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.     

Comparison of Soil Hydraulic Property Measurement Methods

Unsaturated and saturated soil hydraulic properties were determined and compared for three sandy soils at adjacent field sites. Drying soil–water retention curves were measured on soil specimens using a pressure plate apparatus. Saturated hydraulic conductivities (Ks) were measured with a Guelph permeameter and falling head tests. Parameter optimization was used to simultaneously estimate the drying and wetting soil–water retention and hydraulic conductivity curves from cone permeameter and multistep inflow/outflow data. Ks values from all test methods were within an order of magnitude of each other at each site and, as expected, trended with bulk density. The Guelph permeameter generally yielded the highest Ks values. The soil–water retention curves were similar in shape, except for the cone permeameter curves, which had steeper slopes due to rapid flow of water into the soil. Relative hydraulic conductivity curves were similar in character to the soil–water retention curves. Each method provided important information about the soil hydraulic properties. No one method provided the entire range of information provided by all of the tests combined, and no one method was found to be superior to the others.     

Wastewater Reuse Effects on Soil Hydraulic Conductivity

The wastewater total suspended solids (TSS) concentration effects on the saturated hydraulic conductivity, Ks, of a clay and a loam soil were investigated on laboratory repacked soil cores by a constant head permeameter. Both municipal wastewater (MW) and artificial wastewater (AW) with different TSS concentrations were used, with the aim to evaluate, by comparison, the effects of biological activity. The development of a surface sealed layer was investigated in loam soil columns supplied with AW and equipped with water manometers at different depths to detect the hydraulic head gradient changes. In the loam soil, Ks reduced to about 80% of the initial value after infiltration of 175?mm of MW with TSS = 57–68?mg?L?1. Reductions in Ks were more remarkable in the clay soil. An empirical relationship was proposed to predict the relative hydraulic conductivity, Kr, i.e., the ratio between actual and initial hydraulic conductivity versus the cumulative density loading of TSS. Hydraulic head gradients in the top layer (0–20?mm) of the soil columns increased during application of AW, as a consequence of the formation of a sealed layer, denoting that the surface pore sealing was the main mechanism responsible for the observed Ks reductions. Laboratory data were gathered in a numerical simulation code specifically created to assess the consequences of Ks reduction on water movement through the soil profile. Simulation of both ponded and sprinkler irrigation with MW resulted in reduced infiltration and increased surface ponding condition compared to the application of fresh water (FW).     

Estimating the Hydraulic Conductivity of Landfilled Municipal Solid Waste Using the Borehole Permeameter Test

This paper reports the in situ field saturated hydraulic conductivity of municipal solid waste at a landfill in Florida. The saturated hydraulic conductivity (Ks) was estimated at 23 locations using the borehole permeameter test, a method commonly used for determination of the Ks of unsaturated soil. The Ks of the landfilled waste was found to range from 5.4×10?6 to 6.1×10?5?cm/s. The Ks was found to be on the lower end of the range of Ks reported by previous studies. The hydraulic conductivity of the waste decreased with depth, the likely result of greater overburden pressures associated with deep locations of the landfill. Permeability values (kw) of the landfilled waste calculated based on Ks were compared with permeability values estimated using air as the fluid (air permeability, ka). Values of ka were found to be approximately three orders of magnitude greater than those of kw. The lower permeability of the waste to water was primarily attributed to entrapped gas. Other factors such as potential clogging of media and short-circuiting of air along the well may also have contributed to the differences in ka and kw.     

Hydraulic Conductivity Measurement from On-the-Fly uCPT Sounding and from VisCPT

Detailed profiles of hydraulic conductivity are recovered from the deployment of direct-push permeameters at the Geohydrologic Experimental and Monitoring Site, Kansas. Measurements with thin tapered tips, and with standard cone penetration test (uCPT) tips, show only minor differences, suggesting that tip-local disturbance effects are small, and that routine uCPT measurements are therefore representative of pristine conditions. Permeameter measurements are correlated against closely deployed uCPT measurements, estimates of hydraulic conductivity from uCPT sounding correlations, and from grain size correlations derived from both vision CPT (VisCPT) and from cone metrics. On-the-fly evaluations of hydraulic conductivity require that the tip-local pressure field is both steady and partially drained. Continuous penetration is shown to yield pore pressures sufficiently close to steady to enable conductivities to be directly determined. Cone metrics of cone resistance, sleeve friction, and pore pressure ratio are shown to be sufficient to discriminate between partially drained and undrained behavior, and therefore to define the permissible regime where conductivities may be determined from uCPT sounding data. Estimates of hydraulic conductivities from uCPT sounding data are shown to correlate with independently measured magnitudes of hydraulic conductivity recovered using the permeameter tests. However, most of hydraulic conductivities from the permeameter tests (4.5?cm length screen) are underpredicted, suggesting that storage effects, the inability to reach a steady state, or the effects of dilation may influence the response. Profiles of hydraulic conductivities evaluated from the on-the-fly method also correlate well with the permeameter measurements. Predictions from soil classification and from VisCPT methods are also capable of estimating conductivities, with soil classifications giving the closest correlations of these two for this particular suite of data.     

Postconstruction Changes in the Hydraulic Properties of Water Balance Cover Soils

Hydraulic properties of soils used for water balance covers measured at the time of construction and one to four years after construction are compared to assess how the hydraulic properties of cover soils change over time as a result of exposure to field conditions. Data are evaluated from ten field sites in the United States that represent a broad range of environmental conditions. The comparison shows that the saturated hydraulic conductivity (Ks) can increase by a factor of 10,000, saturated volumetric water content (θs) by a factor of 2.0, van Genuchten’s α parameter by a factor of 100, and van Genuchten’s n parameter can decrease by a factor of 1.4. Larger changes occur for denser or more plastic fine-textured soils that have lower as-built Ks, α, and θs and higher as-built n, resulting in a reduction in the variation in hydraulic properties that can be attributed to compaction. After two to four years, many water balance cover soils can be assumed to have Ks between 10?5 and 10?3?cm/s, θs between 0.36 and 0.40, α between 0.002 and 0.2?kPa?1, and n between 1.2 and 1.5. The data may be used to estimate changes in hydraulic properties for applications such as waste containment, where long-term maintenance of hydraulic properties in shallow engineered soil layers is important.     

Study of Variation of Saturated Hydraulic Conductivity with Time

The variation of the saturated hydraulic conductivity with time, as a function of temperature, has been studied involving field measurement at the College of Aboureyhan Research farm. The College of Aboureyhan is a part of the University of Tehran and the above-mentioned farm is located in the lowland of the southeast of Tehran, Iran. For the purposes of this research study it was planned to measure and record the field data in a plot of 18?m2. The hydraulic conductivity data were measured in 18 test points inside the study area using the inverse auger-hole method. Experiments were carried out from August 16, 2005 to June 14, 2006. The recorded filed data were then used to calculate the saturated hydraulic conductivity data using Excel software. The relationship between soil temperature, water temperature, and also water’s viscosity with hydraulic conductivity, respectively, were determined. The results of the statistical analysis involving SAS software demonstrated that the variation of temperature can considerably affect the saturated hydraulic conductivity values. The results showed that the lowest values of Ks were obtained in the winter when the water, soil, and air temperature were minimal and these values increased when the temperature increased. The effect of the means of daily K values (values measured in each sample date Kd) and their corresponding soil temperature adjusted values on drain spacing was determined compared with the average of total K values.?The maximum over- and underestimation of drain spacing was 19.1 and 23.3%, respectively, for measured values. These estimations were 9 and 16% for adjusted ones. Also, using the average values of K measured in the soil temperature range of 17–23°C resulted in a lower over- or underestimation of drain spacing.     

Validation of a Predictive Form of Horton Infiltration for Simulating Furrow Irrigation

Due to spatially varying conditions the improvement of furrow irrigation efficiency should be sought not just for a limited number of furrows or for one specific irrigation event. A simplified predictive modeling approach of the averaged advance-infiltration process is proposed in this paper. Horton’s equation, derived from the asymptotic form of the Talsma-Parlange infiltration equation, allows us to use a predictive approach for the advance infiltration process by means of the exact solution of the Lewis and Milne water balance equation. The references to the works of White and Sully, for a surface point source, result in the use of parameters which characterize the hydraulic properties of the soil: Δθ (saturated water content minus initial water content); Ks (saturated conductivity); and λc (macroscopic capillary length). The physical meaning of parameters involved in the proposed modeling is attested using field experiments carried out in a loamy soil plot context. Assuming a same Δθ measured value before irrigation for the whole of a 30 furrow sample, the averaged values of λc and Ks obtained from calibration on the advance trajectory are comparable to those derived from local infiltration tests (disk permeameter and double ring methods). The applicability of the model is then extended to heavy clay soil where the parameters λc and Ks still agree with the values proposed in the literature. This paper can be considered as a contribution to the development of a tool for evaluating the impact of irrigation practices on the efficiency at the plot and cropping season scale.     

Determination of Hydraulic Conductivity Using Piezocone Penetration Test

An elastoplastic, finite-strain, coupled theory of mixtures in an updated Lagrangian reference frame is applied to the piezocone penetration test to estimate the hydraulic conductivity of the soil via analysis of the steady-state excess pore pressure generated during piezocone penetration. The results of this approach were compared with piezocone penetration test data. It showed that reliable hydraulic conductivities can be estimated conveniently without performing pore pressure dissipation tests. This study also shows that the change in the dimensionless excess pore pressure (excess pore pressure is normalized by the effective overburden pressure) at the cone tip is almost constant when the dimensionless hydraulic conductivity (hydraulic conductivity is normalized by the penetration speed and cone radius, hereafter called DLHC) is less than 10?7 or greater than 10?4. It is also shown that the drainage condition around the cone tip is close to a fully undrained condition when the DLHC of the soil is less than 10?7, while it is close to a fully drained condition when the DLHC of the soil is greater than 10?4.     

Numerical Modeling of Nonhomogeneous Behavior of Structured Soils during Triaxial Tests

The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studies. Both end restraint and partial drainage can cause bulging of the triaxial specimen around mid-height. Inhomogeneities due to partial drainage influence the stress–strain behavior during destructuring, a characteristic feature of a structured soil. With an increase in the strain rate, the change in voids ratio during destructuration reduces, but, in contrast, the mean effective stress at which destructuration commences was found to increase. It is shown that the stress–strain behavior of the soil calculated for a triaxial specimen with inhomogeneities, based on global measurements of the triaxial response, does not represent the true constitutive behavior of the soil inside the test specimen. For most soils analyzed, the deviatoric stress based on the global measurements is about 25% less than that for the soil inside the test specimen, when the applied axial strain is about 30%. Therefore it can be concluded that the conventional global measurements of the sample response may not accurately reflect the true stress–strain behavior of a structured soil. This finding has major implications for the interpretation of laboratory triaxial tests on structured soils.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

First-Order Solutions for the Buckling Loads of Euler-Bernoulli Weakened Columns

In this work, closed-form expressions for the buckling loads of a weakened column with different boundary conditions are presented. The cracked-column model is based on the well-known method consisting of dividing the column into two segments connected by a rotational linear spring whose flexibility is related to the crack size and the geometry of the cross section. For the formulation of closed-form expressions, the perturbation method is used and the results are compared with those found by directly solving the eigenvalue problem.     

Piecewise-Linear Model for Large Strain Radial Consolidation

A piecewise-linear model for radial consolidation, called RCS1, is presented. RCS1 accounts for vertical strain, soil self-weight, hydraulic conductivity anisotropy, radial and vertical flows, soil smear, partial drain penetration, unload/reload effects, time-dependent loading, and variable hydraulic conductivity and compressibility during the consolidation process. Soil constitutive relationships are specified using discrete data points and can take nearly any desired form. Soil strains are assumed to occur in the vertical direction and lateral strains are neglected. Drain hydraulic resistance is also neglected. Essentially exact agreement is observed for RCS1 uniform applied stress simulations and Barron free strain theory for problems involving very small strains. RCS1 uniform settlement simulations and Barron equal strain theory are not in exact agreement due to the approximation involved in the Barron theory. For realistic loading and soil conditions, differences are observed between RCS1 uniform applied stress and uniform settlement simulations due to differences in hydraulic conductivity and cross sectional area available for flow near the vertical drain. Estimates of settlement and excess pore pressure obtained using RCS1 are in good agreement with field measurements for a recently preloaded site over San Francisco Bay Mud with prefabricated vertical drains.     

Effects of Silt Content and Void Ratio on the Saturated Hydraulic Conductivity and Compressibility of Sand-Silt Mixtures

The hydraulic conductivity, the coefficient of consolidation, and the coefficient of volume compressibility play major roles on the pore pressure generation during undrained and partially drained loading of granular soils with fines. This paper aims to determine how much these soil parameters are affected by the percentage of fines and void ratio of the soil. The results of a large number of flexible wall permeameter tests performed on 60 specimens of two poorly graded sands with 0, 5, 10, 15, 20, and 25% nonplastic silt are presented and discussed. Hydraulic conductivity measurements were done at effective confining stresses of 50–300 kPa. The evaluation of the data shows that the hydraulic conductivity and the coefficient of consolidation of sands with 25% silt content are approximately two orders of magnitude smaller than those of clean sands. The coefficient of volume compressibility of the sand-silt mixtures is affected in a lesser degree by void ratio, silt content, and confining stress. The influence of the degree of saturation on the laboratory-measured k values is also discussed.     

Measuring the Hydraulic Conductivity of Soil–Bentonite Backfill

The hydraulic conductivity of soil–bentonite backfill in three pilot-scale cutoff walls was measured using laboratory tests on disturbed samples, laboratory tests on undisturbed samples, piezocone dissipation tests, and piezometer tests (also known as slug tests or single-well tests). In addition, a global measurement of the average hydraulic conductivity of the soil–bentonite backfill in one of the cutoff walls was made using the pilot-scale test facility. Two main factors distinguish these five different methods of measuring hydraulic conductivity: remolding and sample size. Remolding of samples tested in American Petroleum Institute filter press equipment significantly reduced their hydraulic conductivity compared to the hydraulic conductivity of undisturbed samples, which were of similar size. For the other tests, where the degree and extent of remolding were less significant, hydraulic conductivity was found to increase as sample size increased, with the global measurement producing the highest value. The existence of bentonite filter cakes on trench walls reduces the influence of sample size on the equivalent hydraulic conductivity of the barrier. Findings regarding locating defects with a piezocone and hydraulic fracture in piezometer tests are also presented.     

Effective Soil Density for Propagation of Small Strain Shear Waves in Saturated Soil

This technical note defines an “effective soil density” that controls the velocity of small strain shear waves in saturated soil. Biot theory indicates that the ratio of effective density to saturated density will generally range from 0.75 to 1.0 and is a function of specific gravity of solids, porosity, hydraulic conductivity, and shear wave frequency. For many geotechnical applications, effective density will be equal to saturated density for low hydraulic conductivity soils (clays and silts) and may be less than saturated density for high hydraulic conductivity soils (clean sands and gravels). The findings are relevant to applications involving the propagation of small strain shear waves through saturated soil, and in particular for laboratory and field tests in which shear modulus is back-calculated from measured shear-wave velocity.     

1D Time-Domain Solution for Seismic Ground Motion Prediction

A full time-domain solution for predicting earthquake ground motion based on the 1D viscoelastic shear-wave equation is presented. The derivation results in a time-domain equation in the form of an infinite impulse response filter. A solution in the time domain has several advantages including causality, direct modeling of impulsive and transient processes, and ease of inclusion of nonlinear soil behavior. The method is applicable to any arbitrarily layered silhouette presented as SH-wave velocity, damping coefficient, and mass density profiles for designated soil intervals. For nonlinear evaluations, an equivalent-linear formulation is incorporated and the standard modulus and damping degradation curves become part of the input set. Input motion can be either rock-outcrop or body-wave motions measured or estimated at the bottom of the geologic profile, and the output is the estimated ground motion time history. Application of the method to vertical array strong motion records from Garner Valley, and Wildlife Site, Calif., shows that predicted surface (and interval) ground motion is virtually identical to that measured. The differences between the results of linear and nonlinear analyses are negligible for most cases. A comparison of the time-domain model with SHAKE shows that SHAKE fails to accurately predict time histories in some situations, whereas the time-domain solution always yields satisfactory predicted surface ground motions.     

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.     

On-Site Nonlinear Hysteresis Curves and Dynamic Soil Properties

Strong motion records at five vertical array sites in Japan are used to examine soil shear modulus and material damping as a function of shear strain during large earthquakes. Acceleration data from the sites are processed directly for evaluation of site shear stress-strain hysteresis curves for different time windows of the record. Results of the analysis demonstrate a significant nonlinear ground response at the sites with surface peak ground accelerations exceeding 90 gal. The results of shear stress-strain hysteresis curves are also used to estimate variation of soil shear modulus and material damping characteristics with shear strain amplitude at each site. The identified shear modulus-shear strain and damping ratio-shear strain relationships are in general agreement with published laboratory results. These response interpretations are also compared with the results of a frequency-domain analysis by using the spectral ratio (uphole∕downhole) technique. There is general agreement between the time- and frequency-domain results. The results illustrate the significance of the site nonlinearity during strong ground motions as well as the accuracy of the dynamic soil properties obtained from laboratory tests.