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Since 1900, Semarang City has been meeting its industrial water needs by pumping groundwater through its underlying aquifers. The trend toward exploiting groundwater resources has driven the number of deep wells and their production capacity to increase, and therefore leads to the water table to drop from time to time, which has been marked as one of the primary causes of land subsidence there. The main aim of the current study was to numerically model the temporal and spatial evolution of groundwater table under excess abstraction so that a groundwater management strategy can be accordingly drawn up for ensuing the sustainability of groundwater resources in the future. A series of numerical simulations were carried out to take into account hydrogeological data, artificial and natural discharges of deep wells, and boundary effects in Semarang City. The groundwater modeling is calibrated under two flow conditions of the steady state from 1970 to 1990 and the transient state from 1990 to 2005 for six observation wells distributed in Semarang City. Four scenarios that reflect potential management strategies were developed, and then their effectiveness was systematically investigated. The results of our study indicate that the implementation of proper groundwater control management and measure is able to restore the groundwater level to rise back in Semarang City, and in turn achieve the sustainability of groundwater resources.
Weicheng Lo; Sanidhya Purnomo; Dwi Sarah; Sokhwatul Aghnia; Probo Hardini. Groundwater Modelling in Urban Development to Achieve Sustainability of Groundwater Resources: A Case Study of Semarang City, Indonesia. Water 2021, 13, 1395 .
AMA StyleWeicheng Lo, Sanidhya Purnomo, Dwi Sarah, Sokhwatul Aghnia, Probo Hardini. Groundwater Modelling in Urban Development to Achieve Sustainability of Groundwater Resources: A Case Study of Semarang City, Indonesia. Water. 2021; 13 (10):1395.
Chicago/Turabian StyleWeicheng Lo; Sanidhya Purnomo; Dwi Sarah; Sokhwatul Aghnia; Probo Hardini. 2021. "Groundwater Modelling in Urban Development to Achieve Sustainability of Groundwater Resources: A Case Study of Semarang City, Indonesia." Water 13, no. 10: 1395.
Hydro-meteorological risks are a growing issue for societies, economies and environments around the world. An effective, sustainable response to such risks and their future uncertainty requires a paradigm shift in our research and practical efforts. In this respect, Nature-Based Solutions (NBSs) offer the potential to achieve a more effective and flexible response to hydro-meteorological risks while also enhancing human well-being and biodiversity. The present paper describes a new methodology that incorporates stakeholders’ preferences into a multi-criteria analysis framework, as part of a tool for selecting risk mitigation measures. The methodology has been applied to Tamnava river basin in Serbia and Nangang river basin in Taiwan within the EC-funded RECONECT project. The results highlight the importance of involving stakeholders in the early stages of projects in order to achieve successful implementation of NBSs. The methodology can assist decision-makers in formulating desirable benefits and co-benefits and can enable a systematic and transparent NBSs planning process.
Laddaporn Ruangpan; Zoran Vojinovic; Jasna Plavšić; Dong-Jiing Doong; Tobias Bahlmann; Alida Alves; Leng-Hsuan Tseng; Anja Randelović; Andrijana Todorović; Zvonimir Kocic; Vladimir Beljinac; Meng-Hsuan Wu; Wei-Cheng Lo; Blanca Perez-Lapeña; Mário J. Franca. Incorporating stakeholders’ preferences into a multi-criteria framework for planning large-scale Nature-Based Solutions. Ambio 2020, 50, 1 -18.
AMA StyleLaddaporn Ruangpan, Zoran Vojinovic, Jasna Plavšić, Dong-Jiing Doong, Tobias Bahlmann, Alida Alves, Leng-Hsuan Tseng, Anja Randelović, Andrijana Todorović, Zvonimir Kocic, Vladimir Beljinac, Meng-Hsuan Wu, Wei-Cheng Lo, Blanca Perez-Lapeña, Mário J. Franca. Incorporating stakeholders’ preferences into a multi-criteria framework for planning large-scale Nature-Based Solutions. Ambio. 2020; 50 (8):1-18.
Chicago/Turabian StyleLaddaporn Ruangpan; Zoran Vojinovic; Jasna Plavšić; Dong-Jiing Doong; Tobias Bahlmann; Alida Alves; Leng-Hsuan Tseng; Anja Randelović; Andrijana Todorović; Zvonimir Kocic; Vladimir Beljinac; Meng-Hsuan Wu; Wei-Cheng Lo; Blanca Perez-Lapeña; Mário J. Franca. 2020. "Incorporating stakeholders’ preferences into a multi-criteria framework for planning large-scale Nature-Based Solutions." Ambio 50, no. 8: 1-18.
Soils are naturally present in the form of stratified layers, each being distinguishable from adjacent layers by a distinctive set of hydraulic and elasticity properties. Lo et al. (2020) have recently presented a theoretical model of poroelasticity that provides a detailed description of simultaneous solid framework deformation and immiscible fluid flow in a two-layer soil system that is made up of upper unsaturated and lower saturated zones caused by a vertical constant surface load under semi-permeable boundary drainage conditions. Due to the existence of different moisture contents (partial and full saturations) in the upper and lower layers, excess pore fluid pressure does not exhibit a symmetric distribution with respect to depth. Therefore, an exact, analytical solution for fully permeable boundary drainage conditions cannot be determined readily by applying scaling transformations and spatial translations from our recent result even though the coupled model equations possess an invariance feature. In this paper, a well-defined boundary-value problem based on the decoupled model equations of poroelasticity generalized for a two-fluid system is rigorously formulated for a double-layer (unsaturated-saturated) soil profile that allows water drainage at both top and bottom surfaces. Using Laplace time transformation, we derive the closed-form, exact-analytical solution accounting for the intricate interaction between deformable solid matrix and compressible interstitial fluids in such a two-layer system. The solution takes a more complicated form than that for the semi-permeable case. Boundary drainage conditions indeed affect the development of excess pore water and air pressures along with the time evolution of total settlement. We show that when the bottom boundary of the saturated layer overlain by the unsaturated layer with a lower hydraulic conductivity is impervious, the curve describing the relationship between the depth and excess water pressure at the interface has a negative slope, whereas the slope is positive when the boundary is pervious. The total settlement in the lower saturated layer would thus achieve an equilibrium state faster.
Weicheng Lo; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. Poroelastic theory of consolidation for a two-layer system with an upper unsaturated soil and a lower saturated soil under fully permeable boundary conditions. Journal of Hydrology 2020, 596, 125700 .
AMA StyleWeicheng Lo, Ronaldo I. Borja, Jiao-Hong Deng, Jhe-Wei Lee. Poroelastic theory of consolidation for a two-layer system with an upper unsaturated soil and a lower saturated soil under fully permeable boundary conditions. Journal of Hydrology. 2020; 596 ():125700.
Chicago/Turabian StyleWeicheng Lo; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. 2020. "Poroelastic theory of consolidation for a two-layer system with an upper unsaturated soil and a lower saturated soil under fully permeable boundary conditions." Journal of Hydrology 596, no. : 125700.
The spatiotemporal variability in precipitation could have a significant impact on ground subsidence. In this paper, we utilize a previously developed one-dimensional theory of consolidation for a two-fluid system, the generalization of Biot's theory, to investigate the impact of a time-dependent fluid flux across the surface of an unsaturated soil on the solid deformation and pore pressure responses. We consider three prescribed fluid flux patterns and the associated gradient of pore water pressure: constant, periodic, and exponential flux patterns. We employ a Fourier series representation and Laplace transformation in the space and time domains to derive a complete set of closed-form analytical solutions, including the complementary and particular solutions, describing both transient and steady-state excess pore water and pore air pressure responses as well as the total settlement induced by the fluid flux. Using two different types of soil, i.e. clay and sand, we demonstrate the dependence of the solution on the initial water saturation and hydraulic conductivity in the saturated and unsaturated regimes. Results of this study reveal that the fluid flux across the surface could have a significant impact on the dissipation of excess pore water pressure and the time evolution of the total settlement of the ground surface. The effect on the pore water pressure is more significant for sand than for clay irrespective of moisture content, mainly because of the much higher hydraulic conductivity of sand. Finally, we show that the hydraulic conductivity has a dominant effect on the consolidation behaviors of saturated and unsaturated soils subjected to surface fluid flux.
Weicheng Lo; Juiche Chang; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions. Journal of Hydrology 2020, 595, 125671 .
AMA StyleWeicheng Lo, Juiche Chang, Ronaldo I. Borja, Jiao-Hong Deng, Jhe-Wei Lee. Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions. Journal of Hydrology. 2020; 595 ():125671.
Chicago/Turabian StyleWeicheng Lo; Juiche Chang; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. 2020. "Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions." Journal of Hydrology 595, no. : 125671.
Natural soils often exhibit stratification, thus resulting in distinct flow and deformation patterns within each stratum as acted on by applied compaction stress or induced fluid pressure gradient. A comprehensive theoretical model of poroelasticity is rigorously established in the current study, which provides a detailed mathematical treatment of soil deformation and pore fluid pressure change through the upper unsaturated and lower saturated zones caused by time-invariant external loads. This double-layer system consists of an upper soil layer bearing air and water simultaneously, whereas a lower soil layer remains entirely saturated. A linear transformation that exactly separates our coupled model equations into analytically solvable coordinates is first achieved. Then, a boundary-value problem involving these equations under a semipermeable drainage scenario is formulated as a representative example, which complies with the physical constraint to ensure the continuity of pore water flux and pressure at the interface. The problem is solved analytically using Laplace transformation, and next computed numerically with hydraulic and elasticity parameters corresponding to a saturated clay overlain by an unsaturated sand to evaluate the excess pore fluid pressure and total settlement in each zone. A parametric study is also performed to examine the effect of initial water content and soil texture on the deformation behavior of the soil as well as on the development of the pore fluid pressure. The excess pore water pressure in each zone is mutually affected; therefore, if the upper unsaturated zone has a lower hydraulic conductivity, it would hinder, as compared to the opposite condition, the dissipation of the excess pore water pressure in the lower saturated zone as a consequence of water drainage blockage occurring in the former. Thus, a significant implication of our results is that change in thickness of the lower saturated zone created by land surface stress loads will always be overestimated when its interaction with the hydromechanical behavior of the upper unsaturated zone is neglected.
Weicheng Lo; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading. Journal of Hydrology 2020, 588, 124997 .
AMA StyleWeicheng Lo, Ronaldo I. Borja, Jiao-Hong Deng, Jhe-Wei Lee. Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading. Journal of Hydrology. 2020; 588 ():124997.
Chicago/Turabian StyleWeicheng Lo; Ronaldo I. Borja; Jiao-Hong Deng; Jhe-Wei Lee. 2020. "Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading." Journal of Hydrology 588, no. : 124997.
In recent years, more studies have been focusing on the transient behaviors of the movement of soil water and changes in matric potential, which require the measurement of the rapid changes in matric potential or capillary pressure. Because of the delayed response, the value of the matric potential measured using a tensiometer may not precisely reflect the actual matric potential during a transient condition. We performed a series of experiments to analyze the effect of grain size, effective saturation, and the hydraulic conductivities of ceramic cup and porous media on the response time of a tensiometer. The outcomes suggested that a decrease of hydraulic conductivity of the ceramic cup significantly increases the response time. Moreover, the response time measured under unsaturated conditions did not follow an ideal exponential decay. This finding was consistent with the existing theories, based on which, we proposed three models to describe the time-varied response function. These models were applied to correct the measured matric potential for dynamic water retention curve (WRC), and the findings were compared with those of other existing methods used for measuring the matric potential. We found that the incorporation of the theory of response time significantly reduced the discrepancy between the matric potential measured using two ceramic cups with different response times during dynamic drainage. We concluded that the delayed response of a tensiometer can have a significant effect on the measurement of the transient matric potential or capillary pressure and can be corrected using response time equations.
Yi-Zhih Tsai; Ming-Liang Cheng; Qun-Zhan Huang; Weicheng Lo; Ming-Hsu Li; Shao-Yiu Hsu. Effect of effective saturation and ceramic cup properties on the response time of tensiometers. Journal of Hydrology 2019, 582, 124445 .
AMA StyleYi-Zhih Tsai, Ming-Liang Cheng, Qun-Zhan Huang, Weicheng Lo, Ming-Hsu Li, Shao-Yiu Hsu. Effect of effective saturation and ceramic cup properties on the response time of tensiometers. Journal of Hydrology. 2019; 582 ():124445.
Chicago/Turabian StyleYi-Zhih Tsai; Ming-Liang Cheng; Qun-Zhan Huang; Weicheng Lo; Ming-Hsu Li; Shao-Yiu Hsu. 2019. "Effect of effective saturation and ceramic cup properties on the response time of tensiometers." Journal of Hydrology 582, no. : 124445.
A set of closed-form series solutions that account for the transient and steady-state responses of excess pore water pressure and total settlement to one-dimensional consolidation in saturated soils exposed to various typical types of time-dependent external loading with any desired excitation amplitude and period is symmetrically formulated based on the theory of poroelasticity. The mathematical approach developed in the current study is quite general so that it can be straightforward extended to arbitrary waveform shapes of harmonic loading after they are simply represented in terms of Fourier trigonometric series. These solutions are numerically calculated to evaluate variations in excess pore water pressure and total settlement due to vertical consolidation in saturated soils with two very different magnitudes of intrinsic permeability, Soil A (higher) and Soil B (lower), as representative examples using two illustrative periods per cycle. Our results show that within excitation frequencies we examined, the excess pore water pressure exhibits greater cyclic swings in Soil B than that in Soil A as harmonic stress compression and relaxation are added, but an inverse trend is observed for total settlement. As compared to static external loading, the excess pore water pressure persists longer with periodic fluctuation in the presence of cyclic loading, but less total settlement is induced in Soil B. The discrepancy in the latter (total settlement) between the static and cyclic loading is most significant in Soil B, reflecting a physical implication that low permeability leads to a slower dissipation of excess pore water pressure, thus causing less settlement with time.
Jiao-Hong Deng; Jhe-Wei Lee; Weicheng Lo. Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading. Journal of Hydrology 2019, 573, 395 -405.
AMA StyleJiao-Hong Deng, Jhe-Wei Lee, Weicheng Lo. Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading. Journal of Hydrology. 2019; 573 ():395-405.
Chicago/Turabian StyleJiao-Hong Deng; Jhe-Wei Lee; Weicheng Lo. 2019. "Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading." Journal of Hydrology 573, no. : 395-405.
A rigorous mathematical framework is presented for the development of a set of coupled partial differential equations to describe the consolidation of saturated soils under the simultaneous action of external static loads and gravity forces. These equations generalize the Biot model of poroelasticity in a systematic manner to well account for additional momentum exchange arising from the physical mechanisms involved in gravitational compaction due to changes in volumetric fraction and material density of each constituent. A boundary-value problem is then formulated as a representative example to quantitatively examine gravity effect on the dissipation of excess pore fluid pressure and settlement magnitude, and is solved numerically in a finite difference scheme. In the current study, the boundary conditions have been directly calculated in numerical scheme, which improves previous studies to avoid using the approximation of the trapezoidal rule. A physically-consistent parameter, derived fundamentally from the first principle, balance of momentum, is proposed for the first time, which provides an exact measure of the degree to which variations in final total settlement occur due to the presence of gravity effect. This dimensionless parameter takes a closed-form expression that refines our foregoing works, and is quite general since it is applicable to both saturated and variably-saturated soils. Our studies show that the variations are essentially controlled by soil elasticity modulus and height, as well as a derived gravity factor. This factor underlines the importance of the dependency between consolidation behaviors and distinct physical properties of pore fluids. Lastly, a comparative study is carried out, indicating that gravity forces yield more significant impact on unsaturated soils than saturated soils we examined, leading to more relative increment in the final total settlement.
Nan-Chieh Chao; Jhe-Wei Lee; Weicheng Lo. Gravity effect on consolidation in poroelastic soils under saturated and unsaturated conditions. Journal of Hydrology 2018, 566, 99 -108.
AMA StyleNan-Chieh Chao, Jhe-Wei Lee, Weicheng Lo. Gravity effect on consolidation in poroelastic soils under saturated and unsaturated conditions. Journal of Hydrology. 2018; 566 ():99-108.
Chicago/Turabian StyleNan-Chieh Chao; Jhe-Wei Lee; Weicheng Lo. 2018. "Gravity effect on consolidation in poroelastic soils under saturated and unsaturated conditions." Journal of Hydrology 566, no. : 99-108.
Wei-Cheng Lo; Nan-Chieh Chao; Chu-Hui Chen; Jhe-Wei Lee. Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces. Advances in Water Resources 2017, 106, 121 -131.
AMA StyleWei-Cheng Lo, Nan-Chieh Chao, Chu-Hui Chen, Jhe-Wei Lee. Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces. Advances in Water Resources. 2017; 106 ():121-131.
Chicago/Turabian StyleWei-Cheng Lo; Nan-Chieh Chao; Chu-Hui Chen; Jhe-Wei Lee. 2017. "Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces." Advances in Water Resources 106, no. : 121-131.
Flood risk management has become a growing priority for city managers and disaster risk prevention agencies worldwide. Correspondingly, large investments are made towards data collection, archiving and analysis and technologies such as geographic information systems (GIS) and remote sensing play important role in this regard. GIS technologies offer valuable means for delineation of flood plains, zoning of areas that need protection from floods and identification of plans for development and scoping of various kinds of flood protection measures. Flood inundation maps (FIMs) are particularly useful in planning flood disaster risk responses. The purpose of the present paper is to describe efforts in developing new generation of FIMs at the city scale and to demonstrate effectiveness of such maps in the case of the coastal city of Tainan, Taiwan. In the present work, besides pluvial floods, the storm surge influence is also considered. The 1D/2D coupled model SOBEK was used for flood simulations. Different indicators such as Probability of Detection (POD) and Scale of Accuracy (SA) were applied in the calibration and validation stages of the work and their corresponding values were found to be up to 88.1% and 68.0%, respectively. From the overall analysis, it came up that land elevation, tidal phase, and storm surge are the three dominant factors that influence flooding in Tainan. A large number of model simulations were carried out in order to produce FIMs which were then effectively applied in the stakeholder engagement process.
Dong-Jiing Doong; Weicheng Lo; Zoran Vojinovic; Wei-Lin Lee; Shin-Ping Lee. Development of a New Generation of Flood Inundation Maps—A Case Study of the Coastal City of Tainan, Taiwan. Water 2016, 8, 521 .
AMA StyleDong-Jiing Doong, Weicheng Lo, Zoran Vojinovic, Wei-Lin Lee, Shin-Ping Lee. Development of a New Generation of Flood Inundation Maps—A Case Study of the Coastal City of Tainan, Taiwan. Water. 2016; 8 (11):521.
Chicago/Turabian StyleDong-Jiing Doong; Weicheng Lo; Zoran Vojinovic; Wei-Lin Lee; Shin-Ping Lee. 2016. "Development of a New Generation of Flood Inundation Maps—A Case Study of the Coastal City of Tainan, Taiwan." Water 8, no. 11: 521.
The one-dimensional consolidation model of poroelasticity of Lo et al. [16] for an unsaturated soil under constant loading is generalized to include an arbitrary time-dependent loading. A closed-form solution for the pore water and air pressures along with the total settlement is derived by employing a Fourier series representation in the spatial domain and a Laplace transformation in the time domain. This solution is illustrated for the important example of a fully-permeable soil cylinder with an undrained initial condition acted upon by a periodic stress. Our results indicate that, in terms of a dimensionless time scale, the transient solution decays to zero most slowly in a water-saturated soil, whereas for an unsaturated soil, the time for the transient solution to die out is inversely proportional to the initial water saturation. The generalization presented here shows that the diffusion time scale for pore water in an unsaturated soil is orders of magnitude greater than that in a water-saturated soil, mainly because of the much smaller hydraulic conductivity of the former.
Wei-Cheng Lo; Garrison Sposito; Jhe-Wei Lee; Hsiuhua Chu. One-dimensional consolidation in unsaturated soils under cyclic loading. Advances in Water Resources 2016, 91, 122 -137.
AMA StyleWei-Cheng Lo, Garrison Sposito, Jhe-Wei Lee, Hsiuhua Chu. One-dimensional consolidation in unsaturated soils under cyclic loading. Advances in Water Resources. 2016; 91 ():122-137.
Chicago/Turabian StyleWei-Cheng Lo; Garrison Sposito; Jhe-Wei Lee; Hsiuhua Chu. 2016. "One-dimensional consolidation in unsaturated soils under cyclic loading." Advances in Water Resources 91, no. : 122-137.
Wei-Cheng Lo; Chao-Lung Yeh; Jhe-Wei Lee. Effect of viscous cross coupling between two immiscible fluids on elastic wave propagation and attenuation in unsaturated porous media. Advances in Water Resources 2015, 83, 207 -222.
AMA StyleWei-Cheng Lo, Chao-Lung Yeh, Jhe-Wei Lee. Effect of viscous cross coupling between two immiscible fluids on elastic wave propagation and attenuation in unsaturated porous media. Advances in Water Resources. 2015; 83 ():207-222.
Chicago/Turabian StyleWei-Cheng Lo; Chao-Lung Yeh; Jhe-Wei Lee. 2015. "Effect of viscous cross coupling between two immiscible fluids on elastic wave propagation and attenuation in unsaturated porous media." Advances in Water Resources 83, no. : 207-222.
Seismic stimulation, the application of low-frequency stress-pulsing to the boundary of a porous medium containing water and a non-aqueous fluid to enhance the removal of the latter, shows great promise for both contaminated groundwater remediation and enhanced oil recovery, but theory to elucidate the underlying mechanisms lag significantly behind the progress achieved in experimental research. We address this conceptual lacuna by formulating a boundary-value problem to describe pore-pressure pulsing at seismic frequencies that is based on the continuum theory of poroelasticity for an elastic porous medium permeated by two immiscible fluids. An exact analytical solution is presented that is applied numerically using elasticity parameters and hydraulic data relevant to recent proof-of-principle laboratory experiments investigating the stimulation-induced mobilization of trichloroethene (TCE) in water flowing through a compressed sand core. The numerical results indicated that significant stimulation-induced increases of the TCE concentration in effluent can be expected from pore-pressure pulsing in the frequency range of 25–100 Hz, which is in good agreement with what was observed in the laboratory experiments. Sensitivity analysis of our numerical results revealed that the TCE concentration in the effluent increases with the porous medium framework compressibility and the pulsing pressure. Increasing compressibility also leads to an optimal stimulation response at lower frequencies, whereas changing the pulsing pressure does not affect the optimal stimulation frequency. Within the context of our model, the dominant physical cause for enhancement of non-aqueous fluid mobility by seismic stimulation is the dilatory motion of the porous medium in which the solid and fluid phases undergo opposite displacements, resulting in stress-induced changes of the pore volume.
Wei-Cheng Lo; Garrison Sposito; Yu-Han Huang. Modeling seismic stimulation: Enhanced non-aqueous fluid extraction from saturated porous media under pore-pressure pulsing at low frequencies. Journal of Applied Geophysics 2011, 78, 77 -84.
AMA StyleWei-Cheng Lo, Garrison Sposito, Yu-Han Huang. Modeling seismic stimulation: Enhanced non-aqueous fluid extraction from saturated porous media under pore-pressure pulsing at low frequencies. Journal of Applied Geophysics. 2011; 78 ():77-84.
Chicago/Turabian StyleWei-Cheng Lo; Garrison Sposito; Yu-Han Huang. 2011. "Modeling seismic stimulation: Enhanced non-aqueous fluid extraction from saturated porous media under pore-pressure pulsing at low frequencies." Journal of Applied Geophysics 78, no. : 77-84.
A theoretical analysis for the dynamic response of a semi-infinite fluid-bearing porous medium to external harmonic loading is presented in this study based on the decoupled poroelasticity equations of Biot (1962). A corresponding initial and boundary value problem is formulated and the analytical solution for the induced pore pressure and total dilatational stress is determined using the technique of Laplace transforms. To investigate the quantitative impact of inertial effect on the poroelastic response, the problem is also solved analytically in the diffusive model (i.e. inertial terms are ignored). Comparison of the analytical solutions obtained from two different models shows that as inertial effect is accounted for, the response undergoes in a dynamic manner but lags behind the loading by a physical factor equal to the travel time necessary for pressure wave to reach the location that is prescribed. A numerical study is then conducted for water-containing Columbia fine sandy loam at lower excitation frequencies as a representative example. Our numerical results reveal that the dynamic model yields a cyclic response for the induced pore pressure and total dilatational stress with respect to depth, but the diffusive model fails to predict this attribute. Lastly, we find in the dynamic model that effective stress may take on a positive value at some depths due to the existence of time lag in the response of pore fluid to external loading so that the solid skeleton needs to sustain excess fluid pressure. This positive value is crucial for the phenomenon of liquefaction if the loading is substantial enough.
Wei-Cheng Lo; Chu-Hui Chen; Chao-Lung Yeh. Analytical solution for the dynamic response of a saturated poroelastic half-space to harmonic stress loading. Journal of Hydrology 2010, 387, 233 -243.
AMA StyleWei-Cheng Lo, Chu-Hui Chen, Chao-Lung Yeh. Analytical solution for the dynamic response of a saturated poroelastic half-space to harmonic stress loading. Journal of Hydrology. 2010; 387 (3-4):233-243.
Chicago/Turabian StyleWei-Cheng Lo; Chu-Hui Chen; Chao-Lung Yeh. 2010. "Analytical solution for the dynamic response of a saturated poroelastic half-space to harmonic stress loading." Journal of Hydrology 387, no. 3-4: 233-243.
Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations.
Wei-Cheng Lo; Garrison Sposito; Ernest Majer; Chao-Lung Yeh. Motional modes of dilatational waves in elastic porous media containing two immiscible fluids. Advances in Water Resources 2010, 33, 304 -311.
AMA StyleWei-Cheng Lo, Garrison Sposito, Ernest Majer, Chao-Lung Yeh. Motional modes of dilatational waves in elastic porous media containing two immiscible fluids. Advances in Water Resources. 2010; 33 (3):304-311.
Chicago/Turabian StyleWei-Cheng Lo; Garrison Sposito; Ernest Majer; Chao-Lung Yeh. 2010. "Motional modes of dilatational waves in elastic porous media containing two immiscible fluids." Advances in Water Resources 33, no. 3: 304-311.
Poroelasticity theory has become an effective and accurate approach to analyzing the intricate mechanical behavior of a porous medium containing two immiscible fluids, a system encountered in many subsurface engineering applications. However, the resulting partial differential equations in the theory intrinsically take on a coupled form in the terms pertinent to inertial drag, viscous damping, and applied stress, making it difficult to obtain closed-form, steady-state analytical solutions to boundary-value problems except in special cases. In the present paper, we demonstrate that, for dilatational wave excitations, these partial differential equations can be decoupled analytically into three Helmholtz equations featuring complex-valued, frequency-dependent normal coordinates that correspond physically to three independent modes of dilatational wave motion. The normal coordinates in turn can be expressed in the frequency domain as three different linear combinations of the solid dilatation and the linearized increment of fluid content for each pore fluid, or equivalently, as three different linear combinations of total dilatational stress and two pore fluid pressures. These representations are applicable to strain-controlled and stress-prescribed boundary conditions, respectively. Numerical calculations confirm that the phase speed and attenuation coefficient of the three dilatational waves represented by the Helmholtz equations are exactly identical to those obtained previously by numerical solution of the dispersion relations for dilatational wave excitation of a porous medium containing two immiscible fluids. Thus, dilatational wave motions in unsaturated porous media subject to suitable boundary conditions can now be accurately modeled analytically.
Wei-Cheng Lo; Garrison Sposito; Ernest Majer. Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids. Journal of Engineering Mathematics 2008, 64, 219 -235.
AMA StyleWei-Cheng Lo, Garrison Sposito, Ernest Majer. Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids. Journal of Engineering Mathematics. 2008; 64 (2):219-235.
Chicago/Turabian StyleWei-Cheng Lo; Garrison Sposito; Ernest Majer. 2008. "Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids." Journal of Engineering Mathematics 64, no. 2: 219-235.
The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.
Wei-Cheng Lo; Garrison Sposito; Ernest Majer. Low-frequency dilatational wave propagation through fully-saturated poroelastic media. Advances in Water Resources 2006, 29, 408 -416.
AMA StyleWei-Cheng Lo, Garrison Sposito, Ernest Majer. Low-frequency dilatational wave propagation through fully-saturated poroelastic media. Advances in Water Resources. 2006; 29 (3):408-416.
Chicago/Turabian StyleWei-Cheng Lo; Garrison Sposito; Ernest Majer. 2006. "Low-frequency dilatational wave propagation through fully-saturated poroelastic media." Advances in Water Resources 29, no. 3: 408-416.