Cheng Haw Lee

Hydraulic Tomography for Detecting Fracture Zone Connectivity

Fracture zones and their connectivity in geologic media are of great importance to ground water resources management as well as ground water contamination prevention and remediation. In this paper, we applied a recently developed hydraulic tomography (HT) technique and an analysis algorithm (sequential successive linear estimator) to synthetic fractured media. The application aims to explore the potential utility of the technique and the algorithm for characterizing fracture zone distribution and their connectivity. Results of this investigation showed that using HT with a limited number of wells, the fracture zone distribution and its connectivity (general pattern) can be mapped satisfactorily although estimated hydraulic property fields are smooth. As the number of wells and monitoring ports increases, the fracture zone distribution and connectivity become vivid and the estimated hydraulic properties approach true values. We hope that the success of this application may promote the development and application of the new generations of technology (i.e., hydraulic, tracer, pneumatic tomographic surveys) for mapping fractures and other features in geologic media.

A continuum approach for estimating permeability in naturally fractured rocks

Abstract Many models for predicting permeability in rock masses have been proposed. However, most of these models do not relate the conductivity-closure behavior to fracture geometry parameters and geostati stresses. In this study an attempt is made to estimate the permeability tensor as well as the relation between permeability and depth on naturally jointed rocks. The new model includes effects of hydromechanical coupling, normal closure and fracture geometry. The fracture tensor related only to the fracture geometry (aperture, size and orientation) is introduced to formulate a permeability tensor. Fracture aperture, estimated by a simple field investigations, is defined as a function of joint roughness coefficient (JRC), joint wall compression strength (JCS) and geostatic stress. An actual rock mass of jointed andesite rock on the Lan-Yu site, Taiwan was studied to predict the permeability and conducting aperture with depth. Through a comparison of the presented model with three existing models [(1) the simple one parallel fracture set model, (2) the three orthogonal fracture set model, and (3) the random disc fracture model], it was shown that permeability-depth relations for the three orthogonal fracture set model and the new model are almost the same.

A revisit of drawdown behavior during pumping in unconfined aquifers

Received 16 March 2010; revised 7 February 2011; accepted 7 March 2011; published 6 May 2011. [1] In this study, the S‐shaped log‐log drawdown‐time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown‐time behavior of the confined aquifer to the presence of an “additional” source of water. Unlike previous studies,this sourceof water isreinvestigated byexaminingthetemporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1‐D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1‐D vertical flow without an initial unsaturated zone can also yield the S‐shaped drawdown‐time curve as in an unconfined aquifer. We therefore conclude that thetransitionofthewaterreleasemechanismsandverticalflowintheaquiferarethecauseof the S‐shaped drawdown‐time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown‐time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross‐correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S‐shaped drawdown‐time curves observed in the field.

Soil water balance model for precipitation-induced shallow landslides

Precipitation infiltration is one of the most significant triggering factors for slope failure occurrence in many places around the world. Knowledge of the mechanisms leading to precipitation-induced slope failures is of great importance to the management of landslide hazard. In this study, a soil water balance model is developed to estimate soil water flux during the process of infiltration from rainfall data, with consideration of storm periods and non-storm periods. Two important assumptions in this study are given: (1) instantaneous uniform distribution of the degree of saturation and (2) a linear relationship between evapotranspiration and the related degree of saturation. For storm periods, the Brooks and Corey model estimates both the soil water retention curve and soil water parameters. The infiltration partition is employed by an infinite-series solution of Philip in conjunction with the time compression approximation. For none-storm periods, evapotranspiration can be derived for the moisture depletion of soil water. This study presents a procedure for calculating the safety factor for an unsaturated slope suffering from precipitation infiltration. The process of infiltration into a slope due to rainfall and its effect on soil slope behavior are examined using modified Mohr–Coulomb failure criterion in conjunction with a soil water balance model. The results indicate that the matric suction, which is closely related to slope stability, is affected by the degree of saturation controlled by rainfall events.

Estimation of groundwater recharge using water balance model

The main purpose of this paper is to apply a water balance concept with two models in the Ching-Shui watershed to describe the groundwater recharge. First of all, a soil moisture budget model is established to estimate the infiltration, runoff, evapotranspiration, and groundwater recharge in the watershed, where the moisture content of the soil is tracked through time. Secondly, the groundwater recharge was also estimated by the model of the base-flow-record estimation, with the assumption that groundwater evaporation is negligible. In addition, since the analyzed base-flow trends are high, when executing model analysis, the depths of infiltration estimated by stable-base-flow analysis is used to obtain more reasonable groundwater recharge value. The coefficients of groundwater recharge by the precipitation in the Ching-Shui watershed estimated from the established soil moisture budget model and the base-flow model were 12.40% and 9.92%, respectively. Comparison show the result of both models to be close.

Fluid flow and connectivity in fractured rock

A numerical simulation using the boundary integral element method is used to solve fluid flow through a network of discrete fractures. The fracture network is composed of three orthogonal fracture sets, with fracture length, density, and location characterized by appropriate probability distributions. Emphasis is placed on understanding how fracture connectivity influences fluid flow within a network of fractures. Based on the percolation process, a three-dimensional discrete fracture model has been developed to investigate the effect of the percolation factor and the percolation frequency on connectivity and flowrate. The numerical model results indicate that there exists a sharp threshold flowrate for the case of constant mean fracture length and varying fracture volume density as well as for the case of constant fracture volume density and varying mean fracture length. The values of percolation threshold and critical percolation frequency are predicted to be approximately 1.1 and 0.35, respectively, for circular fractures. The results also indicate that an increase in the percolation factor increases the degree of interconnection and, thus, increases the flowrate of a fracture network.

Why hydraulic tomography works

Head measurements at a single observation well during a cross-hole pumping test carry a great amount of information about aquifer heterogeneity other than the average property of the aquifer as implied in Theis analysis of aquifer test. In this commentary, we use simple examples and a probabilistic reasoning approach based on Darcy’s law to unravel this information, buried in the results of quantitative stochastic analyses of flow in heterogeneous aquifers (Bakr et al. 1978; Dagan 1985, 1989) and vadose zones (Yeh et al. 1985a, 1985b, 1985c; Yeh and Zhang 1996). We subsequently use this information to elucidate the principles of hydraulic tomography (HT), sequential pumping tests, or multi-well interference tests (see Yeh and Liu 2000; Illman et al. 2009; Brauchler et al. 2011; Cardiff and Barrash 2011). Consider a pumping test in a one-dimensional heterogeneous confined aquifer (i.e., a horizontal soil column) which contains a pumping and an observation port. Ends of the aquifer are held at the same prescribed constant head, flow is at steady state, and the pumping rate, Q , is known. We now ask what the pumping rate and the drawdown at the observation port tell us about the spatial variation of the aquifer hydraulic conductivity (K ).

Percolation and Dispersion of Mass Transport in Saturated Fracture Networks

Dispersion and transport of mass in a fracture network is a percolation process. Macro-scale dispersion is related to travel time, distance, mass distribution and fracture geometry. This article presents a stochastic, discrete fracture model in conjunction with percolation theory to investigate the dispersion phenomenon and the power law relationship between mean square travel paths displacement 〈 r2 〉 and particle travel time t. For imposed boundary conditions, particle dispersion is simulated to observe percolation thresholds and dispersion trends in different network structures. Simulation results demonstrate that the critical exponent values of t in the percolated networks are extremely close to the theoretical value of 1.27 and occur at certain percolation factors. Below these percolation factors, the exponents of t increase with decreasing percolation factors, above these percolation factors, exponents decrease with increasing percolation factors. In our simulated cases, the proportionality between 〈 r2 〉 and time t is given by t raised to a power between 1.27 and 1.66, depending on the fracture pattern. The coefficient of anisotropic dispersion tensor increases with increasing distance. The percolation process is related to travel time and distance, and cannot be interpreted as a Fickian diffusive process.

Rainfall characteristics for anisotropic conductivity of unsaturated soil slopes

The purpose of this study was to investigate the effects of the anisotropic ratio on the stability of slopes using the reliability index approach. A numerical analysis of the relationship between the three rainfall patterns, advanced, normal and delayed, and the anisotropic ratios was designed. This study also considered three different soil properties (sand, silt, and clay) to simulate rain infiltration. In this study, probability analysis was used to evaluate the stability of unsaturated soil slopes. The finite element computer program Geo-Studio was used to simulate the process of rainwater infiltrating a slope. The pore-water pressure results evaluated from seepage analysis (SEEP/W) were imported into the slope stability program (SLOPE/W). Results for the anisotropic ratio of hydraulic conductivity indicate that when the anisotropic ratios become higher, the reduction in the reliability index is insignificant. In addition, the simulation results indicated that when saturated hydraulic conductivity (ks) was less than rainfall intensities (I), the percentage probability of the occurrence of a landslide was larger than when ks was greater than I. Finally, in the cases of anisotropic ks, stability of the high ratio soil slopes was not found to be sensitive to the reliability index variation during the simulation period. Moreover, when ks was greater than I, slope stability decreased earlier than was the case in the opposite situation.

An approach to evaluate groundwater recharge from streamflow and groundwater records

To assess groundwater recharge, this study provided a composite method combining the recession-curve-displacement method and water-table fluctuation method. First, the initial recharge reference value was determined using the water-table fluctuation method. The corresponding groundwater discharge was then determined from the recharge reference value using the recession-curve-displacement method. Furthermore, the recession segment of the match between groundwater discharge and streamflow was computed. The recharge reference value was repeatedly adjusted to achieve a good fit with the recession segment for groundwater discharge and streamflow, thereby attaining the final groundwater recharge using the proposed method. Finally, the groundwater recharge of the Lanyang Creek basin in Taiwan was estimated as a case study. A comparison of recession-curve-displacement method and proposed composite method are presented. Estimation results show that the number of recharge events, recharge timing of these events, groundwater recharge events that satisfy recession theory, and range of transmissivity can be obtained using the proposed composite method. Comparison results demonstrate that the number of groundwater recharge events obtained with the composite method was greater than that acquired with the recession-curvedisplacement method. However, the annual recharge and seasonal recharge obtained with the recession-curve-displacement method and composite method were close.