Critical Cyclic Stress Ratio Research Articles

Resilient strain and stiffness degradation of Yellow River silt under cyclic loads

The use of natural river silt treated as a ‘waste material’ has become the focus of research in the Yellow River flooded area, especially in the field of highway engineering. It is therefore of great significance to study the deformation and stiffness degradation of Yellow River silt (YRS) under long-term cyclic loads. To this end, a series of undrained cyclic triaxial tests on YRS for a large number of cycles (10 000) was carried out using a triaxial apparatus and the effects of confining pressure and cyclic stress ratio on the resilient strain of the YRS were explored. The critical cyclic stress and the critical cyclic stress ratio between the plastic shakedown state and incremental collapse state of the YRS were determined, and the modulus-softening behaviour of the YRS was assessed. The results of this study not only provide theoretical support for the long-term engineering performance of YRS, but also provide theoretical guidance for the cyclic response of all similar types of subgrade soils.

Critical Dynamic Stress and Cumulative Plastic Deformation of Calcareous Sand Filler Based on Shakedown Theory

Calcareous sand is a special marine soil rich in calcium carbonate minerals, characterized by brittle particles. It is, therefore, widely used as a filling material in the construction of islands and reefs. In this study, a series of cyclic tri-axial tests were conducted on calcareous sand taken from a reef in the South China Sea under different confining pressures and cyclic stress ratio (CSR). Then, applying the shakedown theory, the cumulative deformation of calcareous sand under a long-term cyclic load of aircraft was evaluated. Results showed that with the increase in the effective confining pressure, the stress–strain curves of calcareous sand showed a change from the strain-softening to the strain-hardening state; the volumetric strain of calcareous sand showed a change from shear shrinkage and then shear expansion to continuous shear shrinkage. Calcareous sand showed three different response behaviors under cyclic load: plastic shakedown, plastic creep and incremental plastic failure. With the plastic strain rate as the defining index, this study determined the critical CSR of calcareous sand under different shakedown response statuses and found them to increase with the effective confining pressure. The empirical formula for critical stress was established based on the fitting analysis of critical CSR under different confining pressures, taking the confining pressure as the variable. At the early stage of the cyclic load, calcareous sand samples were under compression. When the resilient modulus grew rapidly and the number of loading cycles continued to increase, the particles of calcareous sand samples were crushed, causing the fine particles to fill the voids among coarse particles, further compacting the samples and increasing the resilient modulus of calcareous sand samples. Hardin’s breakage potential model was adopted to quantitatively describe the particle breakage of calcareous sand samples before and after tests. The results indicated that calcareous sand samples produced obvious particle breakage when the CSR was small. As the CSR increased, the extent of the breakage of the sample particles first increased and thereafter stabilized. This study provides a theoretical reference for the assessment of the dynamic stability of calcareous sand subgrade subjected to traffic loads.

Spatiotemporal evolution of excess pore pressures in a silty seabed under progressive waves during residual liquefaction

Both transient and residual pore pressure responses are induced as ocean waves propagate over a silty seabed. In this study, the spatiotemporal evolution of excess pore pressure in a silty seabed under progressive waves was physically modelled in a large wave flume. Three typical stages were identified in the process of residual liquefaction via flume observations, including quasi-elastic, intensive build-up of residual pore pressure, and continuous liquefaction stages. During the initial quasi-elastic stage before the liquefaction of the silt bed, the transient pore pressure can be well predicted by the analytical solution based on poro-elastic theory. After that, the residual pore pressure builds up intensively to its maximum value, even in the case that the transient pore pressure is nearly negligible at deep soil layer. Once the residual liquefaction occurs, the poro-elastic theory becomes invalid for describing the pore pressure response. The residual liquefaction is not simultaneously induced within the entire bed, but gradually progresses downward from the shallow layer of the silt bed to deeper. The pore pressure amplitude is significantly amplified after the silt liquefies, while no amplitude-amplification was observed within the un-liquefied silt. An amplification ratio (ζ) is proposed to characterize the amplification effect and distinguish the onset of residual liquefaction. The value of ζ during the continuous liquefaction stage is found to be one order of magnitude larger than that in the quasi-elastic stage. Comparisons with the existing centrifuge tests further indicate that the critical cyclic stress ratio for the silt bed is much smaller than that for the sand bed, implying the silt bed is more prone to residual liquefaction.

Long-term deformation and damage analysis of marine clay around seawalls under coupled dynamic-seepage loading

The long-term deformation characteristics and damage degree of soft marine-deposited clay must be evaluated to safely design seawalls. According to abundant field evidence, soft marine-deposited clay tends to experience coupled dynamic loading and seepage loading. Determining the critical load and damage index for these complex loading conditions is imperative. With Tianjin marine-deposited clay as an example, we employed an improved cyclic triaxial instrument to analyse the cumulative plastic strain, water discharge and stress–strain relationship of the clay to understand its long-term deformation development. Based on shakedown theory, the critical cyclic stress ratio (CSR) was determined. A multi-factor damage variable method was proposed to evaluate the damage degree. Its comparison with a traditional mono-factor damage variable method illustrated that this method is effective for damage analyses of marine clay around seawalls under coupled dynamic-seepage loading.

Dynamic Characteristics of Saturated Soft Clay under Constant Confining Pressure Cyclic Loading

The research on the dynamic characteristics of soft clay under cyclic loading has high value. This paper takes Ningbo saturated soft clay as the research object and uses the GCTS true triaxial test system to analyze the effects of consolidated confining pressure and cyclic deviator stress on the axial cumulative strain. The experimental results found that when the number of vibrations and the cyclic stress ratio are the same, the axial cumulative plastic strain increases with the increase of the consolidation confining pressure. When the dynamic stress amplitude is the same, the axial cumulative strain decreases with the increase of the consolidation confining pressure. Under different confining pressures, as the number of vibrations increases, the cumulative axial strain increases. The development law of axial cumulative strain under different cyclic stress ratios is inconsistent, and there is a critical cyclic stress ratio. The experimental results provide a certain reference for engineering seismic design.

Long-term behaviour and degradation of calcareous sand under cyclic loading

Calcareous sand has been used as the main filling material in numerous reef constructions. Therefore, understanding its long-term dynamic engineering geological characteristics under cyclic applications of traffic or wave loading is crucial to the design and prediction of the serviceability of reef infrastructures. Considering this, seven monotonic triaxial tests and 33 high-cycle (25,000 cycles) drained triaxial tests were conducted on calcareous sand with various mean effective stresses (p’) and cyclic stress ratios (ζ). The results show that the development of the accumulated axial strain (ε1acc) has a strong correlation with the positional relationship between the cyclic stress path and critical strength line (CSL) or static strength envelope (SSE) in the p’-q plane. The critical cyclic stress ratio ζc, that represents the cyclic stress path reaching the CSL, is proposed. When ζ>ζc, the growth rate of ε1acc with ζ increases drastically. Moreover, when the cyclic stress path approaches the SSE, ε1acc enters an incremental collapse state. The increase in p’ diminishes the dilatancy of the volumetric strain εv. However, this response of εv reverses from decreasing to increasing with increasing ζ. The resilient modulus (Mr) increases with the number of cycles (N) due to the initial densification. If εv dilation occurs, Mr will decrease with N as particles lose contact. A single parameter for the cyclic stress path ratio (ψ) considering the effects of p’, ζ, and SSE is proposed. Additionally, empirical formulas for calculating the ultimate ε1acc and Mr are established. Furthermore, particle degradation significantly worsens ε1acc and εv, but has a more profound effect on the compressibility of εv. This degradation is also detrimental to Mr. A certain deviation trend of the predicted values from the measured values is found to correspond with the relative particle breakage.

Laboratory study on subgrade fluidization under undrained cyclic triaxial loading

A long-term issue that has hampered the efficient operation of heavy-haul tracks is the migration of fluidized fines from the shallow soft subgrade to the overlying ballast, i.e., mud pumping. This paper presents a series of undrained cyclic triaxial tests where realistic cyclic loading conditions were simulated at low confining pressure that is typical of shallow subgrade beneath a ballast track. Subgrade soil specimens with a low-plasticity index collected from a field site with recent history of mud pumping were tested at frequencies from 1.0 to 5.0 Hz and a cyclic stress ratio (CSR) from 0.1 to 1.0. The experimental results indicate that under adverse loading conditions of critical cyclic stress ratio (CSRc) and frequency, there is upward migration of moisture and the finest particles towards the specimen top and this causes the uppermost part of the soil specimen to soften and fluidize. Conversely, a smaller value of CSR tends to maintain stability of the specimen despite the increasing number of loading cycles. It is noteworthy that for any given combination of CSR and frequency, the relative compaction has a significant influence on the cyclic behaviour of the soil and its potential for fluidization.

Post-liquefaction pore pressure dissipation in sand under cyclic stress triaxial testing

Soil liquefaction has conventionally been studied as a pure undrained condition subject to cyclic shearing in the laboratory. However, in the field, ground settlement and expulsion of pore water in the form of sand boils are frequently observed, which conventional triaxial and simple shear apparatus are unable to replicate. In this study, a novel insight of coupled pore pressure generation and dissipation in liquefiable clean sand is discussed with the use of a modified cyclic triaxial testing set-up. Stress-controlled cyclic triaxial tests with controlled pore water drainage far lower than the soil's permeability were carried out to investigate ‘near-perfect undrained’ conditions, which are more representative of field conditions. Comparison of results from three sets of stress-controlled cyclic triaxial testing were carried out: (a) conventional shearing under an undrained condition; (b) shearing under controlled drainage; and (c) undrained shearing until liquefaction, and thereafter continual shearing under controlled drainage. The critical cyclic shear stress ratio where excess pore pressure dissipation dominates excess pore pressure generation is identified from the coupled cyclic shear loading and pore water drainage tests. In addition, this study also noted a critical void ratio where the soil is no longer susceptible to liquefaction even under considerable shearing amplitudes. These findings may offer guidance on the tolerable cyclic shear stress and minimum degree of densification to avoid occurrence of soil liquefaction in the field.

Empirical Method for Evaluating Resilient Modulus of Saturated Silty Clay under Cyclic Loading

Resilient modulus of soil is crucial for the design of a structure on a foundation subjected to a cyclic loading (e.g., traffic load or machine vibration load). This paper conducted a series of dynamic triaxial tests of saturated silty clay, considering the influence of the factors of cyclic stress ratio (CSR), static deviatoric stress ratio (SDR), and overconsolidation ratio (OCR) on the resilient modulus and dynamic damping ratio of the soil. A cyclic loading with a form of half sine wave was used to model the traffic loading. The results showed that the soil was prone to failure under a higher SDR, even though the applied CSR was less than the critical CSR. The saturated silty clay performed a strain softening behavior and its dynamic properties deteriorated significantly when higher CSR and SDR and lower OCR were involved. Based on the test results, an empirical method with a form of exponential function was proposed to evaluate the resilient modulus of the soil, considering the combined effects of CSR and SDR and OCR. The proposed method was verified through a comparison with the test results in this study and from literatures, and some recommendations for its application were offered.

Experimental Study on Unconfined Compressive and Cyclic Behaviors of Mucky Silty Clay with Different Clay Contents

In this study, the unconfined compressive and cyclic behaviors of saturated mucky silty clay from the reclamation area of Dalian, which has two different clay contents, are investigated using the static and dynamic triaxial test systems. The influence of clay content on the residual strain and residual pore water pressure of undisturbed and reconstituted specimens are discussed. A scanning electron microscope (SEM) is used to observe the microstructures of the specimens. The unconfined compressive test results of the specimen with low clay content exhibits “collapse” characteristics. However, the corresponding specimen with high clay content exhibits a “sustained hardening” trend. The dynamic test results indicate that the residual pore water pressure, residual strain, and difference in the residual strain between the undisturbed and reconstituted specimens increase as the load increases. The ratio of the reconstituted residual strain to the undisturbed residual strain increases as the load increases, and this ratio is larger than the sensitivity of the soil. The residual strain of the specimen with high clay content exceeds the corresponding value of the specimen with low clay content. The stiffness degradation of the high clay content specimen is more obvious than that of the low clay content specimen. A power function-based residual strain model that contains the cyclic stress ratio (CSR) and number of cycles (N) is proposed. This model can be used to describe the residual strain with a CSR less than the critical CSR.

Dynamic behaviour of weathered red mudstone in Sichuan (China) under triaxial cyclic loading

The construction of a high-speed railway (HSR) in Southwest China is being hindered by a severe shortage of high-quality subgrade materials. However, red mudstone is widely distributed in the Sichuan Basin of China. The ability to use weathered red mudstone (WRM) to fill subgrade beds by controlling its critical stress and cumulative strain would enable substantial savings in project investments and mitigate damage to the ecological environment. To better understand the dynamic behaviour of WRM, both monotonic and cyclic triaxial tests were performed. The evolution of the cumulative strain vs. increased loading cycles was measured. The influences of confining pressure and loading cycles on the dynamic modulus, damping ratio, critical cyclic stress ratio (CSR), and dynamic stress level (DSL) were investigated. The relationship between the CSR and loading cycles under different failure strain criteria (0.1%-1.0%) was analysed. The prediction model of cumulative strain was also evaluated. The results indicated that the shear strength of WRM sufficiently meets the static strength requirements of subgrade. The critical dynamic stress of WRM can thus satisfy the dynamic stress-bearing requirement of the HSR subgrade. The critical CSR decreases and displays a power function with increasing confining pressure. As the confining pressure increases, the DSL remains relatively stable, ranging between 0.153 and 0.163. Furthermore, the relationship between the dynamic strength and loading cycles required to cause failure was established. Finally, a newly developed model for determining cumulative strain was established. A prediction exercise showed that the model is in good agreement with the experimental data.

Practical model of deformation prediction in soft clay after artificial ground freezing under subway low-level cyclic loading

Settlement was investigated after the long-term operation of a subway system, particularly at segments where the artificial ground freezing (AGF) method was applied in the soft clay area. In this paper, five group soil samples under different freezing temperatures (−5 °C, −10 °C, −15 °C, −20 °C, and −30 °C, respectively) were prepared to simulate different locations perpendicular to freeze tubes during one AGF circulation. Including one group of undisturbed soils, cyclic tri-axial tests were conducted on all samples, and the dynamic strains were measured and analyzed. The results show that the residual cumulative plastic strain of soft clay after artificial freeze-thaw under subway low-level repeated cyclic loading behaves quite differently from the typical Monismith’s power function development. A hyperbolic model of cumulative plastic strain of soft clay after artificial freeze-thaw is established and the relevant model parameters has been discussed for practical prediction. A critical cyclic stress ratio (CSR) of soft soil can be empirically calculated out by this practical model, only based on soil stress and soil physical state parameters without numerous cyclic tri-axial tests. All the results could provide significant reference for the safe control and environmental protection during AGF construction and subsequent subway operation.

Effects of frequency and cyclic stress ratio on creep behavior of clay under cyclic loading

ABSTRACTThe mechanical behavior of clay subjected to cyclic loading is important to consider in the design of the foundations of many types of structures that must resist cyclic loading, such as subgrades and offshore foundations, because clay undergoes greater settlement under cyclic loading than under static loading. The difference in settlement between these two loading patterns due to creep behavior is affected by the cyclic frequency and the cyclic stress ratio. This study investigated the effects of the frequency and cyclic stress ratio of cyclic loading on the creep behavior of a natural clay in China using stress-controlled triaxial tests. The assessed the following parameters: three frequencies, four cyclic stress ratios, and six vertical stresses. The test results indicate that the soft clay displays accelerated creep behavior under dynamic loads. A specific “limit frequency” (in this case, 0.2 Hz) and a “safe load” at which the strain of the soft clay increases very slowly were observed. The effect of the effective axial stress on the creep behavior increases with the increase in the cyclic stress ratio. Based on the tests, the critical cyclic stress ratio is 0.267 at a certain effective axial stress and frequency.

Determination of traffic-load-influenced depths in clayey subsoil based on the shakedown concept

The determination of the depth of traffic load influence is significant for pavement and embankment design on soft soil. In this study, a method based on strain-controlled criteria is presented to estimate the depths within which the behavior of a saturated clayey subsoil is affected by cyclic traffic loads. Based on the shakedown concept, the following depths of influence can be defined: (1) the threshold depth, beyond which the dynamic effect of the traffic loads is insignificant; (2) the plastic shakedown limit depth, within which the subsoil experiences noticeable and continuous deformation; and (3) the critical failure depth, within which the soil fails due to the accumulation of strain. This method for determining the depths of influence is advantageous because it is applicable to various soil types. The data required for this method consist of vertical stress responses along the soil profile and three cyclic stress limits of the soil. Based on the development of pore pressure and the dynamic strain behaviors during undrained cyclic triaxial tests, the following cyclic stress limits of the soft clay subsoil are determined: a threshold cyclic stress ratio CSRt of 0.03, a plastic shakedown limit stress ratio CSRp of 0.33 and a critical cyclic stress ratio CSRc of 0.44. These cyclic stress limits are used to determine the corresponding depths of influence, which are then used to implement ground improvements and strengthen the dynamic carrying capacity of the road structures.

Assessment of Liquefaction Potential of Guwahati City: A Case Study

The liquefaction potential of saturated cohesionless deposits in Guwahati city, Assam, was evaluated. The critical cyclic stress ratio required to cause liquefaction and the cyclic stress ratio induced by an earthquake were obtained using the simplified empirical method developed by Seed and Idriss (J soil Mech Found Eng ASCE 97(SM9):1249–1273, 1971, Ground motions and soil liquefaction during earthquakes. Earthquake Engineering Research Institute, Berkeley, CA, 1982) and Seed et al. (J Geotech Eng ASCE 109(3):458–483, 1983, J Geotech Eng ASCE 111(12):1425–1445, 1985) and the Idriss and Boulanger (2004) method. Critical cyclic stress ratio was based on the empirical relationship between standard penetration resistance and cyclic stress ratio. The liquefaction potential was evaluated by determining factor of safety against liquefaction with depth for areas in the city. A soil database from 200 boreholes covering an area of 262 km2 was used for the purpose. A design peak ground acceleration of 0.36 g was used since Guwahati falls in zone V according to the seismic zoning map of India. The results show that 48 sites in Guwahati are vulnerable to liquefaction according to the Seed and Idriss method and 49 sites are vulnerable to liquefaction according to the Idriss and Boulanger method. Results are presented as maps showing zones of levels of risk of liquefaction.

Study of Variation of Soil Stress State Based on the Curve of Normalized Strain- Pore Water Pressure

The cyclic behavior of normally consolidated silty clays was investigated by conducting a series of cyclic simple shear tests on one-dimensionally and isotropically consolidated reconstituted samples. The critical cyclic stress ratio was obtained by the normalized axial strain. Based on hysteretic curve of pore water pressure versus strain, dynamic characteristics of silty clay were investigated. The results showed that with increasing of cyclic loading, soil stress state can be divided into steady state, critical state and failure state based on the critical cyclic stress ratio. The hysteresis curve of pore water pressure versus strain was divided into two parts by cross point A. Compared with two parts, the variation law was obtained. When the upper part area was bigger than the lower part area, pore water pressure and axial strain continuously increase with cycle number; when the upper part area was smaller than the lower part area, pore water pressure and axial strain tended to be steady with cycle number.

Critical Cyclic Stress Ratio of Reconstituted Silty Clay under the Cyclic Loading

Critical Cyclic Stress Ratio of Reconstituted Silty Clay under the Cyclic Loading

Effects of Vibration Frequency on Dynamic Properties of Undisturbed Structural Marine Soil

Due to influence by many factors like soil classification, viscosity property and vibration frequency, there is no common view yet about the effect of frequency on dynamic pore pressure and characteristics. In order to study the development of pore pressure, strain and dynamic strength of Hangzhou Bay undisturbed structural silty clay under different vibration frequencies, cyclic triaxial tests were performed. The test results indicate that the frequency has little influence on pore pressure and strain when they didn’t reach the threshold values, but once they exceeded the threshold values the frequency will has strong influence. There is critical cyclic stress ratio when the cyclic stress ratio has not reached that value, the frequency has no influence on dynamic strength. For the given cycles, the higher the frequency is, the bigger the dynamic strength is. And with the increment of frequency, the influence on dynamic is decreased eventually.

Analysis of wave-induced liquefaction in seabed deposits of silt

The dynamic stress introduced in half elastic space by wave loading is characterized by the equation between the magnitude of half cyclic axial stress and cyclic torsion shear stress and the principal stress, whose direction rotates continuously and compression stress on seabed can be calculated by the use of small amplitude wave theory. With relationship curves of saturated silt of liquefaction cycles and cyclic stress ratios obtained by cyclic triaxial-torsional coupling shear tests and curve fitting method to different data points of relative density, it is suggested that the cyclic stress ratio corresponding to constant liquefaction impedance be taken as the critical cyclic stress ratio which implies liquefaction. There exists a linear relationship between critical cyclic stress ratio and relative density under different relative densities. Empirical formula for critical cyclic stress ratios of seabed liquefaction induced by wave loading under different relative densities is established. The possibility of seabed silt liquefaction and its influence factors are analyzed based on the small-amplitude wave theory and the data acquired in laboratory tests.

Critical cyclic stress ratio of undisturbed saturated soft clay in the yangtze estuary under complex stress conditions

There exists a critical cyclic stress ratio when sand or clay is subjected to cyclic loading. It is an index distinguishing stable state or failure state. The soil static and dynamic universal triaxial and torsional shear apparatus developed by Dalian University of Technology in China was employed to perform different types of tests on saturated soft marine clay in the Yangtze estuary. Undisturbed samples were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consolidation parameters. The effects of initial orientation angle of major principal stress, initial ratio of deviatoric stress, initial coefficient of intermediate principal stress and stress mode of cyclic shear on the critical cyclic stress ratio were investigated. It is found that the critical cyclic stress ratio decreases significantly with increasing initial orientation angle of major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientation angle of major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate principal stress is less evident. Under the same consolidation condition, the critical cyclic stress ratio from the cyclic coupling shear test is lower than that from the cyclic torsional shear test, indicating that the stress mode of cyclic shear has an obvious effect on the critical cyclic stress ratio. The main reason is that the continuous rotation in principal stress directions during cyclic coupling shear damages the original structure of soil more than the cyclic torsional shear does.