Mitigation of Liquefaction-Induced Lateral Deformation in a Sloping Stratum: Three-dimensional Numerical Simulation

Finite-element (FE) simulations are increasingly providing a versatile environment for conducting lateral ground deformation studies. In this environment, mitigation strategies may be assessed in order to achieve economical and effective solutions. On the basis of a systematic parametric study, three-dimensional FE simulations are conducted to evaluate mitigation by the stone column (SC) and the pile-pinning approaches. Mildly sloping saturated cohesionless strata are investigated under the action of an applied earthquake excitation. For that purpose, the open-source computational platform OpenSees is employed, through a robust user interface that simplifies the effort-intensive pre- and postprocessing phases. The extent of deployed remediation and effect of the installed SC permeability are investigated. The influence of mesh resolution is also addressed. Generally, SC remediation was found to be effective in reducing the sand stratum lateral deformation. For a similar stratum with permeability in the silt range, SC remediation was highly ineffective. In contrast, pile pinning appeared to be equally effective for the sand and silt strata permeability scenarios. Overall, the conducted study highlights the potential of computations for providing insights toward the process of defining a reliable remediation solution.     

Block Element Method for the Seismic Stability of Rock Slopes

The seismic stability analysis of rock slope is implemented using a block element method (BEM) in this paper. Based on the formulations of the matrices of stiffness, mass, and damping, the dynamic governing equation for the rock block system is established. The Wilson method is used to solve the dynamic governing equation, and the viscoelastic artificial boundary condition is introduced to treat the unbound domain problem. The proposed method is applied to the seismic stability analysis of the intake slope in a hydropower project, from which the dynamic safety factors of key block element combinations during earthquake and their dynamic amplification factors of acceleration are evaluated.     

Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution

An improved accurate closed-form wave function analytic solution of two-dimensional scattering and diffraction of antiplane SH waves by a semicircular cylindrical hill on an elastic half space is presented. In the previous solution, stress and displacement residual auxiliary functions were defined at the circular interface above and below the circular hill. The method of weighted residues (moment method) was used to solve for the unknown scattered and transmitted waves by requiring each term of Fourier series expansion of these auxiliary residual functions to vanish. It was found that the stress residual amplitudes on both (left and right) rims of the hill (ideally should be zero) are not numerically insignificant, irrespective of how many terms used. It was pointed out that the shear stress at the rim is infinite, and that the stress auxiliary function is discontinuous at both rims of the hill, exhibiting a problem for the numerical solution that is more complicated than Gibbs’ phenomenon. The problem with the overshoot of the stress residual amplitudes at the rim was most likely numerical. In this paper, all displacement and stress waves were expressed as cosine functions, and the solution of the circular hill problem was reformulated in this paper, and, for the solution to be correct, the computed stress and displacement residual amplitudes were shown to be numerically negligible everywhere, including those at both rims of the hill. Displacements at higher frequencies are also computed.     

Hydraulic Jumps in Sloping Channels: Sequent Depth Ratio

A large variety of hydraulic jumps on horizontal and sloping inverts at the end of an ogee standard weir is investigated. An ogee standard weir was used to create supercritical flow and slopes of 0.0, ?0.025, ?0.05, ?0.075, and ?0.10 were built downstream of the weir. Based on the momentum equation in the horizontal direction, a method to predict the sequent depth ratio is presented. The theory agrees well with the results of the writers and previous investigators. A correlation was developed to predict the minimum Froude number needed to establish jumps on negative slopes. Observations showed that in those cases where the gravity force component in the jump was opposite to the flow direction, the water surface of the surface roller became undular and unstable. The hydraulic jump on an entirely adverse slope was almost impossible to control. The analysis of experimental data showed that the negative slope of the basin reduces the sequent depth ratio, while a positive slope increases the sequent depth ratio.     

Taxonomy of interpolation constraints on recursive subdivision surfaces

Published online: 14 May 2002     

Rational Coefficients for Steeply Sloped Watersheds

When computing peak discharges for the design of drainage systems using the rational method, it is important to have an accurate value for the rational coefficient (C). For steeply sloped watersheds the origin of values of the rational coefficient are unknown and lack even modeling verification. A model that shows the relationship between the rational coefficient and watershed slope was developed for steeply sloped watersheds. Using Horton’s infiltration equation, Manning’s equation, the velocity method for computing times of concentration, and generalized intensity-duration-frequency curves, a model was developed to test the effect of variation of several watershed characteristics on the relationship between slope and the rational coefficient. Analyses with the model showed that both Manning’s coefficient and land use had the greatest effect on the relationship between C and slope. A mathematical function was then developed from data generated from the Horton–Manning model. This model allows C to be estimated for a given slope and a value of Manning’s coefficient for the land cover. A rational coefficient at a 6% slope is also required input. The model was tested using several watersheds with moderate to steep slopes. This relationship should be used to better estimate values of C on steep slopes, and thereby, lead to more accurately hydrologic designs.     

Experimental Assessment of the Sprinkler Application Rate for Steep Sloping Fields

The Programa para el Manejo del Agua y del Suelo (PROMAS) assists the local farming community in introducing new types of locally available irrigation equipment that are both inexpensive and water efficient. Field experiments enabled determining the maximum application rates that cause zero runoff for slopes above 16% for low-cost sprinkler systems.     

Simple Method for the Design of Microirrigation Paired Laterals on Sloped Fields

In this study, a method for designing paired laterals that meet with required water application uniformity on sloped fields was developed using the energy gradient line approach based on the definition of the best submain position locations in which the same minimum pressure exists in uphill and downhill laterals. The best equation form of best submain position was determined. Also, the solution procedure was introduced to get the final solution to avoid the phenomena of no convergence or slow convergence. In this method, the required water application uniformity was used directly as a computational parameter in designing. When the designed emitter discharge, required water application uniformity and one parameter (either length or diameter) of a paired lateral are provided; the system developed here enables another parameter and the best submain position to be determined for any field slope conditions. Taken together, the results of this study show that final solutions can be obtained quickly and reasonably.     

Relative Buoyancy Dominates Thermal-Like Flow Interaction along an Incline

This paper describes laboratory investigations of the motion between two fixed volumes of dense fluid (surge-type gravity currents) with different salt concentrations that interact above an incline in the presence of ambient stratification. The experiments include both large and small density contrasts between the interacting surges. Initially, the propagation of each fluid mass assumes a thermal-like nature, but then the lower density surge is quickly caught up by the denser fluid flow because of its higher velocity. There are two key process regarding the surge interaction. With a large density contrasting the fluid volumes, the denser flow moves to the front of the current as an intrusion with no mixing. With a small density difference, pronounced mixing occurs between the surges with the development of a homogeneous underflow. A simple energy parameterization is developed to evaluate the source conditions under which the different flow dynamics develop.