Least square criterion for isostasy

Summary Least square criterion has been introduced to specify the order of isostatic compensation of mountains. The hydrostatic stability of the mountains is of basic significance in plate tectonics. However different concepts of isostasy differ in the evaluation of its order. An elegant and rapid technique is developed which extends the symmetric matrix method of root estimation byNegi andGarde [1]³) to provide a stability test through the mathematical expectation of the root increment. Application is illustrated for Rocky Mountains, United States.     

A channel head stability criterion for first‐order catchments

The present analysis derives a stability criterion for long‐term equilibrium channel heads. The concept of finite perturbation analysis is presented, during which the surface is subjected to perturbations of a finite amplitude and resulting changes in flow path structure and slope are computed. Based on these quantities the analysis predicts whether the perturbed location is going to erode, be filled in or remain steady. The channel head is defined geometrically as the focus point of converging flow lines at the bottom of hollows. It is demonstrated that stability at the channel head grows out of the competition between the rate of flow path convergence and the degree of profile concavity. Analytical functions are derived to compute channel head‐contributing area and ‐slope, flow path convergence and profile concavity as a function of perturbation depth, distance from the crest and the initial slope. In a numerical model these quantities point to the long‐term equilibrium channel head position, which is shown to depend also on the width to length ratio of hollows. It is also demonstrated that the equilibrium channel head position is sensitive to the base‐level lowering/non‐dimensional slope length ratio and to the slope of the initial topography. Morphometrical measurements both in the field and on simulated topographies were used to test the theoretical predictions.     

A frequency criterion for optimal node selection in smoothing with cubic splines

When smoothing a function with high‐frequency noise by means of optimal cubic splines, it is often not clear how to choose the number of nodes. The more nodes are used, the closer the smoothed function will follow the noisy one. In this work, we show that more nodes mean a better approximation of Fourier coefficients for higher frequencies. Thus, the number of nodes can be determined by specifying a frequency up to which all Fourier coefficients must be preserved and increasing the number of nodes until this criterion is met. A comparison of the corresponding smoothing results with those obtained by filtering using moving average and moving median filters of corresponding length and a low pass with corresponding high‐cut frequency shows that optimal cubic splines yield better results as they preserve not only the desired low‐frequency band but also important high‐frequency characteristics.     

An erosion criterion for gravel-bed rivers

A theoretically-based erosion criterion is developed for gravel-bed rivers which incorporates the effect of both grain geometry and turbulent velocity fluctuations. It is derived from a balance of instantaneous drag, lift, and gravity forces operating on individual grains and is calculated for spherical grains arranged in three distinct geometries. To accommodate the temporal variation in bed shear stress, the model includes a stochastic element based on the characteristics of turbulence derived from the flume evidence of McQuivey (1973a, b). In terms of the Shields parameter, results show reasonable agreement with the range of observations quoted from the field and with the experimental data of Fenton and Abbott (1977). Finally, the argument is generalized to cover applications in the wider context of field conditions including a range of grain sizes and flow conditions.     

A fragmentation criterion for highly viscous bubbly magmas estimated from shock tube experiments

When a highly viscous bubbly magma is sufficiently decompressed, layer-by-layer fracturing propagates through the magma at a certain speed (fragmentation speed). On the basis of a recent shock tube theory by Koyaguchi and Mitani [Koyaguchi, T., Mitani, N. K., 2005. A theoretical model for fragmentation of viscous bubbly magmas in shock tubes. Journal of Geophysical Research 110 (B10), B10202. doi:10.1029/2004JB003513.], gas overpressures at the fragmentation surface are estimated from experimental data on fragmentation speed in shock tube experiments for natural volcanic rocks with various porosities. The results show that gas overpressure at the fragmentation surface increases as initial sample pressure increases and sample porosity decreases. We propose a new fragmentation criterion to explain the relationship between the gas overpressure at the fragmentation surface, the initial pressure and the porosity. Our criterion is based on the idea that total fragmentation of highly viscous bubbly magmas occurs when the tensile stress at the midpoint between bubbles exceeds a critical value. We obtain satisfactory agreement between our simulation and experiment when we assume that the critical value is inversely proportional to the square root of bubble wall thickness. This fragmentation criterion suggests that long micro-cracks or equivalent flaws (e.g., irregular-shaped bubbles) that reach the midpoints between bubbles are a dominant factor to determine the bulk strength of the bubbly magma.     

A comparative study of the different procedures for seismic cracking analysis of concrete dams

Different procedures are compared for the three-dimensional seismic cracking analysis of gravity and arch dams during strong earthquakes. The fracture procedures include the extended finite element method with cohesive constitutive relations, crack band finite element method with plastic-damage relations, and the finite element Drucker−Prager elasto-plastic model. These procedures are used to analyze the nonlinear dynamic response of Koyna dam to the 1967 Koyna earthquake and the seismic cracking of the Dagangshan arch dam subjected to design earthquake. The cracking process and profiles of the two dams using the three different procedures are compared. The applicability and the suitability of the three procedures for seismic cracking analysis of gravity and arch dams are discussed.     

A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

Containment criterion for contaminant isolation by cutoff walls

A rigorous solution is developed from first principles to guide the preliminary design of cutoff walls installed to contain the migration of contaminants from source zones. The full analytic solution is used to develop a criterion for determining the configuration and hydraulics of optimal wall designs. The solution is used to demonstrate the interaction between the properties of the wall, the Darcy flux, and the concentration of contaminants at the outside face of the well. For a particular wall design, the containment criterion can be used to estimate the long-term concentration that will develop at the outside face of the wall. Alternatively, for a given concentration on the outside face of the cutoff wall, the containment criterion can be used to estimate the Darcy flux required to balance the outward diffusion of contaminants. The results of numerical simulations are presented to evaluate the analytic approach. The numerical results confirm that for a wall with known transport properties, a specified Darcy flux is associated with a unique outside contaminant concentration.     

A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

A semi-empirical formula for evaluating residual strain of soils under earthquake loading

A new semi-empirical formula for evaluating the residual strain of soils under earthquake loading is presented in this paper based on the incremental method and the increment model proposed by the authors. When the incident loading is uniform, the results calculated by the new formula are nearly the same as those by the existing formula. For excitation of the random earthquake loading, the results calculated by the new formula are compared to the results obtained by dynamic triaxial tests. The dynamic triaxial tests had been performed considering different seismic waves, confining stresses,consolidation ratios, and types of cohesive soils. The comparison between the calculated and tested results indicate that the presented formula can efficiently and practically describe the time-dependent process of the soil residual strains under actual seismic loads.     

A critical review of methods for pile design in seismically liquefiable soils

Collapse and/or severe damage to pile-supported structures are still observed in liquefiable soils after most major earthquakes. Poor performance of pile foundations remains a great concern to the earthquake engineering community. This review paper compares and contrasts the two plausible theories on pile failure in liquefiable soils. The well established theory of pile failure is based on a flexural mechanism; where the lateral loads on the pile (due to inertia and/or lateral spreading) induce bending failure. This theory is well researched in the recent past and assumes that piles are laterally loaded beams. A more recent theory based on buckling instability treats the piles as laterally unsupported slender columns in liquefiable soils and investigates the buckling instability (bifurcation). The objective of this paper is to investigate the implications to practical pile foundation design that flow from both these theories. Provisions for design made by major international codes of practice for pile design including the Japanese Highway Code (JRA) will be considered. The necessity for such codes to consider alternative forms of failure mechanisms such as the buckling instability of piles in liquefied ground will be discussed. S. Bhattacharya–Previously Departmental Lecturer in Engineering Science, University of Oxford, UK and Fellow of Somerville College, Oxford. S. P. G. Madabhushi–Fellow of Girton College, Cambridge.     

A strength distribution criterion for minimizing torsional response of asymmetric wall‐type systems

In order to mitigate the effect of torsion during earthquakes, most seismic codes of the world provide design guidelines for strength distribution based on the traditional perception that element stiffness and strength are independent parameters. Recent studies have pointed out that for an important class of widely used structural elements such as reinforced concrete flexural walls, stiffness is a strength‐dependent parameter. This implies that the lateral stiffness distribution in a wall‐type system cannot be defined prior to the assignment of elements' strength. Consequently, stiffness eccentricity cannot be computed readily and the current codified torsional provisions cannot be implemented in a straightforward manner. In this study, an alternate guideline for strength distribution among lateral force resisting elements is presented. To develop such a guideline, certain issues related to the dynamic behaviour of asymmetric wall‐type systems during a damaging earthquake were examined. It is shown that both stiffness and strength eccentricity are important parameters affecting the seismic response of asymmetric wall‐type systems. In particular, results indicate that torsional effects can be minimized by using a strength distribution that results in the location of the centre of strength CV and the centre of rigidity CR on the opposite sides of the centre of mass CM. Copyright © 2001 John Wiley & Sons, Ltd.     

一个中国大陆地区7级以上地震判定指标被再次验证

笔者曾利用统计显著性检验方法给出了中国大陆地区5级以上地震年频次与7级以上地震发生关系的判定指标,他们是：①当5级以上地震年频次N5＜10时,其后第6年我国大陆地区将发生7级以上地震;②当5级以上地震年频次N5＞31时,其后第6年我国大陆地区发生7级以上地震的可能性不大.2007年,中国大陆地区5级以上地震年频次为6次,预示2013年中国大陆地区可能会发生7级以上地震.2013年4月20日四川芦山7.0级地震再次使前一个判定指标得到验证.     

A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models

A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami.     

Hydraulic conductivity prediction for sandy soils

The potential for petroleum-contaminated soils to impact ground water is evaluated using the soil leachability model in South Carolina and Georgia. In this model, the Green and Ampt (1911) equation is used to estimate unsaturated flow with saturated hydraulic conductivity (K(S)) values obtained using the Rawls and Brakensiek (1989) equation from inputs of percent sand- and clay-sized particles. However, many soils have > 70% sand-sized particles, which is the maximum amount for which the Rawls and Brakensiek equation is valid. Therefore, 70 sets of K(S) and particle-size data from the literature for southeastern United States sandy soils were analyzed to develop a new equation for estimating K(S). A multiple linear regression model with an adjusted R2 = 0.65 (p < 0.0001) was developed from percent clay- and sand-sized particle data. Eight additional sets of data were used to validate the model. The root mean square deviation and maximum squared difference, (yi - yi(2)), values for the new model are smaller than those obtained using the Rawls and Brakensiek equation, or Rosetta, a neural network-based model (Schaap 1999). The new model provides estimates that are within an order of magnitude for all but one of the test data sets. Rosetta predicts K(S) within one order of magnitude of measured values for six test data, and predicts K(S) within two orders of magnitude for the other two. The Rawls and Brakensiek predictions are within one order of magnitude for four test data, but are two or more orders of magnitude too high for the remaining four points. The new equation is recommended for estimating K(S) for sandy southeastern United States soils for which inputs are limited to percent sand and clay.     

Dynamics of cracking and swelling clay soils: Displacement of skeletal grains,optimum depth of slickensides,and rate of intra-pedonic turbation

Grumusols (Vertisols), though having a uniformly high clay content with depth, commonly exhibit a coarsening upward in the sand fraction, either of skeletal grains or of nodules. The non-uniform way in which the wetting front advances in swelling clay soils, with preferred advance and swelling around the coarse grains, produces upward directional forces and uplifting of the grains, thus producing the observed textural differentiation in the coarse fraction. From observations of slickenside distribution in the profile, and using published data on the ratio of lateral to vertical stresses and swelling pressure distribution with depth, a concept of optimum depth for slickensides is developed. Generally at 150–200cm, below the depth of cracking, this depth depends in part on climatic conditions. Below the optimal depth increased overburden pressure and smaller moisture variations restrain the extent of swelling and deformation, above it drying produces cracks and obliterates large slickensides, though a strong bimasepic microfabric remains. The extent of intrapedonic turbation was estimated from measurements of the volume of cracks and of surface material falling into the cracks. It indicates a turnover time of several hundred to a few thousand of years. This agrees with the known increase of radiocarbon ages of organic matter (MRT) with depth which in Vertisols (Grumusols) is only slightly slower than in non-turbating Udolls (Chernozems) and Udalfs (Lessivés). The moderate rate of homogenization due to intrapedonic turbation does not prevent the development of a normal organic carbon profile and it is slower than the upswelling of coarse grains by upward directional forces. The development of shear planes and slickenside structures is a rapid process and not dependent on turbation.     

A simple method for the determination of ionic diffusion coefficients in flooded soils

Soil cores from river marginal wetlands from the Torridge and Severn catchments in the UK were collected to study rates of soil denitrification at different sites and at two stations (levee and backplain depression) at the river margin. Half the cores were sterilized prior to flooding to destroy the denitrifying bacteria. After flooding and equilibration, monitoring the concentration of amended nitrate in the supernatant of the sterile cores over a period of 7 days provided a simple procedure for the estimation of the diffusion coefficient of the nitrate ion in the flooded soils. An expression was developed that permitted this diffusion coefficient to be extracted from the slope of a plot of supernatant concentration versus (time)^1/2. The values obtained, at 15 °C, varied from 2·4 to 6·8 × 10^?10m²s^?1. Sterile cores are usually treated as controls in denitrification experiments; this work develops a procedure whereby they may yield useful soil process information. Copyright © 2001 John Wiley & Sons, Ltd.     

A transmitting boundary for the dynamic finite element analysis of cross anisotropic soils

The problem of the transmitting boundary used in the dynamic finite element analysis of layered axisymmetric soil models with non-axisymmetric displacements is considered. Each layer is modelled as a homogeneous, viscoelastic cross anisotropic medium with a vertical axis of material symmetry.