Estimation of the Small-Strain Stiffness of Clean and Silty Sands using Stress-Strain Curves and CPT Cone Resistance

The initial, linear elastic range of a soil stress-strain curve is often defined by the small-strain elastic modulus E₀ or shear modulus G₀. In the present study, simpler and effective methods are proposed for the estimation of the small-strain stiffness of clean and silty sands; these are based on triaxial compression test results and the CPT cone resistance q_c. In the method based on stress-strain curves obtained from triaxial compression tests, an extrapolation technique is adopted within the small-strain range of a transformed stress-strain curve to obtain estimates of the small-strain elastic modulus. Calculated small-strain elastic modulus values were compared with the values measured using bender element tests performed on clean sands and sands containing nonplastic fines. The results showed that the method proposed produces satisfactory estimates of the small-strain elastic modulus for practical purposes. In the CPT-based method, two G₀-q_c correlations available in the literature were evaluated. For isotropic conditions, both correlations produced reasonably good estimates of G₀ for clean sands but overestimated it for silty sands. A G₀-q_c correlation which is proposed takes into account the effect of silt content of the sand and stress anisotropy.     

干砂最大剪切模量的共振柱与弯曲元试验

对德国 4 种干砂试样进行了共振柱与弯曲元对比试验,旨在分析弯曲元法测定砂土最大剪切模量时存在问题和解决方法。研究表明：时域初达法判定的剪切波传播时间较其他方法具有更好的稳定性;弯曲元试验测定最大剪切模量输入电压脉冲频率的减小而减小,衰减程度因砂土类型而异,该影响随围压的增大而减弱;对比分析表明,弯曲元与共振柱试验测定的最大剪切模量具有良好的线性关系,对柏林砂和不伦瑞克砂,存在一个临界最大剪切模量,小于该临界值时,弯曲元测值大于共振柱测值,而大于该临界值时,前者小于后者,两者差值随土样刚度增大而增大。对比研究指出,弯曲元试验尽可能采用合适高频脉冲电压作为激发电压,实践中应事先与共振柱试验进行对比。     

Influence of anisotropic stress path and stress history on stiffness of calcareous sands from Western Australia and the Philippines

Investigation of dynamic properties of carbonate/calcareous soils is important in earthquake and offshore engineering as these soils are commonly encountered in large-scale projects related with energy geomechanics and land reclamation.In this study,the stiffness and stiffness anisotropy of two types of calcareous sands(CS)from the Western Australia and the Philippines were examined using bender elements configured in different directions in stress path setups.Stiffness measurements were taken on specimens subjected to constant p’compression/extension and biaxial stress paths and additional tests were performed on three types of silica sands with different geological origins and particle shapes,which were used as benchmark materials in the study.Compared with the three brands of silica sands,the stiffness of the CS was found to be more significantly influenced by anisotropic loading;an important observation of the experimental results was that stress anisotropy had different weighted influences on the stiffness in different directions,thus influencing stiffness anisotropy.Comparisons were made between the specimens subjected to complex loading paths,and respected model parameters as suggested from published expressions in the literature.These comparisons further highlighted that calcareous soils have different responses in terms of stiffness,stiffness anisotropy and loading history,compared with that of silica-based sands.     

钙质砂小应变初始剪切模量试验研究

砂土的初始剪切模量Gmax是反映土体刚度的一个重要的力学参数.利用多方向的弯曲元测试技术,对取自波斯湾人工岛礁的钙质砂小应变初始剪切模量进行研究,分析了不均匀系数Cu、平均粒径D50及应力历史对钙质砂水平(GHH)和垂直平面(GHV和GVH)上剪切模量的影响.结果 表明:各向同性固结下,钙质砂的Gmax各向异性显著,表...     

固化粉土小应变剪切模量与强度增长相关性研究

小应变剪切模量和无侧限抗压强度是表征固化土刚度和强度特性的两个重要参数。简要介绍了弯曲元测试技术的原理及其在试验中存在的问题,采用压电陶瓷弯曲元测试技术对水泥和木质素固化剂固化粉土试样在不同养护龄期下的小应变剪切模量进行了测试,同时对相应龄期下试样进行了常规无侧限抗压强度试验,通过引入归一化参数G28和UCS28对不同固化土的小应变剪切模量和无侧限抗压强度之间的相关关系进行分析,提出了固化土刚度与强度的相关性模型,可为地基处理中固化土的无损测试与加固效果评价提供新的方法。结果表明,水泥、木质素固化粉土的小应变剪切模量随养护龄期增加而增加,养护龄期28 d内增长显著,28 d后增长趋于平稳;相同类型固化土不论固化剂掺量多少,其小应变剪切模量随养护时间的发展在本质上是相同的;固化土归一化无侧限抗压强度表现出与小应变剪切模量相似的发展趋势;提出的固化土归一化模型可作为一种土体强度无损检测的新方法。     

A unified approach to link small-strain shear modulus and liquefaction resistance of pumiceous sand

Natural pumiceous (NP) sands containing pumice particles, a type of volcanic soil, are commonly found in the central part of the North Island in New Zealand. The pumice particles are highly crushable, compressible, lightweight and angular, making engineering assessment of their properties problematic. In this paper, several series of bender element and undrained cyclic triaxial tests were performed on reconstituted and undisturbed NP sands to determine their small-strain shear modulus (G_max) and cyclic resistance ratio (CRR). Furthermore, similar tests were also conducted on normal hard-grained sands (e.g., Toyoura sand) for the purpose of comparison. The results showed that the NP sands have considerably lower G_max compared to normal sands, resulting in their higher deformability during the initial stages of the cyclic loading test. The high angularity of NP sands play an important role toward the end of the cyclic loading and contributed to their higher CRR. Next, the ratio of CRR/G_max for each sample was correlated to a level of strain denoted as cyclic yield strain (ε_ay), which was found to be significantly dependent on the percentages of pumice particles present in the natural soils. On the other hand, the ε_ay was found to be less sensitive to the consolidation stress (σ′_c) and the relative density (Dr) of the materials. For example, over different values of σ′_c and Dr, NP sands have substantially higher values of cyclic yield strain due to their lower G_max and higher CRR when compared with those of ordinary sands.     

Application of Micromechanics Model to Study Anisotropy of Soils at Small Strains

A micromechanics model is used to analyse the stiffness anisotropy of soils at small strains. Five material constants for a cross-anisotropic elastic material are related to micromechanics variables such as fabric anisotropy, contact stiffness, particle radius, and the number of contacts in a given volume of particulate assembly. The analytical results from the model are compared with the published experimental data on small-strain stiffness anisotropy in order to estimate typical soil fabric conditions of sands and clays. The relationship between the small-strain shear modulus obtained from triaxial tests and shear tests is examined using the micromechanics model. The analysis shows that, when a soil is stiffer in the horizontal direction, the shear modulus evaluated from the conventional triaxial drained tests underestimates G_vh and G_hh. The opposite is true when a soil is stiffer in the vertical direction. When a soil is sheared in undrained condition, the measured shear modulus is closer to G_vh than G_hh, especially when the soil is stiffer in the horizontal direction. The effect of soil anisotropy on the stiffness measured from different stress paths in triaxial condition is investigated.     

循环应力历史对饱和软黏土小应变剪切模量的影响

饱和软黏土的小应变剪切模量Gmax是其基本力学参数。在进行饱和软黏土的有效应力动力分析时,往往认为小应变剪切模量Gmax只随着有效应力的降低而衰减,而不受动荷载应力历史的影响,因此基本采用静力状态下得到的小应变剪切模量代替相同有效应力时动力状态下的小应变剪切模量。但是,对于饱和软黏土,目前并没有足够多的试验数据证明这一假设。基于这一考虑,通过GDS动三轴及弯曲元测试系统,研究了循环应力历史对饱和软黏土小应变剪切模量的影响,试验结果表明循环应力历史对Gmax的影响较大,采用静力状态下得到的Gmax代替动力状态下的Gmax并不可取。同时,发现可以使用小应变剪切模量的突变来表征饱和软黏土的结构破坏。     

Dynamic properties of calcareous and siliceous sands under isotropic and anisotropic stress conditions

The strain-dependent dynamic properties of sand are generally described by their relative density and mean effective stress, while the contribution of other factors, like soil origin, mineralogy, grain morphology, and initial stress anisotropy, have not been fully recognized. This paper presents the results of an experimental study on the shear modulus and damping ratio of calcareous and siliceous sands of different origins and their identical grain size distribution and stress-density states. Resonant column and cyclic triaxial tests were conducted on reconstituted samples of these two sands obtained from coastal areas. The significance of the initial effective confining pressure and stress anisotropy on the dynamic properties of the sands is evaluated and compared. It is demonstrated that the small-strain shear modulus of the calcareous sand is more affected by an increase in mean effective confining pressure than the siliceous sand. However, the effect of the initial shear on the secant shear modulus of the sands is unique. Based on the test data, a rigorous correction factor is proposed to account for the influence of the initial stress anisotropy on the small-strain shear modulus of the sands. A comparison between the strain-dependent dynamic properties of the calcareous and siliceous sands reveals that the calcareous sand has a higher secant shear modulus, lower damping ratio, and higher linear and volumetric threshold strain. Since the stress-density states and grain size distribution of the two sands were identical in the experiments, the discrepancy in the dynamic properties can be attributed to other factors, including sand origin, grain angularity, mineralogy, and formation processes, which are not commonly taken into account in the current practice.     

利用弯曲元测量上海原状软黏土各向异性剪切模量的试验研究

在许多发达国家例如英国,土体的小应变特性已被广泛应用于预测地下建筑物施工引起的地表变形。尽管上海的城市地下基础、基坑与隧道开挖日益增多,但是关于上海原状软黏土小应变剪切模量的研究几近空白。利用装有霍尔局部应变传感器与弯曲元测试系统的三轴仪对上海软黏土剪切刚度的固有各向异性进行了研究。在等向应力状态下对方形原状上海软黏土试样进行了两组试验。试验结果表明：较之传统的初达波法和峰-峰法,互相关法一定程度上提高了弯曲元试验中确定剪切波速的客观性。由于土体水平向层理结构与颗粒间胶结作用的影响,上海软黏土呈现出明显的各向异性,实测最大剪切刚度的固有各向异性比（G_0(hh)/G_0(hv)）约为1.21。利用孔隙比函数F(e)=e^-1.3能够很好的描述不同平面内最大剪切模量与土体应力状态的相互关系。     

Stiffness decay characteristics and disturbance effect evaluation of structured clay based on in-situ tests

The structure of the sedimentary clay influences its mechanical behavior in non-negligible ways. This paper proposes an effective approach for investigating the in-situ stiffness characteristics from shear modulus and strain decay curves (G–γ curves) based on self-boring pressuremeter and seismic dilatometer tests. To evaluate the excavation disturbance effects on the structured clay, the stiffness parameters from pre-bored pressuremeter tests are compared with the results of self-boring pressuremeter tests. The result indicates that the complete in-situ G–γ curves can be acquired by integrating the strain-dependent tangent shear modulus G_t from self-boring pressuremeter tests and the small-strain modulus G₀ from seismic dilatometer tests. Simultaneous observations of the G–γ curves with hyperbolic shapes in semi-logarithmic coordinates at the same strain scale show the similarity of the stiffness decay mode of the soil at different depths. The increase in the measured values of G_t and G₀ with depth can be attributed to the improved consolidation pressures and cemented strength in the structured clay. Additionally, the G/G₀–γ curves measured by the in-situ tests generally agree well with the results predicted by the Stokoe model. The excavation disturbance weakens the stiffness of the structured clay, as evidenced by G_t from the pre-bored pressuremeter data being significantly smaller than that from self-boring pressuremeter tests at the same depth. Based on quantitative analysis, the disturbance degree computed from the measured results has a low sensitivity to the soil depth and a strong negative correlation with the strain level of the soil. This study provides an effective method for predicting the stiffness parameters of structured soil based on in-situ tests.     

Horizontal stiffness evaluation of geogrid-stabilized aggregate using shear wave transducers

Lateral restraint resulting from the interlock between geogrid and aggregate is recognized as a primary mechanism governing the load-bearing behavior of a geogrid-stabilized pavement base course. However, the level of geogrid–aggregate interlock and the local stiffness enhancement due to the lateral restraint has not been adequately quantified. In this paper, a new experimental method is proposed to evaluate the stiffness enhancement provided by the interlock of the geogrid–aggregate composite system using shear wave transducers. Repeated load triaxial tests were conducted to determine the resilient modulus and deformation characteristics of both geogrid-stabilized and unstabilized base course aggregates. The stabilized test specimens were evaluated for two geogrid types with rectangular and triangular apertures. For the shear wave measurements, three pairs of bender elements fixed at each mounting base were installed diametrically on the triaxial test specimens at three different locations above the mid-height level, where the horizontal shear modulus profiles of the geogrid-stabilized and unstabilized specimens were determined. The experimental results indicate that the shear modulus profiles obtained as a function of confinement changed significantly based on the geogrid inclusion and type, whereas there were no considerable changes in the resilient moduli from the different specimens, as they were only influenced by the applied stress states. The shear moduli estimated in the vicinity of the geogrid were greater than those at locations farther away from the geogrid, which was installed at the mid-height of the specimen. The shear modulus profiles varied according to the confining stress, and the shear modulus ratio of the stabilized to unstabilized specimens clearly demonstrated the stiffness enhancement provided by the two different geogrids. Accordingly, the shear modulus profiles estimated from the horizontal shear wave measurements of the bender element can be effectively used to determine the mechanically stabilized layer characteristics of a geogrid, and therefore quantify the local stiffness enhancement provided by the geogrid–aggregate interlock.     

Laboratory measurements of small strain properties of dry sands by bender element

The S-wave and P-wave velocities in dry sands are simultaneously measured by a single pair of bender elements (BE) incorporated into a standard resonant column (RC) apparatus with a torsional shear (TS) function. The small strain properties, including shear modulus G₀, constrained modulus M₀ and Poisson's ratio υ, are determined for specimens at various densities and confining pressures. The results show that the G₀ values obtained from the BE tests agree well with those from RC and TS tests, indicating the reliability of the signal interpretation and the testing system. Furthermore, the G₀ data of the present test series is in good agreement with the data from the literature. The results also show that G₀ increases faster than M₀ as the soil density and the confining pressure increase. In terms of Poisson's ratio, it decreases with an increasing soil density and confining pressure and generally lies in the range of 0.18–0.32 for the tested sands. Empirical equations are established to approximately estimate Poisson's ratio from the measured G₀ or M₀ values.     

砂土小应变动力特性弯曲–伸缩元联合测试试验研究

近年来弯曲元在小应变动力特性测试中得到了广泛应用,但对弯曲–伸缩元的联合测试研究较少,国内对弯曲–伸缩元联合测试的研究几近空白。采用弯曲–伸缩元对福建砂进行了剪切波和压缩波联合测试,通过更宽区段激发频率和不同分析方法对剪切波速和压缩波速的确定进行了系统分析,得到了可靠的剪切波和压缩波传播时间确定方法。采用10~20 k Hz峰值法和互相关法可较方便准确地确定剪切波传播时间;压缩波初始到达较易判断,激发频率对压缩波速影响较小。利用弯曲–伸缩元联合测试得到剪切模量G_0和侧限模量M_0,试验结果表明围压和孔隙比对G_0的影响程度均较对M_0的影响程度大。通过剪切波速和压缩波速可计算得到泊松比,随密实度和围压的增大泊松比均以线性规律减小。为弯曲–伸缩元的进一步应用提供了有效的方法。     

上海黏性土的初始剪切模量试验研究

以上海天然沉积黏性土②~⑥层土为研究对象,利用共振柱仪器实现了各土层在不同固结压力下的弯曲元和共振柱试验,得到了各层土体小应变水平下的初始剪切模量。试验结果表明,利用弯曲元试验时域初达波法和时域峰值法能得到与现场单孔波速原位测试结果相一致的剪切波速;共振柱试验得到的土体小应变初始剪切模量与弯曲元试验结果基本一致。分析表明,在所试验的各层土中,第③层淤泥质粉质黏土和第④层淤泥质黏土的剪切模量相对较小,第⑥层土的剪切模量最大;第②、⑤层土的剪切模量接近,且大于③、④层,小于第⑥层土,这与土样的实际天然状态是相吻合的。利用Rampello公式可较好地拟合上海黏性土的初始剪切模量,所得的拟合曲线可用来确定各土层在不同深度处的初始剪切模量。     

A note on influence of stress anisotropy on the Poisson's ratio of dry sand

In this study, extender and bender element tests were conducted investigating the small-strain Poisson's ratio of variable sands, with a focus on the effect of stress anisotropy in order to quantify the sensitivity of Poisson's ratio to the applied deviatoric stress. Four different uniform sands were tested, including a biogenic sand, a crushed rock and two natural sands, covering a wide range of particle shapes. From these sands, eleven samples were prepared in the laboratory and were tested under variable stress paths,maintaining a constant mean effective pressure while increasing the deviatoric compressive load. Under the application of these given stress paths, the data analysis indicated that the sensitivity of Poisson's ratio to the stress ratio was more pronounced for sands with irregularly shaped particles in comparison to sands with fairly rounded and spherical grains. For sands with very irregularly shaped particles, the increase of Poisson's ratio from the isotropic to the anisotropic stress state reached 50%, while this increase for natural sands with fairly rounded particles was in the order of 20%.     

Local stiffness characteristic of geogrid-stabilized aggregate in relation to accumulated permanent deformation behavior

Accumulated permanent deformation is the primary source of damage in a pavement unbound aggregate base layer. Mechanical stabilization with the help of a geogrid installed in unbound aggregate base provides lateral restraint to the flexible pavement, however, the local stiffness characteristic of geogrid-stabilized aggregate in relation to permanent deformation behavior is not clearly known. This study presents variations in shear modulus properties of geogrid-stabilized and unstabilized aggregate specimens in relation to permanent deformation accumulation. To characterize the local stiffnesses near and far away from geogrid, two pairs of bender elements were inserted in triaxial specimens as shear wave transducers. With the number of load cycles, the variations in the shear wave velocities at two different specimen heights were monitored. The test results show that, after the specimen preparation, the shear modulus near the geogrid was greater than that far away from the geogrid. Further, the shear modulus estimated at both levels of unstabilized specimen was similar to that estimated far away from geogrid in the mechanically stabilized specimen. This study demonstrates that the local stiffness of aggregate can be monitored by using the bender elements in relation to trends in permanent deformation behavior, and suggests the bender element systems can be effectively used to validate the benefits of geogrid stabilization by quantifying local stiffnesses at various levels of accumulated permanent deformation.     

Small strain stiffness and stiffness degradation curve of Bangkok Clays

The small strain stiffness and the stiffness degradation curve of soils are required in advanced numerical analyses of geotechnical engineering problems. The shear modulus at small strain (G_max) and the reference shear strain parameter (γ_0.7) are, for instance, two of the input parameters in a finite element analysis with the hardening soil model with small strain stiffness. The stiffness and strength parameters for the hardening soil model of soft and stiff Bangkok Clays has recently been published (Surarak et al., 2012). This paper is a continuation on the previous study on the stiffness of Bangkok Clay, and focuses on the small strain characteristics. The data are from the Bangkok MRT Blue line project as well as comprehensive studies at Chulalongkorn University and the Asian Institute of Technology. Based on these laboratory and field testing data, the parameters G_max and γ_0.7 can be determined using well-known empirical correlations and the concept of threshold shear strain. Finally, a comparison between the measured data and predictions is made.     

Relationship between Shear Wave Velocity and Stresses at Failure for Weakly Cemented Sands During Drained Triaxial Compression

Small strain shear modulus (G_max) has been a parameter of choice used to assess the strength and deformation behavior of cemented and other sensitive soils. The influence of density, effective confining stress, stress anisotropy, and cement content on shear wave velocity (v_s)/shear modulus has been studied extensively and published. There are, however, very few studies on the effects of cement/strength degradation during shear on the shear wave velocity/shear modulus, which may be important for reliable and accurate prediction of mechanical behavior of cemented sands. The objective of this study is to evaluate the effect of cement degradation on shear wave velocity/shear modulus by measuring continuously the shear wave velocity during shear. A laboratory testing program was performed using samples of silty sand artificially cemented with Ordinary Portland Cement (OPC). Shear wave velocity was measured continuously within the triaxial cell during the shear phase using torsional ring transducers. G_max was calculated using the shear wave velocity and the corresponding density during shear. Results from this study suggest that G_max reaches a peak value before σ′₁ reaches a failure stress and this behavior is believed to be an indicator of bond breakage or destructuring. G_max calculated at various stages during shear showed that the cement and modulus degradation can be represented by a simple index using G_max. The results of this study suggest that there may be a unique relationship between small strain shear modulus and effective stresses at failure for dilative soils implying that in situ shear wave velocity measurements may be used to estimate effective stress strength parameters or as a precursor to failure in weakly cemented soils.     

Strength enhancement of geotextile-reinforced carbonate sand

The mechanical behavior of carbonate sand reinforced with horizontal layers of geotextile is invetigated using a series of drained compression triaxial tests on unreinforced and reinforced samples. The main factors affecting the mechanical behavior such as the number of geotextile layers, their arrangement in specimens, confining pressure, particle size distribution, geotextile type and relative density of samples were examined and discussed in this research. To make a precise comparison between the behavior of reinforced siliceous and carbonate sand, triaxial tests were performed on both types of sands. Results indicate that geotextile inclusion increases the peak strength and strain at failure, and significantly reduces the post-peak strength loss of carbonate specimens. The amount of strength enhancement rises as the number of geotextile layers increases while two other parameters including confining pressure and particle size affect adversely. The strength enhancement of reinforced carbonate sand is greater than the corresponding siliceous sample at high axial strains. Reinforced and unreinforced carbonate specimens exhibit more contractive behavior than their corresponding siliceous samples and tend to dilate at higher axial strains. By increasing the relative density of the samples, the peak strength of reinforced specimens rises due to enhanced interlocking between geotextile layers and sand particles. This process continues as long as the geotextile is not ruptured. The utilization of geotextiles with high mass per unit areas was found to be uneconomical due to slight differences between the strength augmentation of geotextiles with high and low mass per unit areas. It should be noted that geotextile layers limit the lateral expansion of specimens which leads to changing the failure pattern from a shear plane to bulging between the adjacent layers of geotextile.