Cyclic Stress Ratio Research Articles

Development patterns of the dynamic elastic modulus of saturated coral sand under different drainage conditions

Long-term cyclic loading can have a significant effect on the modulus of sand, and the influence on saturated coral sand has yet to be established. In this paper, the significant influence of non-plastic fines content (FC) and relative density (Dr) on dynamic elastic modulus (E) of saturated coral sand has been evaluated by a series of cyclic triaxial drainage tests. The results show that the dynamic elastic modulus increases rapidly at the beginning of loading; then the growth slows down and finally stabilizes. In general, the development of E is influenced collectively by FC, Dr and cyclic stress ratio (CSR). The initial dynamic elastic modulus Ed-1 and steady-state dynamic elastic modulus Ed-s increase with the increase of Dr, and decrease as FC increases. The linear fitting equations are given by introducing the equivalent skeleton void ratio esk*. Furthermore, the relative dynamic elastic modulus Er is defined as the ratio of Ed-N to Ed-s, and the prediction equation for Er was developed to provide a basis for the engineering mechanical parameters of coral sands under long-term loads.

Undrained cyclic responses of sandy soils improved by soybean-induced calcium carbonate precipitation

ABSTRACT This study investigates the behaviour of sandy soils under cyclic conditions, emphasising the efficacy of soybean-induced calcium carbonate precipitation (SICP) treatment in mitigating liquefaction. Analysis of shear wave velocity and undrained cyclic responses was conducted, with a focus on understanding deformation response and development of excess pore pressure. Results revealed CaCO3 content as a definitive indicator for improvements in soil stiffness, with its distribution influenced by soil’s relative density and number of SICP injections. Enhanced cementation efficacy was observed in denser or deeper layers of sand column, attributed to prolonged SICP retention. A marked correlation between shear wave velocity and CaCO3 content highlighted SICP’s role in enhancing the liquefaction resistance of loose sandy soils. Dynamic triaxial testing showed the nuanced strain behaviours across varying relative densities and cyclic stress ratio (CSR) values, emphasising the strengthening influence of CaCO3 formations in the soil matrix. The empirical equation served as a testament to the potential of SICP in soil stabilisation endeavours. The intervention of SICP treatment presents a potent tool for bolstering soil stability, especially in regions susceptible to seismic activities. The insights garnered advocate for further research aimed at harnessing and optimising this soil improvement technique on a global scale.

A novel approach to predicting liquefaction-induced settlements using Kolmogorov–Arnold Networks (KANs)

Soil liquefaction refers to the loss of strength and bearing capacity of soil under dynamic loads. Structures built on liquefied soils experience settlement. In this study, the newly developed Kolmogorov–Arnold Networks (KAN) method, an innovative artificial neural network technique, was utilized to predict liquefaction-induced settlement. The KAN method, which extends beyond the traditional Multi-Layer Perceptron (MLP) approach, was compared with the Random Forest method for benchmarking purposes. Using data derived from laboratory and field studies, models were constructed using both methods, and their performances were analyzed. According to the results, the KAN model outperformed the RF model in terms of R2, MAE, MSE, and RMSE metrics. Additionally, the feature importance analysis on the KAN model identified cyclic stress ratio (csr) and corrected SPT blow count (n1_60) as the most significant variables. These results underscore the potential of the KAN method in enhancing predictive accuracy and reliability in geotechnical applications, paving the way for its broader acceptance and implementation in real-world scenarios.

Effect of torsional shear stress on the deformation characteristics of clay under traffic load

The soft clay under the road ground will suffer cyclic torsional shear stress encountered traffic load in addition to axial stress, which will cause further deformation of clay. To investigate the effect of torsional shear stress on the cumulative axial strain of clay, a series of undrained tests under cardioid stress path were performed on K0 consolidated undisturbed samples by using a hollow cylinder apparatus (HCA). The effect of vertical cyclic stress ratio (VCSR) and shear stress ratio (η) on the deformation and degradation characteristics of clay was investigated. The results indicate that there is inconsistency between the strain path and stress path. The increase in η further accelerates the accumulation of axial strain, which resulted from the degradation of clay induced by torsional shear stress. Considering the VCSR and η, a calculation method of degradation index was developed. Furthermore, a cumulative axial strain prediction model of clay under the cardioid stress path was established considering the degradation. This model addresses the limitation of traditional prediction models by considering the impact of torsional shear stress on cumulative axial strain.

Analysis of Liquefaction in Tailings Deposits by Fem Modeling of Undrained Cyclic Triaxial

In this article, a numerical calibration procedure for undrained cyclic triaxial tests is presented to evaluate the liquefaction potential in sand and silt samples from mining tailings in northern Chile. The numerical modeling of an axisymmetric specimen involved two stages: isotropic consolidation using the Hardening Soil Small (HSS) model and a cycling phase employing the UBC3D-PLM model to simulate the onset of liquefaction using the criterion that the excess pore pressure ratio Ru should exceed 0.8. The results demonstrate that the UBC3D-PLM modeling calibrated with experimental data from cyclic triaxial tests effectively represents the excess pore pressure in both sandy and silty soils from mining tailings. The accuracy of the modeling decreases when a single set of parameters is applied to the same soil at different cyclic stress ratios (CSR), highlighting the need for specific calibrations for each loading.

Study on Pore Water Pressure Model of EICP-Solidified Sand under Cyclic Loading

Under traffic load, earthquake load, and wave load, saturated sand foundation is prone to liquefaction, and foundation reinforcement is the key measure to improve its stability and liquefaction resistance. Traditional foundation treatment methods have many problems, such as high cost, long construction period, and environmental pollution. As a new solidification method, enzyme-induced calcium carbonate precipitation (EICP) technology has the advantages of economy, environmental protection, and durability. Through a triaxial consolidated undrained shear test under cyclic loading, the impacts of confining pressure (σ3), cementation number (Pc), cyclic stress ratio (CSR), initial dry density (ρd), and vibration frequency (f) on the development law of pore water pressure of EICP-solidified sand are analyzed and then a pore water pressure model suitable for EICP-solidified sand is established. The result shows that as σ3 and CSR increase, the rise rate of pore water pressure of solidified sand gradually accelerates, and with a lower vibration number required for liquefaction, the anti-liquefaction ability of solidified sand gradually weakens. However, as Pc, ρd, and f rise, the increase rate of pore water pressure of solidified sand gradually lowers, the vibration number required for liquefaction increases correspondingly, and its liquefaction resistance gradually increases. The test results are highly consistent with the predictive results, which show that the three-parameter unified pore water pressure model is suitable for describing the development law of A-type and B-type pore water pressure of EICP-solidified sand at the same time. The study results provide essential reference value and scientific significance in guidance for preventing sand foundations from liquefying.

Dynamic behavior of kaolin clay under bidirectional cyclic loading for suction bucket foundation

The stability of offshore wind turbine (OWT) foundations is largely influenced by the dynamic characteristics of marine clay. In offshore engineering, marine clays may exposed to bidirectional cyclic stresses. To empirically examine the influence of different cyclic stress magnitudes on the dynamic characteristics of marine clay at different depth, a sequence of dynamic triaxial tests is conducted on marine kaolin clay, encompassing diverse values of the cyclic stress ratio (CSR) and effective confining pressure (p'0). Some valuable inferences have been drawn: At low cyclic stress ratios (CSR≤0.3), the axial strain (εa), stiffness (k), and excess pore water pressure (EPWP) of the specimen exhibit logarithmic increase, logarithmic decrease, and logarithmic accumulation, respectively. Under high cyclic stress ratio conditions (CSR＞0.3), the axial strain increases linearly, the stiffness deteriorates linearly, and the logarithmic excess pore water pressure accumulates. After analyzing the dynamic characteristics data of kaolin clay, the correlation between excess pore water pressure and axial strain was established. By analyzing the vertical cyclic mechanism of suction bucket foundation, a prediction model for suction bucket foundation under vertical cyclic loading was established based on the dynamic characteristics of marine clay and the model was validated. The comparison between the validation outcomes and the experimental outcomes shows good agreement. This study provides certain guidance for the design of suction bucket foundations for OWTs.

Results of the cyclic triaxial testing on mechanically-biologically treated waste.

Accurate assessment of the dynamic strength characteristics of mechanically-biologically treated (MBT) waste is crucial for the construction and safe operation of landfill sites. Herein, samples of MBT waste from the Hangzhou Tianziling landfill were collected and subjected to consolidated undrained cyclic triaxial tests under four confinement levels and six cyclic stress ratios (CSRs). Under cyclic loading, the MBT waste exhibited a critical CSR. If the CSR exceeds the critical value, the MBT waste specimen rapidly undergoes deformation and failure. Dynamic strength of MBT waste decreases with an increase in the number of cyclic vibrations and increases with an increase in confining pressure. Considering the influence of cyclic vibrations and confining pressure, a formula for dynamic strength in terms of cyclic vibrations and confining pressure has been established. The dynamic shear strength parameter ranges for MBT waste were obtained under different seismic magnitudes. We compared the dynamic and static shear strength parameters of MBT waste and municipal solid waste. These study findings can serve as a reference for the dynamic stability analysis of MBT waste landfills.

Exploring the Macroscopic Behavior and Microstructure Evolution of Lightly Cemented Sand in the Post-Liquefaction Process Using DEM.

This study investigates the post-liquefaction monotonic undrained shearing behavior of cemented sand at the macro- and microscales, using the discrete element method. A series of cyclic undrained triaxial tests with different stress amplitudes and post-liquefaction monotonic undrained triaxial tests were simulated on cemented sand with diverse cement contents (CCs). For comparison, a series of monotonic undrained triaxial tests on cemented sand without liquefaction (virgin cemented sand) were also modeled. The macroscopic behavior was analyzed in conjunction with the microscopic characteristics of the assembly, such as the deviator fabric of contact normal orientation, mechanical coordination number, energy components, and bond breakage. The results show that the DEM model can capture the effect of CC and cyclic stress ratio (CSR) on the undrained shear strength, stiffness, and pore pressure observed in laboratory experiments. Referring to the virgin specimen, with an increase in CC, the mechanical coordination number and the input work increment increase, while the deviator fabric for total contacts changes irregularly, leading to a greater initial stiffness and shear strength. In the case of the liquefied specimen, the smaller initial mechanical coordination number results in a very low initial stiffness regardless of CC. Contrary to the uncemented sand, both the mechanical coordination number and the input work increment decrease with an increasing CSR for the cemented sand. The microstructure evolution governs the effect of cementation level and liquefaction history on the macroscopic post-liquefaction behavior.

Experimental study on the dynamic properties of soft clay with sand interlayers under cyclic loading

Unlike uniform soils, soft clays with sand interlayers in coastal soft clays, can affect their mechanical properties, potentially impacting underground-construction safety and stability. Consolidated undrained cyclic triaxial tests were conducted to study the dynamic properties and deformation behavior of clay, focusing on how the thickness ratio between the sand and clay layers and the cyclic-stress ratio influence the pore pressure, axial strain, shear-modulus ratio, and normalized damping ratio. The results indicate that higher thickness ratios and cyclic-stress ratios lead to a faster decay of the shear-modulus ratio, quicker increases in pore pressure, faster strain accumulation, and fewer cycles to failure. The normalized damping ratio has three different forms: decreasing, decreasing then increasing, and increasing. However, at a cyclic-stress ratio of 0.2 and thickness ratio of 0.25, the samples exhibit better dynamic characteristics. Soft clay with sand layers exhibits characteristics in line with the stability theory. At low thickness and cyclic-stress ratios, purely elastic and elastically stable phases are observed. As the thickness and cyclic-stress ratios increase, it transitions to plastic stability and incremental failure.

Equivalent stress concept to account for the effect of local cyclic stress ratio on transverse cracking in tension–tension fatigue

Presented test results on transverse cracking in cross-ply laminates upon tension–tension cyclic loading show that the increase of crack density depends not only on the maximum transverse stress in the cycle but also on the local cyclic stress ratio RTloc in the analyzed layer. To include the effect of the RTloc in the model with statistical failure stress distribution for crack initiation (based on Weibull distribution) adapted for fatigue, an equivalent stress is introduced in a similar manner as the equivalent strain energy release rate has been used for delamination crack propagation. The equivalent stress in the layer is defined as a power function of the maximum stress and the stress ratio in the layer. It was found, testing laminates with two different fiber contents that higher the local stress ratio in 90-layer, higher the transverse cracking resistance. Transverse crack density simulation using the developed equivalent stress model has been validated against test results.

Experimental Study on Cyclic Simple Shear Test of Coastal Tidal Soft Soil

Based on undrained cyclic simple shear tests conducted on coastal tidal soft soil under various conditions of cyclic stress ratios and moisture contents, this study investigated the influence of these factors on the dynamic properties of the soil. The findings indicated that with increasing moisture content and stress cycle ratio, the stress–strain hysteresis loop gradually expanded, resulting in a higher strain difference and a transition from a dense to a sparse curve pattern. Moreover, the symmetry of the hysteresis loop was lost in the later stages of shearing. With an increase in the number of cycles, the cumulative shear strain gradually increased, and the increase in the cyclic ratio of water content to stress reduced the number of cyclic shear cycles required to achieve failure, thereby accelerating the soil’s failure rate. A predictive formula was developed based on the experimental results to estimate the failure cycles as a function of the cyclic stress ratio and moisture content. Furthermore, the softening index decreased gradually with an increasing number of cycles, and a higher moisture content and cyclic stress ratio accelerated the soil’s softening process. It was observed that under the conditions of optimal moisture content, the soil exhibited a slower softening rate during the initial stage of shearing.

Effect of loading frequency and cyclic stress ratio on undrained cyclic behaviors of clay-structure interface with various overconsolidation ratios

The widely used suction caissons in offshore engineering are commonly subject to cyclic loads including the wind, wave, and current. For proper design and sustainable maintenance of the suction caisson foundations, it is essential to investigate the dynamic response of the clay-structure interface. This research conducted a series of clay-structure interface cyclic shear tests under constant volume equivalent undrained state using a modified direct simple shear device to fully investigate the effects of cyclic stress ratio (CSR), loading frequency, and overconsolidation ratio (OCR) on the dynamic response of the interface. The interface shear strength, relative shear displacement, the number of cycles to failure (Nf), and interface pore water pressure were analyzed. Results show that the Nf is strongly affected by CSR and loading frequency. A model is proposed to describe the decrease in the Nf with increasing CSR under a given loading frequency and OCR. The Nf increases approximately linearly with loading frequency on a double-logarithmic scale. Additionally, the contour diagrams, defining the Nf as a function of interface average and cyclic shear stress under various OCRs, are proposed to predict the failure behaviors of clay-structure interface subjected to various loading combinations. Besides, the development models are established respectively to describe the evolutions of accumulated interface pore pressure (Uia) against the number of cycles (N) and cyclic relative shear displacement (Wcy), presenting better capability to describe the development of Uia. The findings in this study hold potential implications for determining whether the failure occurs under corresponding loading conditions and predicting interface pore pressure development.

Cyclic behavior of port-said soft clay in cyclic direct simple shear tests

A thick deposit of soft clay, known as “Port-Said Clay” (PSC), is commonly encountered in the northern formations close to the Mediterranean shores of Egypt. The growing level of development, including transportation corridors like highways and tunnels, in areas rich with PSC necessitated an in-depth study to characterize its dynamic behavior. This study presents a first comprehensive experimental investigation of the dynamic behavior of the soft PSC using Cyclic Direct Simple Shear Tests. The effects of plasticity index (PI), loading frequency (f), and cyclic stress ratio on the cyclic resistance, shear modulus, shear modulus reduction ratio, pore water pressure generation, and damping ratio was investigated. The results showed that all the investigated behavior parameters are primarily sensitive to PI and f. The conclusions drawn from this study on PSC open the way to further laboratory-based investigations of the dynamic behavior of PSC, in addition to numerical modelling of the seismic interaction between PSC and different types of structures.

Undrained behavior of marine clay under one-way cyclic loading with variable confining pressure

Settlement of roads or railway caused by traffic loading has a serious effect on the safety and service performance of transport infrastructures constructed on soft marine clay. While simple cyclic triaxial test with constant confining pressure (CCP) were used in most of the previous studies, a series of cyclic triaxial tests with variable confining pressure (VCP) were carried out on normally consolidated (NC) and overconsolidated (OC) reconstituted Wenzhou soft clay in this paper to study the undrained behavior of soft marine clay due to surcharge preloading as well as cyclic traffic loading. VCP test is able to approximate the complicated stress path than CCP test caused by traffic loading. The test results indicate that NC specimens show significantly different pore water pressure (u) evolution compared with OC specimens. However, a change in the overconsolidation ratio (OCR) of OC specimens does not have a significant influence on variation of u with identical cyclic stress ratio (CSR) and total stress path (η). The slope of the effective stress path is dependent on the total stress path under which the specimen was loaded cyclically, regardless of the OCR and whether variable confining pressure was applied. The slope of the effective stress path is broadly in line with the slope of corresponding total stress path. In addition, the development of permanent axial strain (εpa) due to one-way cyclic loading was shown to depend significantly on the values of η and OCR. Both the variable confining pressure and OCR limited the strain accumulation of saturated marine clay under undrained one-way cyclic loading. Finally, the effects of η and OCR on the magnitude of εpa after 1000 loading cycles are quantified and incorporated in a power law function for the permanent deformation prediction of soft marine clay due to traffic loading.

Liquefaction resistance and small strain stiffness of silty sand: Effects of host sand gradation and fines content

In this paper, a well designed experimental study comprising undrained cyclic triaxial and bender element tests was carried out on five sand-silt mixtures with three grain size ratios (Rd) and three sand uniformity coefficients (Cus). The results reveal that at given fines content (FC) and void ratio, the liquefaction resistance (CRR) of the mixtures decreases as Rd increases from 9.7 to 27.8 or Cus from 1.50 to 4.46, and the CRR of the mixture at the highest Rd or Cus becomes as low as nearly 50% of that at the lowest Rd or Cus. The equivalent relative density (Dr*) based on the binary packing theory can be utilized to capture the coupled effects of host sand gradation and FC on the CRR of sand-silt mixtures. A novel finding is that a universal relationship exists between the liquefaction resistance and the shear modulus normalized by the minimum void ratio function of host sand (GN') for different FCs, initial effective confining pressures, sample preparation methods (SPMs), and host sand gradations. Based on the comprehensive laboratory test data, the empirical CRR15-GN' correlation is proposed and further adjusted for the field liquefaction triggering analysis based on the shear wave velocity (Vs). Soil can be considered non-liquefiable when its equivalent shear wave velocity exceeds 225 m/s or the applied cyclic stress ratio (CSR) is below 0.088. Comparisons with the previously established liquefaction triggering boundary curves validate the applicability of the proposed curve for initial evaluation of the liquefaction resistance of sandy soils, indicating laboratory studies can complement in-situ investigations for Vs-based liquefaction assessment.

Laboratory tests on the traffic-induced cyclic behavior of anisotropically overconsolidated clay under different drainage conditions

In road engineering on clay foundation, the subgrade clay is often anisotropically overconsolidated, and the drainage boundary is commonly partially drained. Considering that few laboratory studies focused on the traffic-induced cyclic behaviors of anisotropically overconsolidated clay, and investigated intensively the differences in deformation between undrained and partially drained conditions, this study performs a series of one-way cyclic tests on the overconsolidated clay with various consolidation stress ratios (K) under different drainage conditions. The emphasis is put on the comparison of undrained and partially drained tests in terms of the permanent axial strain and its accumulated rate, resilient modulus and damping ratio. Test results indicate that the relative magnitude of permanent axial strain and its accumulated rate between the two drainage conditions is highly related to cycle number, K and CSR, with decreasing K and increasing CSR exacerbating the difference. The resilient modulus of partially drained tests is greater than that in undrained tests overall, while the relative relationship of degradation index between the two drainage conditions is reversed. In addition, the increase of consolidation-induced anisotropy degree promotes the strain development and improves the resilient stiffness, which should be noted for the traffic-induced deformation of subgrade clay. Based on the shakedown theory, the allowable cyclic stress ratio is determined as 0.44, and it is affected little by K or drainage condition. Finally, prediction models of permanent axial strain and resilient modulus are established for the anisotropically overconsolidated clay under both drainage conditions, where the deformation prediction is found to be related to the shakedown behavior. It is recommended that the prediction and control of subgrade clay settlement in engineering practice should take into account the in-situ consolidation sate and drainage condition.

A Methodology for Susceptibility Assessment of Wave-Induced Seabed Liquefaction in Silt-Dominated Nearshore Environments

Wave-induced seabed liquefaction significantly jeopardizes the stability of marine structures and the safety of human life. Susceptibility assessment is key to enabling spatial predictions and establishing a solid foundation for effective risk analysis and management. However, the current research encounters various challenges, involving an incomplete evaluation system, poor applicability of methods, and insufficient databases. These issues collectively hinder the accuracy of susceptibility assessments, undermining their utility in engineering projects. To address these challenges, a susceptibility assessment method with the safety factor was developed as the key assessment parameter, allowing for a comprehensive susceptibility assessment across the silt-dominated nearshore environment using Empirical Bayesian Kriging (EBK). The safety factor is determined by combining the cyclic stress ratio (CSR) and the cyclic resistance ratio (CRR), which characterize wave loadings and sediment properties in the study area, respectively. This method was applied in the Chengdao region of the Yellow River Estuary, China, a typical silt-dominated nearshore environment where wave-induced liquefaction events have been reported as being responsible for multiple oil platform and pipeline accidents. By collecting the regional wave and seabed sediment data from cores spanning from 1998 to 2017, the safety factors were calculated, and a zonal map depicting the susceptibility assessment of wave-induced seabed liquefaction was created. This study can serve as a valuable reference for the construction and maintenance of marine engineering in liquefaction-prone areas.

Energy-Based Assessment of Liquefaction Behavior of a Non-Plastic Silt Based on Cyclic Triaxial Tests

Earthquakes cause cyclic shear deformations in soil and build-up of excessive pore water pressure as a result of undrained loading, accompanied with rearrangement of soil particles and degradation in stiffness of the soil due to decrease in effective stresses. During loading, the onset of soil liquefaction is defined as a stress state in which the excess pore water pressure is equalized to the total stress. From this point of view, assessment of the pore water pressure development pattern under cyclic loading has been one of the most salient research topics in geotechnical and earthquake engineering. In this study, results of a series of cyclic triaxial tests on non-plastic silt specimens consolidated under 100 kPa effective isotropic consolidation pressure were used to question the modelling ability of pore pressure development models previously proposed for sands. Tests were performed on specimens of 6 different initial relative densities (Dr) ranging between 30-80% and 10 different cyclic stress ratios (CSR). The key parameters of pore water pressure development and shear deformation in the energy-based model used are relative density, cyclic stress ratio and number of cycles. The results revealed that, these energy-based models have a strong potential in evaluation of pore water pressure development pattern of non-plastic silts. Test results also show that the increase in relative density and decrease in CSR causes a ladderlike behavior among pore water pressure and cyclic shear strain, which is relevantly rendered by energy-based models.

Subgrade soil response to rail loading: Instability mechanisms, causative factors, and preventive measures

The demand for more efficient heavy-haul rail networks over soft subgrades poses significant geotechnical challenges and requires a comprehensive understanding of stress conditions as well as the failure potential of subgrade soil under moving wheel loads and increasing rail speeds. Unfavourable stress conditions in the subgrade can result in various types of failures, three of which are identified in this article: (i) excessive plastic settlement, (ii) progressive shear failure, and (iii) subgrade fluidisation (mud pumping). Through a series of advanced testing schemes using cyclic triaxial, hollow cylinder, and an in-house dynamic filtration apparatus, critical stress conditions and soil characteristics prone to subgrade instability are discussed. The results demonstrate that under adverse combinations of loading frequency (f) and cyclic stress ratio (CSR) the continuous application of cyclic loads can lead to an unstable state of soil where excess pore pressure and axial strain increase rapidly. This study also reveals that low to medium plasticity soils (PI < 22) are more vulnerable to subgrade fluidisation, where the rapid internal migration of pore water transforms the upper soil to a fluid-like state with substantial loss in soil stiffness. The layered response of soil through dynamic filtration tests showed larger hydrodynamic forces induced by differential hydraulic gradients in the top layer during cyclic loading causes moisture to move upwards. Various factors that can influence soil instability such as the degree of compaction degree, clay content, soil fabric and stress rotation are also addressed in this paper. Finally, novel solutions for stabilising subgrade such as a vertical drain-composite system and the use of eco-friendly biopolymers are presented.