Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic performance and damage incurred by monolithic concrete self-centering rocking walls under the effect of axial stress ratio

Self-centering rocking walls offer the possibility of minimizing repair costs and downtimes, and also nullify the residual drift after seismic events, thanks to their self-centering properties. In this paper, the effect of axial stress ratio on the behavior of monolithic self-centering rocking walls is investigated by utilizing a developed finite element model. To verify the validity of the finite element model, results and observed damage in the model are compared with those of a full-scale wall test. The axial stress ratio is varied from 0.024 to 0.30 while keeping the other structural parameters constant. For qualitative damage evaluation, the observed damage in the model compared with expected damage states of desired performance levels. In order to evaluate the incurred damage quantitatively, the amount of crushing and damage in the wall is calculated by utilizing several ratios (crushing ratio and damage ratio). Furthermore, seismic response factors (i.e., μ, R and C_d) are calculated for different axial stress ratio values. The obtained results showed that, in order to satisfy the requirements of desired performance levels, the maximum axial stress ratio should be approximately within the range of 0.10–0.15. In addition, the maximum overall damage ratio and crushing ratio are suggested to be less than 5%. For axial stress ratio higher than 0.15, the flag-shaped pattern of hysteresis curves completely disappeared and the variation of displacement ductility is less sensitive to axial stress ratio. Considering the maximum axial stress ratio limited to 0.150, values of 4 and 3.5 are conservatively proposed as a period-independent response modification factor and displacement modification factor of the investigated structural wall, respectively.     

Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration

The feasibility of polynomial chaos expansion (PCE) and response surface method (RSM) models is investigated for modelling reference evapotranspiration (ET₀). The modelling results of the proposed models are validated against the M5 model tree and multi-layer perceptron neural network (MLPNN) methods. Two meteorological stations, Isparta and Antalya, in the Mediterranean region of Turkey, are inspected. Various input combinations of daily air temperature, solar radiation, wind speed and relative humidity are constructed as input attributes for the ET₀. Generally, the modelling accuracy is increased by increasing the number of inputs. Including wind speed in the model inputs considerably increases their accuracy in modelling ET₀. Mean absolute error (MAE), root mean square error (RMSE), agreement index (d) and Nash-Sutcliffe efficiency (NSE) are used as comparison criteria. The PCE is the most accurate model in estimating daily ET₀, giving the lowest MAE (0.036 and 0.037 mm) and RMSE (0.047 and 0.050 mm) and the highest d (0.9998 and 0.9999) and NSE (0.9992 and 0.9996) with the four-input PCE models for Isparta and Antalya, respectively.     

Research Note: Compact Depth from Extreme Points: a tool for fast potential field imaging

We propose a fast method for imaging potential field sources. The new method is a variant of the “Depth from Extreme Points,” which yields an image of a quantity proportional to the source distribution (magnetization or density). Such transformed field is here transformed into source‐density units by determining a constant with adequate physical dimension by a linear regression of the observed field versus the field computed from the “Depth from Extreme Points” image. Such source images are often smooth and too extended, reflecting the loss of spatial resolution for increasing altitudes. Consequently, they also present too low values of the source density. We here show that this initial image can be improved and made more compact to achieve a more realistic model, which reproduces a field consistent with the observed one. The new algorithm, which is called “Compact Depth from Extreme Points” iteratively produces different source distributions models, with an increasing degree of compactness and, correspondingly, increasing source‐density values. This is done through weighting the model with a compacting function. The compacting function may be conveniently expressed as a matrix that is modified at any iteration, based on the model obtained in the previous step. At any iteration step the process may be stopped when the density reaches values higher than prefixed bounds based on known or assumed geological information. As no matrix inversion is needed, the method is fast and allows analysing massive datasets. Due to the high stability of the “Depth from Extreme Points” transformation, the algorithm may be also applied to any derivatives of the measured field, thus yielding an improved resolution. The method is investigated by application to 2D and 3D synthetic gravity source distributions, and the imaged sources are a good reconstruction of the geometry and density distributions of the causative bodies. Finally, the method is applied to microgravity data to model underground crypts in St. Venceslas Church, Tovacov, Czech Republic.     

Steady flow to a partially penetrating blind‐wall well in a confined aquifer

Wells in aquifers of loose collapsible sediment are cased so that they have a blind wall and gain water only from the bottom. The hydraulic gradient established at the bottom of these wells during pumping brings the aquifer materials in a quicksand state, which may cause abrasion of pipes and pumps and even the destruction of well structure. To examine the quicksand occurrence, an analytical solution for the steady flow to a partially penetrating blind‐wall well in a confined aquifer is developed. The validity of the proposed solution is evaluated numerically. The sensitivity of maximum vertical gradient along the well bottom in response to aquifer and well parameters is examined. The solution is presented in the form of dimensionless‐type curves and equations that can be easily used to design the safe pumping rate and optimum well geometry to protect the well against sand production. The solution incorporates the anisotropy of aquifer materials and can also be used to determine the hydraulic conductivity of the aquifer. Copyright © 2012 John Wiley & Sons, Ltd.     

Airborne VLF Measurements and Variations of Ground Conductivity: A Tutorial

Airborne very low frequency (VLF) data are routinely collected by national agencies and commercial companies together with other passive geophysical measurements of the static magnetic field and radiometric data. The purpose of this paper is to demonstrate that both standard three-component VLF and tensor VLF (TVLF) data contain a lot of useful quantitative and qualitative information about the electrical conductivity distribution in the upper few hundred meters of the crystalline basement. We first give a new derivation of the fundamental transfer functions (the tipper) used in the TVLF technique. We then show that the tipper can be estimated from simultaneous measurements of the wave magnetic fields from at least two transmitters with somewhat different frequencies, and present a simple model by which the maximum error introduced by the difference in frequencies can be found. Single transmitter scalar VLF maps emphasise those conductive structures that have dominant strikes in the direction of the transmitter. Multiple transmitter transfer functions are dependent only upon the underlying conductivity structure. Two dimensional structures can be quantitatively modelled by modern inversion methods developed originally for deep electromagnetic magnetotelluric (MT) soundings. In such cases three-component VLF measurements can be modelled easily upon appropriate rotation of the co-ordinate system to “strike” co-ordinates. Single frequency transfer functions (tippers) have real and imaginary parts that carry information on not only lateral contrasts in conductivity, as usually stated in text books, but, taken together, they provide a robust tool for determining the background conductivity level away from distinct conductors, and they can also be used to discriminate between deep and shallow conductors. Based upon simulations using multi-frequency data, it can be concluded that such a new development would dramatically increase the resolving power of airborne VLF measurements.     

Sensitivity of seismic hazard evaluations to uncertainties determined from seismic source characterization

The sensitivity and overall uncertainty in peak ground acceleration (PGA)estimates have been calculated for the city of Tabriz, northwestern Iran byusing a specific randomized blocks design. Eight seismic hazard models andparameters with randomly selected uncertainties at two levels have beenconsidered and then a linear model between predicted PGA at a givenprobability level and the uncertainties has been performed. The inputmodels and parameters are those related to the attenuation, magnituderupture-length and recurrence relationships with their uncertainties.Application of this procedure to the studied area indicates that effects ofthe simultaneous variation of all eight input models and parameters on thesensitivity of the seismic hazard can be investigated with a decreasingnumber of computations for all possible combinations at a fixed annualprobability. The results show that the choice of a mathematical model ofthe source mechanism, attenuation relationships and the definition ofseismic parameters are most critical in estimating the sensitivity of seismichazard evaluation, in particular at low levels of probability of exceedance.The overall uncertainty in the expected PGA for an annual probability of0.0021 (10% exceedence in 50 yr) is expressed by a coefficient ofvariation (CV) of about 34% at 68% confidence level for a distance ofabout 5km from the field of the major faults. The CV will decrease withincreasing site-source distance and remains constant, CV = 15%, fordistances larger than 15 km. Finally, treating alternative models on theoverall uncertainty are investigated by additional outliers in input decision.     

Numerical Investigation of the Optimum Location for Vertical Drains in Gravity Dams

The seepage beneath a concrete dam causes an upward force acting to the dam foundation, known as uplift. Previous literatures show that implementation of drainage wells in gravity dam foundations causes a reduction in uplift forces. The main aim of these wells is to drain excess seepage flow bypassed from the cutoff wall and to reduce the uplift force. The location of the drains in the foundation plays a key role in reducing the pressure. In the present study, effect of the location of drain pipes from the upstream face of the dam (s), space among them (n) and drain’s diameter (d) in uplift force reduction is investigated. The processes of the study have been performed by the Seep/w software based on the finite element method. Results show that the use of a drain system reduced the uplift forces developed beneath the floor of the structure. If the drain is located close to the face of the dam, it may not be effective in reducing the uplift. On the other hand, shifting it too much away from the upstream face of the dam will lead to increased total uplift. It is, therefore, desirable to find out the location of the drain such that the total uplift is optimum. Optimum location of the vertical drains is not fixed, and by increasing vertical drains distances from each other and also decreasing drain diameter, optimum location would be shifted to the downstream. For example introduction of system of pipe drains to the floor of gravity dams reduced the uplift force acting on the floor by up to 80% for d/l = 0.0004, n/l = 0.024 and s/l = 0.08. This reduction in uplift becomes up to 65% for d/l = 0.0004, n/l = 0.048 and s/l = 0.12. The best location of the drain is such that the total uplift is minimum and this is presented in both design charts and algebraic equations in this study.     

Exploiting transformation-domain sparsity for fast query in multiple-point geostatistics

Multiple-point geostatistics has recently attracted significant attention for characterization of environmental variables. Such methods proceed by searching a large database of patterns obtained from a training image to find a match for a given data-event. The template-matching phase is usually the most time-consuming part of a MPS method. Linear transformations like discrete cosine transform or wavelet transform are capable of representing the image patches with a few nonzero coefficients. This sparsifying capability can be employed to speed up the template-matching problem up to hundreds of times by multiplying only nonzero coefficients. This method is only applicable to rectangular data-events because it is impossible to represent an odd-shaped data-event in a transformation domain. In this paper, the method is applied to speed up the image quilting (IQ) method. The experiments show that the proposed method is capable of accelerating the IQ method tens of times without sensible degradation in simulation results. The method has the potential to be employed for accelerating optimization-based and raster-scan patch-based MPS algorithms.