Learning of Dynamic Soil Behavior from Downhole Arrays

An increasing number of downhole arrays are deployed to measure motions at the ground surface and within the soil profile. Measurements from these arrays provide an opportunity to improve site response models and to better understand underlying dynamic soil behavior. Parametric inverse analysis approaches have been used to identify constitutive model parameters to achieve a better match with field observations. However, they are limited by the selected material model. Nonparametric inverse analysis approaches identify averaged soil behavior between measurement locations. A novel inverse analysis framework, self-learning simulations (SelfSim), is employed to reproduce the measured downhole array response while extracting the underlying soil behavior of individual soil layers unconstrained by prior assumptions of soil behavior. SelfSim is successfully applied to recordings from Lotung and La Cienega. The extracted soil behavior from few events can be used to reliably predict the measured response for other events. The field extracted soil behavior shows dependencies of shear modulus and damping on cyclic shear strain level, number of loading cycles, and strain rate that are similar qualitatively to those reported from laboratory studies but differ quantitatively.     

In Situ Measurement of Nonlinear Shear Modulus of Silty Soil

A new field test method to evaluate in situ nonlinear shear modulus of soils was developed. The method utilizes a drilled shaft as a cylindrical, axisymmetric source for shear loading of soil at depth. The applicability of the test method was studied by conducting small-scale, prototype experiments at a “calibration” field site in Austin, Texas. Numerous conventional in situ and laboratory measurements were performed to characterize the soil at the field site. The “small-scale” nature of the tests involved using a 381?mm (15?in.) diameter, 3.7?m (12?ft) long drilled shaft. Experimental results from this field study provided an opportunity to compare laboratory and field measurements of the G?log?γ and G/Gmax?log?γ curves. This comparison was used to investigate the accuracy of common procedures relating field and laboratory modulus reduction curves. Nonlinear modulus measurements were performed at depths of 1.8?to?2.1?m (6?to?7?ft) in a silt (ML). The field G/Gmax?log?γ curve for this soil at low confining pressures are in general agreement with the laboratory curve from an intact specimen as well as empirical curves.     

Stress Integration Approach in Resonant Column and Torsional Shear Testing for Soils

Determination of strain in resonant column and torsional shear (RC/TS) tests is complicated due to nonuniform stress–strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate levels, however, the approach is less accurate when performing the tests at higher strains. The stress integration approach involving integration of an assumed soil stress–strain model was developed to account for this problem more precisely. This approach was used to generate the plots of equivalent radius ratio versus strain developed based upon shear modulus and damping. Results showed that the equivalent radius ratio curves converge to a value of approximately 0.8 at low strains and decrease as strain increases. The equivalent radius ratio curves based upon damping decrease to significantly lower values at high strain than curves based upon shear modulus. This study suggests that using the same values of equivalent radius ratio to calculate strains for both shear modulus and damping is not appropriate. The stress integration approach provides an accurate analysis technique for evaluating both modulus and damping behavior of soil, over any range of strains in RC/TS testing.     

Small-Strain Behavior of Granular Soils. I: Model for Cemented and Uncemented Sands and Gravels

A simple formulation is presented that predicts the nonlinear small strain behavior of cemented and uncemented granular soils. Its performance is evaluated through the comparison of model predictions to results from laboratory tests. A companion paper evaluates the performance of this model implemented in a site response analysis code through comparison with the measured response at two sites. The formulation for the maximum shear modulus, Gmax, which is selected through the evaluation of existing formulations and data, is presented with the hysteretic model developed to describe the shear modulus reduction and damping increase with increasing strains. Few parameters are needed to predict the small strain response, and correlations between model parameters and index properties of granular materials are presented when possible. The model, SimSoil, is shown to capture the cyclic response for sands and gravels with varying densities over a wide range of pressures measured in laboratory tests, including cases when cementation is present.     

不同影响因素下路用黄河泥沙动剪切模量和阻尼比试验及理论模型研究

沿黄河高速公路建设过程中,黄河泥沙作为路基填料的可行性已经得到验证和重视,然而目前有关黄河泥沙作为路基填料的动力特性的研究较少.本文利用英国GDS动态三轴试验系统,对取自黄河中下游郑州段的泥沙进行应力控制的动三轴试验,探究了围压、相对密实度和试验频率对黄河泥沙动剪应力–动剪应变关系、动剪切模量G和阻尼比D的影响,绘制了动剪应力–动剪应变关系骨干曲线和滞回曲线.结果表明,黄河泥沙的动剪切模量、阻尼比与剪应变关系可以用Hardin双曲线模型描述,围压对G和D的影响较大、试验频率对G和D的影响较小.综合与其他土体的动力特性对比表明,黄河泥沙动剪切模量折减曲线规律以及阻尼比D曲线规律和其他土体相符,其动力特性更接近于粉土和砂土,但与其他土体并不完全一致,具有一定的特殊性.最后,本文考虑了围压、相对密实度的影响,并结合现有经验公式,建立可以较好描述黄河泥沙最大动剪切模量G_max与围压、孔隙比关系的经验公式,同时建立了动剪切模量比G/G_max和D的数学模型,拟合结果显示,建立的模型能较好地描述黄河泥沙的G/G_max和D随剪应变的变化...     

Nonlinear Stress-Strain Relationship of Soil Reinforced with Flexible Geofibers

A nonlinear stress-strain relationship of soil reinforced with flexible geofibers under static loading is derived based on a nonlinear elastic stress-strain relationship of soil and a linear elastic stress-strain relationship of geofibers in the paper. This investigation includes the following aspects: First, the homogenization technique is introduced to find the volume average stress tensor and volume average strain tensor and further an elastic incremental stress-strain relation is introduced to describe deviatoric shear stress-axial strain relationship of equivalent homogeneous geofiber-reinforced soil. Second, the relation of geofiber numbers, content, mechanical behavior, distribution, and geometrical features to shear modulus of geofiber-reinforced soil is expressed and assessed by employing an elastic energy method. Third, the deviatoric shear stress and axial strain curves of geofiber-reinforced soil are calibrated by laboratory testing data of geofiber reinforced soil samples. Finally, the theoretical computational curves of geofiber reinforced soil are compared with the curves calibrated by testing data of geofiber reinforced soil. The model prediction has a good agreement with experimental results.     

Influence of In Situ Factors on Dynamic Response of Piedmont Residual Soils

The in situ chemical and physical weathering of igneous and metamorphic rocks, indentified as the process of formation of Piedmont residual soils, is a fairly well understood phenomenon. However, the effect this weathering has on the physical, mechanical, and dynamic properties of the rock∕soil is not understood fully. This study focuses on the dynamic shear modulus, G, and material damping ratio, D, of this soil formation for low- to mid-level amplitudes of vibration. The paper presents laboratory test results and correlations that demonstrate the effects that the degree of weathering has on these properties for various levels of confining pressure and shear strain amplitude. A total of 12 specimens of Piedmont residual soils from different depths were tested in a Resonant Column (RC) device. The specimens tested were SM and ML soils according to the USCS classification. The low-amplitude shear modulus and damping values were found to be similar to those reported in the literature from laboratory and in situ tests on the same type of soils. It was found that weathering, void ratio, and apparent overconsolidation ratio exert a noticeable influence on the dynamic response as a result of variations in confining pressure. The understanding of these effects will allow for a better prediction of phenomena such as soil amplification, which may result in damage to existing civil infrastructure founded on these soil deposits. The response in free field soil deposits compared with that of soils experiencing added confining stresses due to foundation loading appears to vary significantly in these geologic formations. Threshold strain and the variation of damping, D, with the normalized shear moduli, G∕Gmax, fall within the same range as those recently reported by other authors in similar soils.     

Seismic Response of Liquid Storage Tanks Incorporating Soil Structure Interaction

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored.     

Model for Dynamic Shear Modulus and Damping for Granular Soils

This paper presents a simple four-parameter model that can represent the shear modulus factors and damping coefficients for a granular soil subjected to horizontal shear stresses imposed by vertically propagating shear waves. The input parameters are functions of the confining pressure and density and have been derived from a generalized effective stress soil model referred to as MIT-S1. The predicted shear moduli and damping factors are in excellent agreement with high quality resonant column test data on remolded sands and confining pressures ranging from 30 kPa to 1.8 MPa. The proposed model has been implemented in a frequency domain computer code. By simulating the variations in stiffness and damping with confining pressure, the proposed model provides a more realistic simulation of ground amplification that does not filter out high frequency components of the base excitation.     

Effects of Disturbance on Undrained Strengths Interpreted from Pressuremeter Tests

Although the cylindrical cavity expansion theory should provide a sound basis for obtaining the undrained shear strength of clays from pressuremeter tests, the interpreted strengths are often inconsistent with data measured in high-quality laboratory tests. This paper investigates how the pressuremeter results are affected by disturbances that inevitably occur during device installation. The installation of self-boring and displacement-type pressuremeters is simulated using strain path analyses, with realistic effective stress-strain-strength properties described by the MIT-E3 model. Derived strengths obtained from the simulated expansion of displacement-type pressuremeters tend to underestimate the in situ∕cavity expansion strength by amounts that depend on the relative volume of soil displaced, the time delay prior to testing, and the initial overconsolidation ratio of the clay. Interpretation procedures using the simulated contraction curves give much more reliable estimates of the true undrained shear strength. The simulated disturbance effects of self boring lead to derived peak shear stresses that are significantly higher than the reference undrained shear strengths. This overestimate depends on the volume of soil removed during installation and is enhanced when the finite membrane length is included in the analyses. Self-boring pressuremeter data from a well-documented test site in Boston confirm the general character of the predicted pressuremeter stress-strain behavior. The theoretical analyses underestimate the peak strengths derived from self-boring pressuremeter (SBPM) expansion tests, but match closely the measured postpeak resistance in the strain range of 3–6% (saddle point condition). Saddle point strengths are similar in magnitude to the shear strengths measured in laboratory undrained triaxial compression tests at this site. The current predictions are not able to explain the very high shear strengths derived from the SBPM contraction curves.     

Vertically Loaded Single Piles in Gibson Soil

The available closed-form solutions for vertically loaded piles have been, strictly speaking, limited to homogeneous soil, or nonhomogeneous soil with the shear modulus as a power of depth. The latter solutions—based on a zero shear modulus at ground surface—are generally sufficiently accurate for normally consolidated soil. For overconsolidated soil, however, there is generally a nonzero shear modulus at the surface, which may affect pile response. In this note, rigorous closed-form solutions are established to account for the nonhomogeneity of soil profile with nonzero shear modulus at ground surface. The solutions are developed using a load transfer approach, and are shown to give satisfactory results in comparison with a more rigorous continuum-based numerical approach, when the proposed load transfer factors are adopted.     

Seismic Compression of Two Compacted Earth Fills Shaken by the 1994 Northridge Earthquake

Seismic compression is defined as the accrual of contractive volumetric strain in unsaturated soil during strong shaking by earthquakes. We document and analyze two case histories (denoted school site and site A) of ground deformation from seismic compression in canyon fills strongly shaken by the Northridge earthquake. Site A had ground settlements up to about 18 cm, which damaged a structure, while the school site had settlements up to about 6 cm. For each site, we perform decoupled analyses of shear and volumetric strain. Shear strain is calculated using one-dimensional and two-dimensional ground response analyses, while volumetric strain is evaluated from shear strain using material-specific models derived from simple shear laboratory testing that incorporates important effects of fines content and as-compacted density and saturation. Analyses are repeated using a logic tree approach in which weights are assigned to multiple possible realizations of uncertain model parameters. At the school site, predicted settlements appear to be unbiased. At site A, the analyses successfully predict the shape of the settlement profile along a section, but the weighted average predictions are biased slightly too low. We speculate that the apparent site A bias can be explained by limited resolution of the site stratigraphy, bias in laboratory-derived volumetric strain models, and/or uncertainty in the estimated earthquake-induced settlements.     

Analytical Solution for Biot Flow–Induced Damping in Saturated Soil during Shear Wave Excitations

This paper presents a theoretical study of Biot flow–induced damping in saturated soil during shear wave excitations. The solid skeleton is treated as equivalent linear. Biot flow–induced damping is evaluated for the cases of resonant column tests and site response analysis, based on the spectral response of a soil column/layer under harmonic torsional/horizontal excitations. Closed-form analytical solutions indicate that Biot flow–induced damping is hydraulic conductivity and frequency dependant. At the first resonance in a resonant column test, Biot flow–induced damping is dependent on a dimensionless hydraulic conductivity parameter K. For K within the range of 0.01 to 100, corresponding to coarse sands and clean gravels, Biot flow–induced damping may have an important contribution to total soil damping, especially at small strain levels. For site response analysis, Biot flow–induced damping should be considered for coarse sands and clean gravels, but can be practically neglected for fine sands, silts, and clays. The effects of soil porosity, mass coupling, and non-Poiseuille flow on Biot flow–induced damping are discussed.     

Stochastic Finite-Element Analysis of Seismic Soil–Structure Interaction

A procedure is presented for the probabilistic analysis of the seismic soil-structure interaction problem. The procedure accounts for uncertainty in both the free-field input motion as well as in local site conditions, and structural parameters. Uncertain parameters are modeled using a probabilistic framework as stochastic processes. The site amplification effects are accounted for via a randomized relationship between the soil shear modulus and damping on the one hand, and the shear strain of the subgrade on the other hand, as well as by modeling the shear modulus at low strain level as randomly fluctuating with depth. The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented by their coordinates with respect to the polynomial chaos basis. These coordinates are then evaluated by a combination of weighted residuals and stratified sampling schemes. The expansion can be used to carry out very efficiently, extensive Monte Carlo simulations. The procedure is applied to the seismic analysis of a nuclear reactor facility.     

Strain-Dependent Dynamic Properties of Remolded Sand-Clay Mixtures

A series of undrained cyclic torsional simple shear tests using hollow cylindrical torsional shear apparatus was carried out to investigate the dynamic shear moduli and damping properties of clayey specimens with various sand contents and plasticity indices. The clayey soils used were collected from various sites along the coast of west Japan. Among these clayey soils, a clay sample with intermediate plasticity and another with high plasticity were mixed with silica sand at different proportions in order to examine the dynamic properties of sand-clay mixtures. In addition, experiments were carried out on undisturbed and remolded natural clay specimens with various plasticities. The effects of plasticity, loading frequency and confining pressure on the strain dependent normalized shear modulus and damping ratio were examined. Based on the results, empirical correlations for predicting the normalized shear modulus and damping ratio of remolded sand-clay mixtures at various shear strain levels were proposed.     

In Situ Pore-Pressure Generation Behavior of Liquefiable Sand

To overcome current limitations in predicting in situ pore-pressure generation, a new field testing technique is used to measure directly the coupled, local response between the induced shear strains and the generated excess pore pressure. The pore-pressure generation characteristics from two in situ liquefaction tests performed on field reconstituted specimens are presented, including the pore- pressure generation patterns at various strain levels, the observed stages of pore-pressure generation, and pore-pressure generation curves. Comparisons of the in situ pore-pressure generation curves with data in the literature and from laboratory strain-controlled, cyclic direct simple shear tests support the in situ testing results. In addition, the effects of effective confining stress on threshold shear strain and pore- pressure generation curves are discussed. Comparisons of the rate of pore-pressure generation among the in situ tests, laboratory strain-controlled tests, and a model based on stress-controlled tests reveal that in situ pore pressures generated in reconstituted soil specimens during dynamic loading develop more similarly to those from cyclic strain-controlled laboratory testing. This observation implies that the evaluation of induced strains rather than induced shear stresses may be more appropriate for the simulation of pore-pressure generation.     

Small-Strain Behavior of Granular Soils. II: Seismic Response Analyses and Model Evaluation

Using the recorded response at two vertical array sites, the SimSoil model presented in the companion paper is evaluated. The SimSoil model, which describes the small strain nonlinear behavior of granular materials, is implemented as a material model in AMPLE2000, a nonlinear, one-dimensional site response analysis code. Shear wave velocity profiles and laboratory test data available for both the La Cienega site, which was instrumented over 250?m, and the Lotung site, which was instrumented over 47?m, were used to determine SimSoil model parameters. Predictions from AMPLE2000 are compared with the measured response at several elevations for earthquakes that resulted in both nonlinear and nearly linear soil behavior. Using the available laboratory data and known input motions, the predictions of the response at these sites matched the recorded response well for varied magnitudes of shaking with a single set of parameters for each site.     

Nonlinear Analysis of Torsionally Loaded Piles in a Two-Layer Soil Profile

This paper presents a method for predicting the nonlinear response of torsionally loaded piles in a two-layer soil profile, such as a clay or sand layer underlain by rock. The shear modulus of the upper soil is assumed to vary linearly with depth and the shear modulus of the lower soil is assumed to vary linearly with depth and then stay constant below the pile tip. The method uses the variational principle to derive the governing differential equations of a pile in a two-layer continuum and the elastic response of the pile is then determined by solving the derived differential equations. To consider the effect of soil yielding on the behavior of piles, the soil is assumed to behave linearly elastically at small strain levels and yield when the shear stress on the pile-soil interface exceeds the corresponding maximum shear resistance. To determine the maximum pile-soil interface shear resistance, methods that are available in the literature can be used. The proposed method is verified by comparing its results with existing elastic solutions and published small-scale model pile test results. Finally, the proposed method is used to analyze two full-scale field test piles and the predictions are in reasonable agreement with the measurements.     

Effects of Low-Number Previbration Cycles on Dynamic Properties of Dry Sand

This study presents direct evidence for the influence of the previbration cycles induced in the conventional resonant column tests on the measured dynamic properties of a dry sand. The tests were performed on an energy-injecting virtual-mass resonant column system, under which the material properties can be measured at a very low number of previbration cycles (<20). The test results show that for the sand tested at strain amplitudes beyond the elastic threshold, the influence of previbration is moderate on modulus but very significant on damping, particularly in the low range of the numbers of vibration cycles (<500). This observation is consistent with findings in the literature, which are based on combinations of static and dynamic test data. The effects of the low number of vibration cycles on the normalized modulus reduction and damping curves have also been examined. The results show that the modulus reduction curves are not significantly affected by these previbration cycles, whereas the damping curves in the range exceeding the elastic threshold are.     

Interpretation of Secant Shear Modulus Degradation Characteristics from Pressuremeter Tests

Nonlinear shear modulus degradation characteristics are of interest in many geotechnical engineering applications, such as ground deformation caused by seismic shaking and deep excavations in clay, weathered rock, and stabilized soil. This paper presents an approach to derive the secant shear modulus degradation characteristics from in situ pressuremeter tests, which is based on a digital filter algorithm. The algorithm is described, and data preparation procedures are presented. Use of the algorithm is illustrated by means of pressuremeter data for soils stabilized with deep mixing methods on the Boston central artery/tunnel (CA/T). The nonlinear secant shear modulus degradation characteristics from the digital filter approach are shown to be in good agreement with those from the curve fitting and transformed-strain approaches. They also compare favorably with the results of other in situ and laboratory tests performed in conjunction with the CA/T stabilized soils. The algorithm is implemented by a 26-line MATLAB code in an appendix of the paper.