One-Dimensional Model of Shallow Water Surface Waves Generated by Landslides

A numerical model is presented as the basis for the study of surface waves generated by bank and bottom landslides in rivers. The flow is assumed to be properly modeled by the shallow water equations. The solid movement is introduced in the model as an external action, and assumed rigid and impervious. Two situations are identified in the flow subsequent to a solid movement: longitudinal and transversal sliding. A discussion on the modeling difficulties associated with the latter is included. The flow equations are solved by means of an upwind scheme specially adapted to advancing fronts over dry irregular beds.     

Fully Nonhydrostatic Modeling of Surface Waves

A fully nonhydrostatic model is tested by simulating a range of surface-wave motions, including linear dispersive waves, nonlinear Stokes waves, wave propagation over bottom topographies, and wave–current interaction. The model uses an efficient implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment is incorporated to fully include the nonhydrostatic pressure effect. The model results are verified against either analytical solutions or experimental data. It is found that the model using a small number of vertical layers is capable of accurately simulating both the free-surface elevation and vertical flow structure. By further examining the model’s performance of resolving wave dispersion and nonlinearity, the model’s efficiency and accuracy are demonstrated.     

In Situ Estimate of Shear Wave Velocity Using Borehole Spectral Analysis of Surface Waves Tool

In situ field testing has been performed over the past several years at a silty sand site in Austin, Tex. using the borehole spectral analysis of surface waves (SASW) tool to develop the technique and assess the validity of the method. The borehole SASW tool is an inflatable pressuremeterlike device that allows surface wave measurements to be performed along the wall of an uncased borehole while varying the in situ states of stress. Field results demonstrate the applicability of borehole SASW testing as a method to characterize soil sites and provide information about in situ shear wave velocity and the relationship between shear wave velocity and state of stress. Results from a borehole SASW test conducted at the Austin site are presented herein to demonstrate the applicability and validity of the method.     

Characterization of Spectral Analysis of Surface Waves Shear Wave Velocity Measurement Uncertainty

The spectral analysis of surface waves (SASW) method is a nondestructive test for characterization of the variation with depth of the shear modulus of soils. While the testing procedure is well developed, only one preliminary study has investigated measurement uncertainty associated with SASW, and the methods utilized to quantify measurement uncertainty were prohibitive to routine assessment. Knowledge of this uncertainty, and ability to include its assessment in routine testing, would allow for inclusion of SASW results in reliability-based design and in assessment of the spatial variability of shear modulus. In this study, a large sample of test data was collected from two test sites. Characteristic statistics, statistical distribution, and measurement uncertainty were determined for each phase of SASW. Using the empirical statistical properties and measurement uncertainty results as validation criteria, an analytically based uncertainty assessment system was developed. Phase angle, inverse phase angle, and phase velocity data typically display a coefficient of variation (COV) of 2%, and the COV for combined phase velocity data is typically 1.5%. The COV for shear wave velocity is typically between 5 and 10%, and thus the inversion appears to magnify measurement uncertainty. Phase angle, inverse phase angle, phase velocity, and combined phase velocity data are normally distributed. Shear wave velocity samples at a given depth are generally normally distributed. Using a small sample of experimental data and the analytically based process developed in this study, the measurement uncertainty of SASW test results can be assessed as part of routine testing.     

Numerical Modeling of Basin Irrigation with an Upwind Scheme

In recent years, upwind techniques have been successfully applied in hydrology to simulate two-dimensional free surface flows. Basin irrigation is a surface irrigation system characterized by its potential to use water very efficiently. In basin irrigation, the field is leveled to zero slope and flooded from a point source. The quality of land leveling has been shown to influence irrigation performance drastically. Recently, two-dimensional numerical models have been developed as tools to design and manage basin irrigation systems. In this work, a finite volume-based upwind scheme is used to build a simulation model considering differences in bottom level. The discretization is made on triangular or quadrilateral unstructured grids and the source terms of the equations are given a special treatment. The model is applied to the simulation of two field experiments. Simulation results resulted in a clear improvement over previous simulation efforts and in a close agreement with experimental data. The proposed model has proved its ability to simulate overland flow in the presence of undulated bottom elevations, inflow hydrographs, and colliding fronts.     

Observation and Simulation of Surface Waves in Two Water Supply Reservoirs

Observations and model predictions of progressive surface waves were made for Cannonsville and Schoharie Reservoirs, located in southeastern New York State. These reservoirs are deep with steep bottom slopes and relatively small fetch. The Donelan/Great Lakes Environmental Research Lab model, a parametric second-generation wave model was applied to these reservoirs assuming deep water throughout the domain. This assumption was based on the relatively small waves and steep bottom slopes, resulting in a very narrow region of wave interaction with the bottom along a lee shore. Previous applications of this model have been for water bodies with larger fetch. Observations of wave characteristics were made near the shoreline at two sites in Cannonsville and one site in Schoharie using submerged pressure sensors, from which the height of larger waves was determined. Model hindcasts were made for the observation periods with model inputs being wind speed and direction and water surface elevation. The model performed well in simulating significant wave height determined from observations. Some implications of the use of wave model simulations to predict sediment resuspension in these and other deep lakes and reservoirs are discussed.     

Celerity and Amplification of Supercritical Surface Waves

The amplification of supercritical waves in steep channels is examined analytically using a one-dimensional dynamic solution of the Saint-Venant equations. Existing methods were modified to describe the amplification of surface waves over a normalized channel length rather than over a single wavelength. The results are strikingly different, and a generalized graph shows that short waves amplify the most over a fixed channel length. The maximum amplification parameter over a normalized channel length is 0.53 when F = 3.44. Applications to the flood drainage channel F1 in Las Vegas indicate that the amplitude of waves shorter than 100 m would increase by 65% over a channel length of 543 m. These theoretical results await field verification. Supercritical waves could be dampened by increasing channel roughness to reduce the Froude number below 1.5.     

Installation of Torpedo Anchors: Numerical Modeling

Torpedo anchors are used as foundations for mooring deep-water offshore facilities, including risers and floating structures. They are cone-tipped cylindrical steel pipes ballasted with concrete and scrap metal and penetrate the seabed by the kinetic energy they acquire during free fall through the water. A mooring line is usually connected at the top of the anchor. The design of such anchors involves estimation of the embedment depth as well as short-term and long-term pullout capacities. This paper describes the development of a computational procedure that leads to prediction of torpedo-anchor embedment depth. The procedure relies on a computational fluid dynamics (CFD) model for evaluation of the resisting forces on the anchor. In the model, the soil is represented as a viscous fluid and the procedure is applied to axially symmetric penetration of the seabed. The CFD approach provides estimates of not only the embedment depth but the pressure and shear distributions on the soil-anchor interface and in the soil.     

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.     

Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data

The use of multiple-mode dispersion data in surface wave inversion to derive shear-wave velocity (vs) profiles has increased in the past decade as the inclusion of higher mode data can improve the accuracy of the inversion results. However, the error associated with nonuniqueness in the multiple-mode inversion has not been clarified and quantified. This research focuses on the attempt to improve the accuracy of multiple-mode surface wave inversion result by optimizing the use of multiple-mode dispersion data to reduce the error associated with the nonuniqueness in inversion. In this research, an alternative approach was used where inversion of surface wave dispersion data was performed using three distinct modes. Four different vs profiles, representing regular and irregular cases, were used, and multiple-mode dispersion data were synthesized from these profiles using the dynamic stiffness matrix method as the theoretical model. The dispersion data were then inverted using the Levenberg–Marquardt method. The results demonstrated that, as expected, inclusion of higher modes did not improve the accuracy of the inversion results for the regular profiles. However, inclusion of higher modes significantly improved the uniqueness of the inversions for the irregular profiles. The results also demonstrate that regardless of the nature of the profile, the accuracy of the inversion improves when the starting profile more closely matches the true profile. Of all the inversion approaches investigated, the best approach was one where three successive inversions, using one, two, and three modes, respectively, was used, where the inverted profile from one inversion was used as a starting model for a subsequent inversion that used one additional mode.     

Characterization of Models for Time-Dependent Behavior of Soils

Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena (creep, stress relaxation, and rate effects) observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part is a review of the empirical relations, which apply only to problems of specific boundary conditions and frequently involve natural time alone. The second part deals with different rheological models used for describing the viscous effects in the field of solid mechanics. The rheological models are typically developed for metals and steel but are, to some extent, used to characterize time effects in geomaterials. The third part is a review of constitutive laws that describe not only viscous effects but also the inviscid (rate-independent) behavior of soils, in principle, under any possible loading condition. Special attention is paid to elastoviscoplastic models that combine inviscid elastic and time-dependent plastic behavior. Various general elastoviscoplastic models can roughly be divided into two categories: Models based on the concept of overstress and models based on nonstationary flow surface theory. Although general in structure, both have shortcomings when used for modeling of soils.     

Numerical Modeling of Free Overfall

Free overfall is treated by using two-dimensional steady potential flow theory. Based on the theory of the boundary value problem of analytical function and the substitution of variables we derive the boundary integral equations in the physical plane for solving the free overfall in a rectangular channel. A numerical iterative method has been developed to solve these boundary integral equations. The free water surface profiles, pressure distribution, and the end-depth ratio are calculated for a wide range of bed slopes, bed roughness, and incoming upstream Froude number. The computed results agree well with the available experimental data.     

Numerical Study of Reinforced Soil Segmental Walls Using Three Different Constitutive Soil Models

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade’s single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed.     

Numerical Modeling of Concrete-FRP Debonding Using a Crack Band Approach

In this study, numerical procedures are proposed to predict the structural behavior of concrete members strengthened with fiber-reinforced polymeric (FRP) sheets or plates. The concept of damage band or crack band is introduced and used for predicting the debonding failure of the concrete-epoxy interface formed when FRP sheets or plates are externally bonded to a concrete substrate. In the crack band approach, all the processes taking place during the failure of a concrete-epoxy interface are smeared in a band of fixed width. This makes the approach attractive from a modeling point of view since continuum theories, along with softening relations, can be used to model the damage which causes debonding of the interface. In order to validate this approach, numerical predictions, using the concept of crack band, are compared against experimental results obtained from tests of concrete blocks and reinforced concrete beams strengthened with FRP. In particular, the capability of the proposed numerical approach to predict the load-displacement response, strain distributions, failure sequences, damage distribution, and failure mechanisms experimentally observed is verified. Results presented in this study indicate that the concept of crack band is appropriate when modeling concrete-epoxy interfaces under general states of stresses.     

Two-Dimensional Physical and Numerical Modeling of a Pile-Supported Earth Platform over Soft Soil

This paper focuses on the mechanisms occurring in a granular earth platform over soft ground improved by rigid piles. Two-dimensional physical model experiments were performed using the Schneebeli’s analogical soil to investigate the load transfer mechanisms by arching and the settlement reduction and homogenization. Experimental outputs are compared to results obtained on a numerical model using a plane strain continuum approach. The impact of the constitutive model complexity to simulate the platform material behavior was first assessed, but no large difference was recorded. As far as the proposed model, which takes the main features of the observed behavior satisfactorily into account, the numerical procedure could be validated and the parametric studies extended numerically. Both approaches of this study underlined the main geometrical and geotechnical parameters which should inevitably be taken into account in a simplified design method, namely the capping ratio, the platform height, and the platform material shear strength.     

Interaction of Nonlinear Progressive Waves with Two Serially Arranged Submerged Obstacles

The purpose of the present study is to develop a numerical model for the investigation of water waves propagating over a pair of impermeable submerged obstacles. The mathematic model is formulated by coupling solutions of the Navier–Stokes equations and transport equations for the surface elevation using the volume of fluid method. Based on a staggered computational mesh, an explicit numerical algorithm is employed with a predictor–corrector procedure of pressure and velocity field. The proposed model provides good agreement with other experimental results and validates its good performance. Regarding the spatial harmonic evolutions of various cases, it is noted that the present fluctuating mode of harmonic amplitudes exists upstream and at the gap between obstacles. The results show that the nonlinearity of propagating waves becomes stronger than the initial wave in such areas, and reveals much steeper wave profiles compared to the initial ones. The fluctuating harmonic amplitudes vary with the gap width and form two hydrodynamic cycles. The vortices play an important role in the wave reflection as they form a water column wall to reflect the incoming waves. The reflection ratio depends on the extent of vortex development near the upstream obstacle. The maximum wave reflection occurs in cases with dimensionless gap width S/L equal to 3/8 and 7/8 in this study.     

Modeling the Transient Pumping from Two Aquifers Using MODFLOW

A procedure is proposed for calculating the spatial and temporal variation of drawdown due to pumping a well tapping two aquifers separated by an aquitard, using convolution and MODFLOW. It can take into account the unsteady pumping discharge and cross flow through the intervening aquitard. A discrete pulse kernel method based on superposition/convolution is used to account for the unsteady pumping discharge. The discrete pulse kernels are calculated using MODFLOW. The contributions of the aquifers to the pumped discharge are accounted implicitly and not required to be specified explicitly. Available numerical models (e.g., MODFLOW) require the aquifer contributions that are implicitly controlled, to be specified explicitly. The use of the suggested procedure is illustrated using examples. The contributions of the aquifers are found not in proportion to their transmissivities but vary with time, when the diffusivities of the aquifers are not equal. Applying the new procedure, the numerical models, such as MODFLOW can be used to correctly model the transient pumping from two aquifers with cross flow; thus, it opens up the possibility of numerically accounting for the aquifer heterogeneity while dealing with the flow to a well tapping two aquifers under a transient pumping, which would be otherwise difficult to account for analytically.     

Case Study of an S-Shaped Spillway Using Physical and Numerical Models

The spillway studied in this paper was designed as an “S” shape in plan view, characterized in two curved conduits, steep slopes, and small curvature radiuses. An approach of the combination of physical and numerical models was adopted to study the hydraulic characteristics and examine the feasibility of the design. By setting proper sills whose specific layouts were determined by numbers of experiments at the bottom of the curved conduits, the flow pattern was significantly improved. The k–ε turbulence model was used to simulate the three-dimensional turbulent flow. The free water surface was determined by the volume of fluid method, and the governing equations were solved by the finite volume method. Simulated results of the free water surface and the velocity are in good agreement with measured data. It is shown that S shaped spillways are feasible in practical projects. Moreover, numerical simulations are useful for the design and analysis of S shaped spillways.     

Hydrostatic versus Nonhydrostatic Euler-Equation Modeling of Nonlinear Internal Waves

Basin-scale internal waves are inherently nonhydrostatic; however, they are frequently resolved features in three-dimensional hydrostatic lake and coastal ocean models. Comparison of hydrostatic and nonhydrostatic formulations of the Centre for Water Research Estuary and Lake Computer Model provides insight into the similarities and differences between these representations of internal waves. Comparisons to prior laboratory experiments are used to demonstrate the expected wave evolution. The hydrostatic model cannot replicate basin-scale wave degeneration into a solitary wave train, whereas a nonhydrostatic model does represent the downscaling of energy. However, the hydrostatic model produces a nonlinear traveling borelike feature that has similarities to the mean evolution of the nonhydrostatic wave.     

Effect of Gravity and Initial Stress on Torsional Surface Waves in Dry Sandy Medium

This problem studies the effect of gravity and initial stress on the propagation of torsional surface waves in dry sandy medium. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate. The expansion of the Whittaker function up to quadratic terms shows that two such wave fronts may exist in the medium. Finally, it is concluded that the sandy medium without support of a gravity field cannot allow the propagation of torsional surface waves, where as the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy.