snippets
Micro-mechanical characterization of cyclic resistance of silty sand
The micro-structure of granular mixtures can be constituted in various ways. Depending on the amount of fines present in the mixture, different packing arrangements are possible and correspondingly, different mechanical responses are manifested. Assuming that the constituents of a mixture are uniformly distributed, three types of micro-structures are possible: (i) finer particles are confined within the gaps between coarser particles, (ii) finer particles come between coarser particles at
Constitutive model for simulating cyclic behaviors of sand
An advanced constitutive model proposed by Wang et al. [25], which is based on bounding surface plasticity, is adopted to simulate the undrained cyclic behaviours and predict the post liquefaction shear deformation of sand. The critical state surface fc(σ), bounding surface fm(σ) and dilatancy surface fd(σ) are defined as:where M is the critical state stress ratio, Md is the stress ratio at which reversible dilatancy changes sign from negative
Numerical study on the liquefaction resistance of sand-fine mixtures
The above constitutive model has been implemented in an open-source finite element modelling framework called OpenSees as CycliqCPSP material and it can be used to numerically investigate the liquefaction resistance of two sand-fine mixtures. First, the model is calibrated using cyclic triaxial test results of Toyoura sand-crushed silica (TSS) from Schmidt [39] and Fujian sand-Shanghai clay (FSS) mixtures from Hu [40]. The host sands are Toyoura sand and Fujian sand, both being quartz sand with
Overview of centrifuge testing
Four centrifuge shake table tests were carried out at Tongji University to gain insight into liquefaction induced settlement in silty sand by Wu [43]. The tests were conducted on the 150 g-tonne centrifuge at a centrifugal acceleration of 50 g. The model was subjected to 26 cycles of sinusoidal wave at a frequency of 100 Hz and amplitude of 15 g. This corresponds to a peak acceleration of 0.3 g and a frequency of 2 Hz in prototype scale. The soils tested were mixtures of Fujian sand and
Conclusion and discussions
In this study, OpenSees was adopted to simulate the dynamic responses of silty sands using an advanced constitutive model with calibrated model parameters. A series of parametric studies were conducted to numerically investigate the effects of plastic and non-plastic fines on the liquefaction potential of silty sands. Nonlinear dynamic effective stress analysis was also conducted to simulate the centrifuge shaking table tests on FSS. The surface settlement and excess pore water pressure time
CRediT authorship contribution statement
Ashish Bastola: Simulation, Writing – original draft, preparation. Xiaoqiang Gu: Conceptualization, Methodology, Funding acquisition, Supervision, Writing – review & editing. Kangle Zuo: Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The work presented in this paper is supported by the National Natural Science Foundation of China (Grant nos. 41772283 and 51822809) and the Fundamental Research Funds for the Central Universities. These supports are gratefully acknowledged.
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