Stress-strain transformations and liquefaction of sands

Presented in this paper are the results of the laboratory tests of sands performed for the purpose of defining the characteristics of the dynamic shear stress-shear strain relationships. For this purpose, the transformation of the initial stress-strain characteristics of undrained saturated sands was investigated separately. These transformations take place under conditions of an increase in pore pressure under the effect of sufficiently intensive dynamic excitations. The process of occurrence and development of liquefaction was investigated simultaneously. The obtained results show that the transformation of the stress-strain relationships leads to intensive reduction in the initial dynamic characteristics of sands. At the moment of occurrence of initial liquefaction, for the selected strain, shear moduli are considerably reduced in respect to their initial values. These parameters tend to be further reduced in the phase of post-initial liquefaction. It is concluded that the process of liquefaction of sands can be completely defined through the transformation of the stress-strain relationships.     

An experimental study of the liquefaction strength of silty sands in terms of the state parameter

An elaborate program of monotonic and cyclic triaxial laboratory tests on mixtures of sand and silt with fines content 0%, 15% and 25% was performed to investigate the effect of density, consolidation stress and non-plastic fines on the liquefaction strength. The monotonic tests illustrated that the critical state lines of all mixtures do not cross each other, and are, approximately, parallel to each other. The results of the cyclic tests illustrated that the relationship between the cyclic strength and the state parameter does not depend on the consolidation stress, the soil density and the silt content. Analysis in terms of the state parameter showed that: (i) as the consolidation stress increases, the cyclic strength decreases and this effect is more pronounced as the specimens become denser, especially as the fines content increases and (ii) the cyclic strength decreases as the fines content increases and this effect is more pronounced as the specimens become denser.     

Energy dissipation and seismic liquefaction in sands

A statistical representation of seismic liquefaction is advanced based on the postulate that pore water pressure increases are proportional to the dissipated seismic energy density. The representation, based on approximately fifty case histories, relates the pore pressure increase to earthquake magnitude, distance to centre of energy release, initial effective overburden stressand standard penetration value. The model may be used for analysis ofseismic liquefaction risk. An example analysis for the ‘South of Market Zone’ in San Francisco is carried out in relation to earthquakes on the San Andreas fault.     

Predicting seismic liquefaction potential of sands by optimum seeking method

The feasibility of using the optimum seeking method to assess the seismic liquefaction potential of sands has been investigated. Optimization theory is a very important branch of applied mathematics and has a wide application in the practical world. Using the available field sand liquefaction data, the influence of various factors is quantified using the optimum seeking method. The factors considered are: the earthquake magnitude M, the distance of the site from the source of the earthquake L, the depth of the water table D_w, the depth of the sand deposit D_s, and the standard penetration test (SPT) blow count N. The most important factors have been identified as the earthquake magnitude and the SPT blow count. Prediction results show that the proposed method is effective and feasible. Since neither normalization of the SPT blow count nor calculation of the seismic shear-stress ratio are required, the proposed method is simpler and more direct than the conventional methods of evaluating liquefaction potential.     

Investigation of liquefaction and pore water pressure development in layered sands

This paper presents the results of shaking table model tests which were carried out to investigate the pore water pressure generation and related liquefaction mechanism in layered sand deposits. The experiments were performed on uniform sand columns, silt interlayered sand columns and two layered sand columns deposited at various relative densities and subjected to different input excitations. During the experiments excess pore water pressures were measured by pore pressure transducers installed at three different depths and, surface settlements and thickness of water film developed under less permeable inclusions were measured by a digital camera. The experimental results are discussed and compared to demonstrate the effects of relative density, input acceleration and presence of a silt seam on the generation of excess pore water pressure in sand deposits subjected to dynamic loading. The results showed that the presence of a less permeable silt interlayer within the sand deposit and existence of a loose sand layer underlying dense sand deposits can have significant effect on the pore water pressure generation mechanism.     

A critical state interpretation for the cyclic liquefaction resistance of silty sands

Contrary to many laboratory investigations, common empirical correlations from in situ tests consider that the increase in the percentage of fines leads to an increase of the cyclic liquefaction resistance of sands. This paper draws upon the integrated Critical State Soil Mechanics framework in order to study this seemingly not univocal effect. Firstly the effect of fines on the Critical State Line (CSL) is studied through a statistical analysis of a large data set of published monotonic triaxial tests. The results show that increasing the content of non-plastic fines practically leads to a clockwise rotation of the CSL in (e–ln p) space. The implication of this effect on cyclic liquefaction resistance is subsequently evaluated with the aid of a properly calibrated critical state elasto-plastic constitutive model, as well as a large number of published experimental results and in situ empirical correlations. Both sets of data show clearly that a fines content, less than about 30% by weight, may prove beneficial at relatively small effective stresses (p₀<50–70 kPa), such as the in situ stresses prevailing in most liquefaction case studies, and detrimental at larger confining stresses, i.e. the stresses usually considered in laboratory tests. To the extent of these findings, a correction factor is proposed for the practical evaluation of liquefaction resistance in terms of the fines content and the mean effective confining stress.     

Requirements for soil-specific correlation between shear wave velocity and liquefaction resistance of sands

The application of the simplified method for evaluating the liquefaction potential based on shear wave velocity measurements has increased substantially due to its advantages, especially for microzonation of liquefaction potential. In the simplified method, a curve is proposed to correlate the cyclic resistance ratio (CRR) with overburden stress-corrected shear wave velocity (V_s1). However, the uniqueness of this curve for all types of soils is questionable. The objective of this research is to study whether the correlation between CRR and V_s1 is unique or not. Besides, the necessity of developing the soil-specific correlations is also investigated. Based on laboratory test data, a new semi-empirical method is proposed to establish the soil-specific CRR–V_s1 correlation. To validate the proposed method, a number of undrained cyclic triaxial tests along with bender element tests were performed on two types of sands. Similar experimental data for six other types of sands reported in the literature was also compiled. Applying the proposed method, soil-specific CRR–V_s1 correlation curves were developed for these eight types of sands. It is shown that the correlation is not unique for different types of sands and the boundary curve proposed in the available simplified method can only be used as an initial estimation of liquefaction resistance. Finally, using the results of this study as well as previous ones, a chart is suggested to be used in engineering practice showing the conditions for which a detailed soil-specific CRR–V_s1 correlation study needs to be performed.     

Residual strength after liquefaction: A rheological approach

The motion of a sphere pulled through liquefied sand of low relative density has been observed. Long triaxial specimens were prepared around a 12.7 mm-diameter sphere loaded by a wire/deadweight system. Velocities and drag forces were measured over a large range of shear strains and strain rates. Typical behavior involved a rapid drop to a non-zero minimum drag resistance followed by an increase in resistance with velocity. These results suggest that residual strength of sand after liquefaction is rate-dependent, and that the Bingham Plastic model seems a reasonable fit to the observed behavior over a large range of sliding velocities. Shear stresses calculated from the hydrodynamics of the sphere are of the same order as those inferred from field case histories.     

Influence of fines content on liquefied strength of silty sands

Critical state soil mechanics is a useful framework to understand sand behavior. In this paper, a relationship is developed for estimating undrained critical shear strength of sands based on the critical state framework. The relationship is validated by comparison with laboratory test results and sand liquefied strength from field liquefaction failure case histories. Using this relationship, the influence of fines content on undrained critical shear strength is studied for different combinations of effective stress and density. The parametric study indicates that depending on soil void ratio, effective stress, and the shape and mineralogy of the fine particles, undrained critical strength may increase, remain the same, or decrease as the amount of fines content increases. Both the susceptibility to liquefaction and the severity of strain-softening are affected by adding fines. It is suggested that the critical state parameter is inadequate for describing the behavior of liquefiable sands and sand shearing-compressibility should be taken into account in liquefaction analysis.     

Cyclic resistance and liquefaction behavior of silt and sandy silt soils

The liquefaction behavior and cyclic resistance ratio (CRR) of reconstituted samples of non-plastic silt and sandy silts with 50% and 75% silt content are examined using constant-volume cyclic and monotonic ring shear tests along with bender element shear wave velocity (V_s) measurements. Liquefaction occurred at excess pore water pressure ratios (r_u) between 0.6 and 0.7 associated with cumulative cyclic shear strains (γ) of 4% to 7%, after which cyclic liquefaction ensued with very large shear strains and excess pore water pressure ratio (r_u>0.8). The cyclic ring shear tests demonstrate that cyclic resistance ratio of silt and sandy silts decreases with increasing void ratio, or with decreasing silt content at a certain void ratio. The results also show good agreement with those from cyclic direct simple shear tests on silts and sandy silts. A unique correlation is developed for estimating CRR of silts and sandy silts (with more than 50% silt content) from stress-normalized shear wave velocity measurements (V_s1) with negligible effect of silt content. The results indicate that the existing CRR–V_s1 correlations would underestimate the liquefaction resistance of silts and sandy silt soils.     

Empirical criteria for liquefaction in sands via standard penetration tests and seismic wave energy

Five empirical equations are presented, describing initiation of liquefaction in fully saturated sands, in terms of standard penetration values and initial overburden stress on level ground. These equations are based on 90 case histories of liquefaction, and relate empirically the pore pressure increase to earthquake magnitude, epicentral distance, energy of strong motion at the site, peak ground velocity, Fourier amplitude of velocity and duration of strong motion. The results are given in terms of raw standard penetration values corrected for overburden pressure. For all the models presented, the standard deviation of the residuals, representing the differences between the observed and predicted penetration values is less than six blow counts.     

Cyclic strength and deformation of crushable carbonate sand

Cyclic triaxial tests have been carried out on a skeletal carbonate sand from the west coast of Eire. Results are presented for undrained cyclic shear tests on samples with 80% of relative density consolidated under both isotropic and anisotropic conditions. Failure was defined as a 5% double amplitude cyclic strain and a 5% peak axial strain for stress-reversal and non-reversal stress conditions, respectively. Using this definition the cyclic strength for isotropically consolidated samples was affected by the confining pressure although the angular platey nature of the sand resulted in higher cyclic strengths than for a comparable silica sand. For anisotropically consolidated samples the cyclic strength increased with increasing initial static shear stress while on the other hand the cyclic strength normalised in the usual way with respect to the initial confining pressure decreased as this pressure increased.     

Strain energy based evaluation of liquefaction and residual pore water pressure in sands using cyclic torsional shear experiments

In this study, cyclic hollow cylinder torsional tests were conducted on the reconstituted specimens of Toyoura sand in a practical range of initial density and stress states. The results were employed to evaluate the liquefaction resistance and residual pore water pressure of sand using the strain energy concept. A simple pore water pressure (PWP) model with two calibration parameters was developed for the prediction of residual pore pressure as a function of cumulative strain energy density and the capacity energy of sand. Capacity energy is defined as the cumulative strain energy that is required for liquefaction onset. Based on the results of the tests, an equation is then presented for the estimation of capacity energy in terms of relative density and initial effective confining pressure of sand. This equation is shown to work well as a state boundary curve, which can discriminate between the liquefied and non-liquefied field case histories. Several extra tests were also performed to investigate the effect of initial static shear stress on the proposed PWP model and capacity energy. The results show that initial shear stress has a minor effect on the trend of the proposed PWP model; however, it definitely affects the capacity energy. The final part of the paper aims to confirm reasonable performance of the proposed PWP model by the available observations of seismically induced pore water pressure in shaking table, centrifuge, and real site conditions.     

在二维应力状态下地震触发砂土液化动应力条件

在二维应力状态下,地震在土体中不仅产生动水平剪应力τｈｄ,而且也引起在一般情况下不可忽略的竖向与水平动正应力关「σｖｄ－σｈｄ」／２,二者定义为动偏应力之二分量,均应是评估土体或土工结构物变形及其稳定性的主要因素。本文给出了在地震动偏应力二分量共同作用下,土单元中最大往返剪切作用面及其上最大动剪应力比「τｄ／σｓ」ｍａｘ的确定方法。据此,提出了地震触发砂土液化的应力条件及液化判别准则。     

Evaluation of state indices in predicting the cyclic and monotonic strength of sands with different fines contents

State parameter, ψ, has been widely used to combine the influence of void ratio, e, and stress level, p′, on the soils behavior. Stress ratio, R_s, and modified state parameter, ψ_m, have also been proposed for the same purpose. This paper aims to evaluate and compare the different state indices in combining the effect of fines content, density and stress level for five different types of sands, by processing a large number of previously published experimental data. The use of the recently established concept of equivalent interparticle void ratio, e^⁎, in definition of the state indices is also evaluated. The results indicate that the influence of fines presence, in addition to the e and p′, on the behavior is favorably reflected by the state indices. Unique correlations were derived between the cyclic or monotonic strength and each of the state indices, independent of the fines content. The correlations, for all the different types of soils, fell into limited types of common formulations. ψ and R_s worked generally better than ψ_m, whether defined in terms of e or e^⁎. The extension of straight part of critical state line was found to be an appropriate reference line for calculating R_s used in conjunction with e or e^⁎.     

Cyclic shearing and liquefaction of soil under irregular loading: an incremental model for the dynamic earthquake-induced deformation

The paper presents a mathematical model for the deformation of soil under irregular cyclic loading in the simple-shear conditions. The model includes the possible change in the effective pressure in saturated soil due to the cyclic shearing, the reciprocal influence of the effective pressure on the response of the soil to the shear loading, and the pore pressure dissipation due to the seepage of the pore fluid. The hysteresis curves for the strain–stress relationship are constructed in such a way that they produce both the required backbone curve and the required damping ratio as functions of the strain amplitude. At the same time, the approach enables the constitutive functions involved in the model to be specified in various ways depending on the soil under study. The constitutive functions can be calibrated independently of each other from the conventional cyclic shear tests. The constitutive model is incorporated in the boundary value problem for the dynamic site response analysis of level ground. A numerical solution is presented for the dynamic deformation and liquefaction of soil at the Port Island site during the 1995 Hyogoken-Nambu earthquake.     

The timing of liquefaction and its utility in liquefaction hazard evaluation

The behavior of liquefiable soils, and of soil deposits containing liquefiable soils, can change dramatically upon triggering of liquefaction. This suggests that knowledge of the timing of liquefaction, e.g., whether it occurs early or late in a particular ground motion, would be useful in predicting the potential effects of liquefaction. The relatively recent availability of strong motion records from instruments underlain by liquefiable soils provides a new type of case history – one in which the ground motion intensity at the time of triggering can be identified. The paper reviews procedures for identification of the time of triggering, and shows how that time can be used to judge the relative performance of empirical triggering models. It also introduces a framework for the use of timing information in the development of improved procedures for evaluation of the effects of liquefaction.     

Porosity measurement of heavy oil sands

Porosity measurement is an important step for petrophysical characterization of reservoir rocks, as porosity is essential for analysing elastic properties and estimating the capacity of rocks to hold hydrocarbon resources. Commonly used porosity measurement methods fail to work on heavy oil sands, because of the loose fragile sand frame and solid-like irreducible heavy oil. We develop three methods to measure the porosity of heavy oil sands, which are feasible and affordable in most laboratories. Method 1 involves calculating the bulk volume of the sample by measuring its physical dimensions directly. Method 2 uses calibrated sample weight and volume (after removing the protecting foil cover and metal clips). Method 3 first applies pressurizing on samples and then measures the weight and volume of the bare samples. The measurement results of the three methods are then compared and method 3 is determined as the most reliable, which is also verified by the porosity log. Finally, an analysis of the potential sources of errors associated with method 3 is performed.     

Modelling cyclic elastic behaviour of sands

The cyclic stress-strain behaviour of cohesionless soils is considered to be composed of elastic and inelastic components, and the cyclic elastic stress-strain relationships for one type of uniform sand are investigated by conducting isotropic and laterally constrained compression tests under low frequency cyclic loads. The effects of relative density, stress history, and stress state on the cyclic elastic behaviour are studied. Simple and practically applicable elastic stress-strain models are developed based on Hertzian contact theory. It was observed in both types of tests that elastic strains can accurately be modelled by a power function of stresses.     

Recording-based identification of site liquefaction

Reconnaissance reports and pertinent research on seismic hazards show that liquefaction is one of the key sources of damage to geotechnical and structural engineering systems. Therefore, identifying site liquefaction conditions plays an important role in seismic hazard mitigation. One of the widely used approaches for detecting liquefaction is based on the time-frequency analysis of ground motion recordings, in which short-time Fourier transform is typically used. It is known that recordings at a site with liquefaction are the result of nonlinear responses of seismic waves propagating in the liquefied layers underneath the site. Moreover, Fourier transform is not effective in characterizing such dynamic features as time-dependent frequency of the recordings rooted in nonlinear responses. Therefore, the aforementioned approach may not be intrinsically effective in detecting liquefaction. An alternative to the Fourier-based approach is presented in this study, which proposes time-frequency analysis of earthquake ground motion recordings with the aid of the Hilbert-Huang transform （HHT）, and offers justification for the HHT in addressing the liquefaction features shown in the recordings. The paper then defines the predominant instantaneous frequency （PIF） and introduces the PiF-related motion features to identify liquefaction conditions at a given site. Analysis of 29 recorded data sets at different site conditions shows that the proposed approach is effective in detecting site liquefaction in comparison with other methods.