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Variability quantification of excess pressure head in heterogeneous deformable aquifers. (English) Zbl 07163034
Summary: The direct effect of changes in applied total stresses on fluid-saturated geologic materials is reflected in fluctuations in pore pressure. The quantification of these pressure changes has traditionally been based on the classical poroelasticity theory, developed ignoring the natural variability in aquifer properties (parameters). Uncertainty of excess pore pressure prediction is therefore expected to be large when applying the classical model to field aquifer systems which generally have high degree of heterogeneity. Very limited attention to this issue has been paid. The motivation for this work is to quantify the uncertainty associated with the classical model, the spatial variability of the predicted excess pressure head in the field, where the groundwater flow is produced by the changes in total stress. The stochastic methodology used to develop the results of this study is based on the nonstationary spectral approach. It is found that the heterogeneity and correlation length scale of the log hydraulic conductivity process, and the pore compressibility parameter play essential roles in enhancing the variability in excess pressure head. In addition, the pore pressure head distribution predicted using the classical poroelasticity theory is subject to large uncertainty at a large depth in heterogeneous aquifers.
76 Fluid mechanics
74 Mechanics of deformable solids
Full Text: DOI
[1] Hsieh, P. A.; Bredehoeft, J. D.; Farr, J. M., Determination of aquifer transmissivity from earth tide analysis, Water Resour. Res., 23, 1824-1832 (1987)
[2] van Der Kamp, G.; Gale, J. E., Theory of earth tide and barometric effects in porous formations with compressible grains, Water Resour. Res., 19, 538-544 (1983)
[3] Lam, K. Y.; Zhang, J.; Zong, Z., A numerical study of wave propagation in a poroelasticity medium by use of localized differential quadrature method, Appl. Math. Model., 28, 487-511 (2004) · Zbl 1147.74318
[4] Ohno, M.; Sato, T.; Notsu, K.; Wakita, H.; Ozawa, K., Groundwater-level changes due to pressure gradient induced by nearby earthquakes off Izu Peninsula, 1997, Pure appl. Geophys., 163, 647-655 (2006)
[5] Roeloffs, E., Poroelastic techniques in the study of earthquake-related hydrologic phenomena, Adv. Geophys., 37, 135-195 (1996)
[6] Viesca, R. C.; Templeton, E. L.; Rice, J. R., Off-fault plasticity and earthquake rupture dynamics, 2. Effects of fluid saturation, J. Geophys. Res., 113, B09307 (2008)
[7] Liu, Z.; Bird, P., Two-dimensional and three-dimensional finite element modelling of mantle processes beneath central South Island, New Zealand, Geophys. J. Int., 165, 1003-10028 (2006)
[8] Neuzil, C. E.; Pollock, D. W., “Erosional unloading and fluid pressures in hydraulically ”tight“ rocks”, J. Geol., 91, 179-193 (1983)
[9] Ni, G-H.; Liu, Z-Y; Lei, Z-D; Yang, D-W; Wang, L., Continuous simulation of water and soil erosion in a small watershed of the loess plateau with a distributed model, J. Hydrol. Eng., 13, 392-399 (2008)
[10] Gibson, R. E., The progress of consolidation in a clay layer increasing in thickness with time, Geotechnique, 8, 171-182 (1958)
[11] Hermanrud, C.; Venstad, J. M.; Cartwright, J.; Rennan, L.; Hermanrud, K.; Nordgård Bolås, H. M., Consequences of water level drops for soft sediment deformation and vertical fluid leakage, Math. Geosci., 45, 1-30 (2013)
[12] Wang, H. F., Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology (2000), Princeton University Press: Princeton University Press Princeton, New Jersey, N. J.
[13] Barry, S. I.; Mercer, G. N.; Zoppou, C., Deformation and fluid flow due to a source in a poro-elastic layer, Appl. Math. Model., 21, 681-689 (1997) · Zbl 0905.76087
[14] Tempone, P.; Fjaer, E.; Landrø, M., Improved solution of displacements due to a compacting reservoir over a rigid basement, Appl. Math. Model., 34, 3352-3362 (2010) · Zbl 1201.86010
[15] Budhu, M.; Ossai, R.; Adiyaman, I., Ground movements from aquifer recharge and recovery, J. Hydrol. Eng., 19, 790-799 (2014)
[16] Ferronato, M.; Gambolati, G.; Teatini, P.; Bau, D., Stochastic poromechanical modeling of anthropogenic land subsidence, Int. J. Solids Struct., 43, 3324-3336 (2006) · Zbl 1121.74351
[17] Frias, D. G.; Murad, M. A.; Pereira, F., Stochastic computational modeling of highly heterogeneous poroelastic media with long-range correlations, Int. J. Numer. Anal. Meth. Geomech., 28, 1-32 (2004) · Zbl 1075.74525
[18] Yeh, H.-D.; Lu, R.-H.; Yeh, G.-T., Finite element modelling for land displacements due to pumping, Int. J. Numer. Anal. Meth. Geomech., 20, 79-99 (1996) · Zbl 0869.73063
[19] Rojstaczer, S., Determination of fluid flow properties from the response of water levels in wells to atmospheric loading, Water Resour. Res., 24, 1927-1938 (1988)
[20] Domenico, P. A.; Schwartz, F. W., Physical and Chemical Hydrogeology (1998), John Wiley & Sons: John Wiley & Sons New York, N. Y
[21] Detournay, E.; Cheng, A. H-D., Fundamentals of poroelasticity, (Fairhust, C., Comprehensive Rock Engineering: Principles, Practice and Projects, Vol. II, Analysis and Design Method (1993), Pergamon Press: Pergamon Press New York)
[22] Neuzil, C. E., Hydromechanical coupling in geologic processes, Hydrogeol. J., 11, 41-83 (2003)
[23] Boutt, D. F., Poroelastic loading of an aquifer due to upstream dam releases, Ground Water, 48, 580-592 (2010)
[24] Francisco, L.; Antonio, G-J.; Miguel, A. S.; Francisco, J. S-S., Numerical modelling of pore pressure variations due to time varying loads using a hybrid technique: the case of the Itoiz reservoir (Northern Spain), Geophys. J. Int., 180, 327-338 (2010)
[25] Sophocleous, M.; Bardsley, W. E.; Healey, J., A rainfall loading response recorded at 300m depth: Implications for geological weighing lysimeters, J. Hydrol., 319, 237-244 (2006)
[26] van Der Kamp, G.; Maathuis, H., Annual fluctuations of ground water levels as a result of loading by surface moisture, J. Hydrol., 127, 137-152 (1991)
[27] Bakr, A. A.; Gelhar, L. W.; Gutjahr, A. L.; MacMillan, J. R., Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one- and three-dimensional flows, Water Resour. Res., 14, 263-271 (1978)
[28] Gelhar, L. W., Stochastic Subsurface Hydrology (1993), Prentice Hall: Prentice Hall Englewood Cliffs, New Jersey, N. J.
[29] Chiles, J-P.; Delfiner, P., Geostatistics: Modeling Spatial University (1999), John Wiley & Sons: John Wiley & Sons New York , N. Y. · Zbl 0922.62098
[30] Rubin, Y., Applied Stochastic Hydrogeology (2003), Oxford University Press: Oxford University Press New York, N. Y.
[31] Dagan, G., Flow and Transport in Porous Formations (1989), Springer: Springer New York, N. Y.
[32] Zhang, D., Stochastic Methods for Flow in Porous Media: Coping with Uncertainties (2002), Academic Press: Academic Press San Diego, Calif.
[33] Gutjahr, A. L.; Gelhar, L. W., Stochastic models of subsurface flow: infinite versus finite domains and stationarity, Water Resour. Res., 17, 337-350 (1981)
[34] Zhang, D.; Winter, C. L., Moment equation approach to single phase fluid flow in heterogeneous reservoirs, Soc. Petrol. Eng. J., 4, 118-127 (1999)
[35] Guadagnini, A.; Neuman, S. P., Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 2. Computational examples, Water Resour. Res., 35, 3019-3039 (1999)
[36] Haberman, R., Elementary Applied Partial Differential Equations: With Fourier Series and Boundary Value (1998), Prentice Hall: Prentice Hall Upper Saddle River, New Jersey · Zbl 0949.35001
[37] Duffy, C. J.; Gelhar, L. W., A frequency domain analysis of ground-water quality fluctuations: Interpretation of field data, Water Resour. Res., 23, 1115-1128 (1986)
[38] Gelhar, L. W., Stochastic analysis of phreatic aquifers, Water Resour. Res., 10, 539-545 (1974)
[39] Jimenez-Martınez, J.; Longuevergne, L.; Le Borgne, T.; Davy, P.; Russian, A.; Bour, O., Temporal and spatial scaling of hydraulic response to recharge in fractured aquifers: Insights from a frequency domain analysis, Water Resour. Res., 49 (2013)
[41] Li, S-G.; McLaughlin, D., A nonstationary spectral method for solving stochastic groundwater problems: Unconditional analysis, Water Resour. Res., 27, 1589-1605 (1991)
[42] Farlow, S. J., Partial Differential Equations for Scientists and Engineers (1993), Dover: Dover New York · Zbl 0851.35001
[43] Yeh, T.-C.; Gelhar, J. W.; Gutjahr, A. L., Stochastic analysis of unsaturated flow in heterogeneous soils, 1. Statistically isotropic media, Water Resour. Res., 21, 447-456 (1985)
[44] Stewart, J., Calculus: Early transcendentals (2003), Thomson Learning Inc
[45] Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products, (Jeffrey, A. (1980), Academic Press: Academic Press New York) · Zbl 0521.33001
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