Cyclic Shear Strain Research Articles

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 (Vs) measurements. Liquefaction occurred at excess pore water pressure ratios (ru) 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 (ru>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 (Vs1) with negligible effect of silt content. The results indicate that the existing CRR–Vs1 correlations would underestimate the liquefaction resistance of silts and sandy silt soils.

Strain-Controlled Cyclic Simple Shear Tests on Sand with Radial Strain Measurements

AbstractStrain-controlled cyclic simple-shear tests were performed on silica sand with radial strain measurements. The specimens were tested under a constant K0 condition and subjected to cyclic loading and postcyclic monotonic loading. Threshold cyclic shear strain, volumetric strain, secant shear modulus, and damping ratio are investigated. Generally, the volumetric strain behavior in this study agreed well with literature findings that were investigated using the conventional cyclic direct simple shear test (without radial constraints). Radial strain during monotonic simple shear (postcyclic loading) was found to be a good parameter in monitoring the onset of flow slide in cohesionless soil. The concept of threshold cyclic shear strain, γt, was adequately applied in assessing the specimen volume change. Dynamic engineering properties, including equivalent shear modulus and damping ratio, were also studied. The damping ratio was found to decrease when the cyclic shear strain amplitude was greater than 2...

Threshold Load Factor for Liquefaction Triggering Evaluations

The Vs-based chart developed by Andrus and Stokoe (2000) becomes less conservative when a constant cyclic shear strain, γc, is used for liquefaction triggering (Dobry et al. 2015), where Vs = shear wave velocity. Specifically, natural silty sands in the Imperial Valley of California, heavily preshaken by earthquakes, have a triggering resistance for a given normalized Vs significantly higher than uncompacted clean and silty sand fills. A higher γc is required for triggering in the natural sands than in the fills (0.1–0.2% versus 0.03%). Dobry et al. (2015) reached this conclusion within the usual liquefaction chart format, plotting CSR 1⁄4 τ c=σ 0 v0 1⁄4 0.65ðamax=gÞðσv0=σ 0 v0Þrd versus normalized shear wave velocity, Vs1 1⁄4 Vsð100=σ 0 v0Þ (σ 0 v0 in kPa). The next logical step would be to plot γc directly versus Vs1. However, using γc is not practical for several reasons. The authors propose instead use of the threshold load factor (TLF)

Cyclic Pore Water Pressure Generation and Stiffness Degradation in Compacted Clays

AbstractCyclic hollow cylinder torsional tests were performed in undrained conditions on 12 compacted clay specimens collected from two types of dams (an earth-core rock-filled dam and an earth-zone dam) in Thailand. The cyclic degradation, cyclic pore water pressure generation, and volumetric cyclic threshold shear strain were studied via multistage strain-controlled tests. The testing program encompassed five overconsolidation ratios (OCRs), 1, 1.5, 2, 3.5, and 4, where six to eight cyclic strain-controlled stages were applied in each test with frequency f=2 Hz. The results reveal that the volumetric threshold shear strain amplitude of these compacted clays ranged between approximately 0.009 and 0.025% and generally increased substantially with the plasticity index (PI). The cyclic pore water pressures normalized by σc′ are consistently lower than previous ones using other types of clays tested with other types of devices at comparable cyclic shear strain amplitudes. The cyclic degradation and cyclic p...

Cyclic Shear Strain Needed for Liquefaction Triggering and Assessment of Overburden Pressure Factor Kσ

AbstractThis paper has two objectives. The first is to evaluate the cyclic shear strain needed to trigger liquefaction, γcl, in clean and silty sands in the field during earthquakes as an alternative to the currently used cyclic resistance ratio (CRR). The second objective is to explore the effect of a high effective overburden pressure, σv0′, on the value of CRR. The first objective is accomplished mainly by using an equation relating γcl and CRR valid for shear wave velocity–based liquefaction charts. This equation is supplemented with laboratory results from undrained cyclic strain-controlled tests as well as large-scale and centrifuge model shaking experiments. It is shown that for recent uncompacted clean and silty sand deposits and earthquake magnitude Mw=7.5, γcl≈0.03%, with this value increasing to γcl≈0.3% (in some cases to 0.6%) in denser and overconsolidated, preshaken, and compacted sands. These small values of γcl in the field are controlled by two factors: excess pore pressure buildup in the...

Dynamic shear modulus and damping ratio of frozen compacted sand subjected to freeze–thaw cycle under multi-stage cyclic loading

Frozen soil plays an important role on the stability of railway and highway subgrade in cold regions. However, the dynamic properties of frozen soil subjected to the freeze–thaw cycles have rarely been investigated. In this study, cryogenic cyclic triaxial tests were conducted on frozen compacted sand from Nehe, Heilongjiang Province in China which was subjected to the closed-system freeze–thaw cycles. A modified Hardin hyperbolic model was suggested to describe the backbone curves. Then, dynamic shear modulus and damping ratio versus cyclic shear strain were analyzed under the different freeze–thaw cycles, temperatures, initial water contents, loading frequencies and confining pressures. The results indicate that the freeze–thaw process plays a significant effect on the dynamic shear modulus and damping ratio, which slightly change after one freeze–thaw cycle. Dynamic shear modulus increases with increasing initial water content, temperature, loading frequency and confining pressure. Damping ratio increases with increasing initial water content, while decreases with increasing temperature and loading frequency. The effect of confining pressure on the damping ratio was found not significant. Furthermore, the empirical expressions were formulated to estimate dynamic shear modulus and damping ratio of the frozen compacted sand. The results provide guidelines for evaluating the infrastructures in cold regions.

Lateral Response Comparison of Unbonded Elastomeric Bearings Reinforced with Carbon Fiber Mesh and Steel

The vertical and horizontal stiffness used in design of bearings have been established in the last few decades. At the meantime, applicability of the theoretical approach developed to estimate vertical stiffness of the fiber-reinforced bearings has been verified in different academic studies. The suitability of conventional horizontal stiffness equation developed for elastomeric material, mainly for steel-reinforced elastomeric bearings, has not been tested in detail for use of fiber-reinforced elastomeric bearings. In this research, lateral response of fiber mesh-reinforced elastomeric bearings has been determined through experimental tests and the results have been compared by corresponding values pertaining to the steel-reinforced bearings. Within the test program, eight pairs of fiber mesh-reinforced bearings and eight pairs of steel-reinforced bearings are subjected to different levels of compressive stress and cyclic shear strains. Fiber-reinforced elastomeric bearings may be more favorable to be used in seismic regions due to lower horizontal stiffness that can result in mitigation of seismic forces for levels of 100% shear strain. Damping properties of these types of fiber mesh-reinforced bearings depend mostly on the selection of elastomeric material compounds. Suggestions have been made for the lateral response of fiber-reinforced elastomeric bearings. It has also been determined that the classical equation for lateral stiffness based on linear elastic behavior assumptions developed for elastomeric bearings does not always apply to the fiber-reinforced ones.

Experimental Characterization of the Tridimensional Gradient of Microstructure Induced by RCF in the Rolling Band of Rails

The aim of this study is to increase understanding of the relationship between RCF cracking and plastic deformation of the pearlitic microstructure. Following a multi-technical and multi-scale characterization of the worn rail surface, the multidirectional gradient of mechanical properties below the running band is studied with a microstructural point of view. In order to achieve the characterization of the running band and to quantify the influence of the microstructural/mechanical gradient on the global fatigue behavior, this experimental methodology has been based on the combination of several microstructural investigations by optical and scanning electron microscopy (FEG-SEM) in both rolling and transverse directions, microindentation performed on the gradient profile and determination of quantitative data on the pearlitic aggregates through the gradient by Electron backscatter Diffraction (EBSD). Due to the severe plastic deformation, material experiences progressively work hardening and the pearlitic microstructure is modified. In the middle of the running band where the contact patch envelope is more frequent, the pearlitic colonies below the worn rail surface are fractured by accumulation of cyclic and severe shear strain. The resulting lamellar structure of ferrite and cementite is elongated and aligned in the direction of shear strain as the interlamellar spacing decreases. On the contrary, at both sides of the running band where the contact with wheel is rare, the surface is rougher, the pearlitic colonies remain unaffected and the lamellae are not oriented preferentially. The examination of the running band and the microstructure gradient by quantitative analysis will contribute to improve the modeling of rail failure by RCF by enabling to include microstructural data.

Effects of cyclic shear stress and average shear stress on the cyclic loading failure of marine silty sand

This paper presents the cyclic direct simple shear (CDSS) tests to explain the long term cyclic behavior of marine soil deposits. Cyclic behavior of marine soil deposits depend on the number of loading cycles, vertical effective stress, cyclic shear strain amplitude, relative density, and cyclic and average shear stresses. In addition, the study investigates the effect of cyclic and average shear stresses on the cyclic behavior of marine soil deposits subjected to long term cyclic loading. Design graphs are plotted from the CDSS test results. These results are then modeled and can be used to design offshore structures such as offshore wind turbine foundations, and also used to assess the cyclic shear strength of soil beneath the foundation.

Cyclic secant shear modulus versus pore water pressure in sands at small cyclic strains

Cyclic strain-controlled behavior of fully saturated sands in undrained condition is analyzed at small cyclic shear strain amplitudes, γc, around the threshold shear strain for cyclic pore water pressure buildup, γtp≈0.01%. The cyclic triaxial and simple shear test results obtained in the past by different researchers and the results of new cyclic simple shear tests reveal that: (i) at very small γc below γtp where there is no buildup of cyclic pore water pressure, ΔuN, with the number of cycles, N, the cyclic secant shear modulus, GSN, initially increases with N for 10–20% of its initial value GS1 and then levels off or just slightly decreases, (ii) at small γc between γtp≈0.01% and 0.10–0.15%, ΔuN continuously increases with N while the modulus GSN first increases for up to 10% of GS1 and then gradually decreases, and (iii) at γc larger than approximately 0.15%, relatively large ΔuN develops with N while the modulus GSN constantly and significantly decreases. This means that at γc between γtp and 0.10–0.15% the sand stiffness initially increases with N in spite of the reduction of effective stresses caused by the cyclic pore water pressures buildup. In this range of γc, the pore water pressure ΔuN can reach up to 40% of the initial effective confining stress before GSN drops below GS1. The microstructural mechanisms believed to be responsible for such a complex behavior are discussed. It is suggested that during cyclic loading the changes at mineral-to-mineral junctions of grain contacts can cause soil stiffening while, at the same time, the buildup of cyclic pore water pressure causes the softening.

Liquefaction Potential of Recent Fills versus Natural Sands Located in High-Seismicity Regions Using Shear-Wave Velocity

The liquefaction potential of clean and silty sands is examined on the basis of the field measurement of the shear-wave velocity, Vs. The starting point is the database of 225 case histories supporting the Andrus-Stokoe Vs-based liquefaction chart for sands, silts, and gravels. Only clean and silty sands with nonplastic fines are considered, resulting in a reduced database of 110 case histories, which are plotted separately by type of deposit. A line of constant cyclic shear strain, γcl≈0.03%, is recommended for liquefaction evaluation of recent uncompacted clean and silty sand fills and earthquake magnitude, Mw=7.5. The geologically recent natural silty sand sites in the Imperial Valley of southern California have significantly higher liquefaction resistance as a result of preshaking caused by the high seismic activity in the valley. A line of constant cyclic shear strain, γcl≈0.1–0.2%, is recommended for practical use in the Imperial Valley. Additional research including revisiting available Vs-based and penetration-based databases is proposed to generalize the results of the paper and develop liquefaction charts that account more realistically for deposit type, seismic history, and geologic age.

A strain-based procedure to estimate strength softening in saturated clays during earthquakes

Cyclic softening and strength loss of saturated clays during earthquakes is often an important consideration in engineering problems such as slope stability, dam/levee safety, and foundation bearing capacity. This study proposes a simplified procedure for evaluating cyclic softening (amount of strength loss) that may be expected in saturated clays during earthquakes and illustrates how to implement it in engineering analysis. The procedure has two main steps: (1) estimation of an equivalent cyclic shear strain amplitude and associated number of cycles induced in the soil mass by an earthquake; and (2) estimation of softening and strength loss in the soil mass. A key aspect of the proposed procedure is adoption of a strain-based approach to estimate cyclic softening as opposed to the widely used stress-based approach of liquefaction assessments. A threshold strain concept originating from the strain-based approach is first discussed and the development of a procedure is presented subsequently. The proposed procedure provides reasonable, first-order estimates of cyclic softening consistent with the other developed procedures. In addition, the capability of the procedure is demonstrated with two case histories identified as involving cyclic softening of clays.

Factors affecting shear modulus degradation of cement treated clay

Cement stabilization is often used to improve the bearing capacity and compressibility of soft clays. The present paper aims to investigate the shear modulus degradation of cement treated clay during cyclic loading. A series of cyclic triaxial test was conducted on artificially cement treated marine clay to study the factors affecting the shear modulus degradation. The parameters considered for the study are cement content (2.5–7.5%), curing days (7–28), cyclic shear strain amplitude (0.3–1%), number of loading cycles (1–100) and loading frequency (0.1–0.5Hz). As in the case of natural clays, cement treated clays exhibit stiffness degradation which depends on mix ratio, curing days and loading conditions. The results show that the shear modulus degradation decreases with increase in the shear strain amplitude, cement content and curing days. It is also noted that irrespective of the mix ratio and curing conditions, the degradation decreases with increase in loading frequency. An empirical relationship is proposed to predict the shear modulus degradation based on Idriss׳s degradation model. The performance of the proposed empirical model is validated with the present experimental results.

A practical method for utilization of commercial cyclic testing apparatuses for computation of site response in central Adapazari

We suggest a practical method for estimating strain–modulus–damping relationships for utilization in equivalent-linear site response analyses, so that the necessity for more sophisticated sampling and testing procedures can be justified. The method employs the commercial cyclic testing apparatuses, which have limitations in low-strain ranges, and the in-situ seismic tests. The shear modulus at about 1% cyclic shear strain amplitude and the shear-wave velocity measured in-situ is used for building a hyperbolic relationship between shear stress and shear strain. An extension of Masing׳s rule and the constraint on hysteretic damping at 1% cyclic shear strain amplitude leads to a strain–damping relationship. By putting a particular emphasis on the soils of Adapazarı, a city famous for the concentrated damage on alluvium basin during the 1999 Kocaeli (Mw7.4) earthquake, we demonstrated the usefulness of the method, and concluded that the shear-modulus reduction and damping characteristics of Adapazarı soils can yield to site amplification factors greater than those predicted by strain–modulus–damping relationships presented in literature, and can more efficiently explain the concentration of damage on the alluvium basin. Through the comparisons of spectral amplification factors computed by equivalent-linear site response analyses, we justified the necessity to run a more sophisticated testing program on determination of cyclic stress–strain behavior of Adapazarı soils, and consequently to consider transient nonlinear site-response analyses in order to reduce the possible bias in calculation of spectral amplification factors.

Simulating stiffness degradation and damping in soils via a simple visco-elastic–plastic model

Stiffness degradation and damping represent some of the most well-known aspects of cyclic soil behavior. While standard equivalent linear approaches reproduce these features by (separately) prescribing stiffness reduction and damping curves, in this paper a multiaxial, 3D, viscoelastic – plastic model is developed for the simultaneous simulation of both cyclic curves over a wide cyclic shear strain range.The proposed constitutive relationship is based on two parallel resisting/dissipative mechanisms, purely frictional (elastic–plastic) and viscous. The frictional mechanism is formulated as a bounding surface plasticity model with vanishing elastic domain, including pressure-sensitive failure locus and non-associative plastic flow – which are essential for effective stress analysis. At the same time, the use of the parallel viscous mechanism is shown to be especially beneficial to improve the simulation of the overall dissipative performance.In order to enable model calibration from stiffness degradation (G/Gmax) and damping curves, the constitutive equations are purposely kept as simple as possible with a low number of material parameters. Although the model performance is here explored with reference to pure shear cyclic tests, the 3D, multiaxial formulation is appropriate for general loading conditions.

Experimental and numerical study on circular tunnels under seismic loading

This paper compares the experimental results of a set of centrifuge models of tunnels in sand under seismic loadings with the predictions of finite element dynamic analyses and of simplified methods. In order to characterise the soil behaviour, mobilised shear stiffness and damping ratio of the sand model have been back-calculated from the experimental results according to two different procedures. Starting from the accelerometer measurements, one was based on the transfer functions from surface to base and the other one on the average shear stress–strain cycles along the sand layer. A series of viscoelastic 2D dynamic analyses were performed to simulate the model tests by a linear equivalent approach. The equivalent shear stiffness and damping ratio determined from stress–strain cycles were used as input values for the analyses. The shear stress transfer at the ground-lining interface was back-analysed to calibrate the interface elements used in the numerical code, in order to improve the assessment of the transient changes of hoop force. Finally, the numerical results have been compared to analytical solutions, widely adopted in the design, and to the experimental data in terms of transient increments of internal forces in the lining. Such a comparison indicates that the analytical formulations give a good estimation of the seismic increment of bending moment in the lining and a reasonable lower bound for the transient changes of hoop forces, provided that cyclic shear strains are correctly evaluated.

Torsional fatigue with axial constant stress for Sn–3Ag–0.5Cu lead-free solder

A series of multiaxial ratcheting–fatigue interaction tests have been carried out on Sn–3Ag–0.5Cu lead-free solder specimens. All tests were conducted under cyclic shear strain with the constant axial stress at the room temperature with the shear strain rate of 5×10−3s−1. It was found that the ratcheting strain increased with increasing axial stress and shear strain amplitude while the fatigue life decreased at the same time. The ratcheting strain rate was linear with axial stress in double logarithmic coordinate. The Ohno–Wang II constitutive model was employed to simulate the stress–strain responses. Several fatigue life prediction models were applied to predict the multiaxial ratcheting–fatigue life of the Sn–3Ag–0.5Cu lead-free solder. The Gao–Chen model which adopted the maximum shear strain and the ratcheting strain rate as the damage parameter predicted the multiaxial ratcheting fatigue life well.

해양 실트질 모래의 비배수 동적 거동에 대한 평균 및 반복전단응력의 영향

해상풍력발전기의 기초는 바람, 조류, 그리고 파도 하중을 받기 때문에 해상풍력발전기 기초를 설계하는 데 있어 반복하중을 받는 기초지반의 전단거동 평가가 필요하다. 지반의 비배수 동적 전단거동은 반복하중 횟수, 수직 유효응력, 반복 전단변형률, 상대 밀도, 그리고 평균 및 반복전단응력의 조합에 영향을 받는다. 본 연구에서는 해양 실트질 모래의 비배수 동적 거동에 대한 평균 및 반복전단응력의 영향을 평가하기 위하여 반복단순전단시험(CDSS)을 수행하였으며 상대밀도 85%, 수직 유효응력 200kPa과 300kPa의 시험조건에서 15%의 이중진폭 동적전단변형률(<TEX>${\gamma}_{cyc}$</TEX>)과 영구전단변형률(<TEX>${\gamma}_p$</TEX>)를 파괴 기준으로 적용하였다. 시험결과는 설계 그래프와 등고선도로 나타내었다. 결과에 따르면 해양 실트질 모래의 비배수 동적 거동은 평균 및 반복전단응력과 두가지 전단응력의 조합에 의해 크게 변하는 경향을 보였다. 평균전단응력이 존재하는 경우에는 반복전단변형보다는 영구변형에 의해 파괴가 결정되는 것으로 나타났다. Offshore wind turbine foundations are subjected to wind, current and wave loadings. Hence, both static and cyclic behaviors of foundation's soil are important for the design of offshore wind turbine foundation. Undrained cyclic behaviors of soils depend upon the number of loading cycles, vertical effective stress, cyclic shear strain, relative density, and the combination of cyclic and average shear stresses. In order to evaluate the effect of average and cyclic shear stresses on the undrained cyclic behavior of marine silty sand, cyclic direct simple shear (CDSS) tests are performed with relative density of 85%, vertical effective stress of 200 and 300 kPa, and failure criteria of either 15% double amplitude cyclic shear strain (<TEX>${\gamma}_{cyc}$</TEX>) or permanent shear strain (<TEX>${\gamma}_{p}$</TEX>). The results are presented in the form of design graphs or contour diagrams. The undrained cyclic behavior of marine silty sand is found to be dependent on cyclic and average shear stresses and/or the combination of both shear stresses. It is found that when significant average shear stress exists the permanent or progressive shear strain is the govering failure criteria instead of cyclic shear strain.

Design and validation of an in vitro loading system for the combined application of cyclic compression and shear to 3D chondrocytes-seeded agarose constructs

Physiological loading is essential for the maintenance of articular cartilage by regulating tissue remodelling, in the form of both catabolic and anabolic processes. To promote the development of tissue engineered cartilage which closely matches the long term functionality of native tissue, bioreactors have been developed to provide a combination of loading modalities, which reflect the nature of normal physiological loads. This study describes the design and validation of an in vitro mechanical system for the controlled application of bi-axial loading regimes to chondrocyte-seeded agarose constructs.The computer-controlled system incorporates a robust gripping system, which ensures the delivery of precise values of cyclic compressive and shear strain to 3D cell-seeded constructs. Sample prototypes were designed, optimised using finite element analysis and validated performing compressive and shear fatigue mechanical tests. The horizontal and vertical displacements within the bioreactor are precisely controlled by a dedicated programme that can be easily implemented. The synchronisation of the orthogonal displacements was shown to be accurate and reproducible.Constructs were successfully loaded with a combined compressive and shear loading regimen at 1Hz for up to 48h with no appreciable loss of cell viability or mechanical integrity. These features along with the demonstrated high consistency make the system ideally suitable for a systematic investigation of the response of chondrocytes to a complex physiologically relevant deformation profile.

Assessment of soil–pile–structure interaction influencing seismic response of mid-rise buildings sitting on floating pile foundations

The role of the seismic soil–pile–structure interaction (SSPSI) is usually considered beneficial to the structural system under seismic loading since it lengthens the lateral fundamental period and leads to higher damping of the system in comparison with the fixed-base assumption. Lessons learned from recent earthquakes show that fixed-base assumption could be misleading, and neglecting the influence of SSPSI could lead to unsafe design particularly for structures founded on soft soils. In this study, in order to better understand the SSPSI phenomena, a series of shaking table tests have been conducted for three different cases, namely: (i) fixed-base structure representing the situation excluding the soil–structure interaction; (ii) structure supported by shallow foundation on soft soil; and (iii) structure supported by floating (frictional) pile foundation in soft soil. A laminar soil container has been designed and constructed to simulate the free field soil response by minimising boundary effects during shaking table tests. In addition, a fully nonlinear three dimensional numerical model employing FLAC3D has been adopted to perform time-history analysis on the mentioned three cases. The numerical model adopts hysteretic damping algorithm representing the variation of the shear modulus and damping ratio of the soil with the cyclic shear strain capturing the energy absorbing characteristics of the soil. Results are presented in terms of the structural response parameters most significant for the damage such as foundation rocking, base shear, floor deformation, and inter-storey drifts. Comparison of the numerical predictions and the experimental data shows a good agreement confirming the reliability of the numerical model. Both experimental and numerical results indicate that soil–structure interaction amplifies the lateral deflections and inter-storey drifts of the structures supported by floating pile foundations in comparison to the fixed base structures. However, the floating pile foundations contribute to the reduction in the lateral displacements in comparison to the shallow foundation case, due to the reduced rocking components.