Abstract
Analyses of GNSS (Global Navigation Satellite Systems) data acquired by stations located in karst areas of the Apennine chain (Italy) have revealed a strong correlation between changes in water table levels occurring in the saturated zone of karst aquifers and horizontal ground displacements. Many previous studies have explained this phenomenon by the widening and closing of sub-vertical water-filled fractures of the rock mass due to the hydraulic head rising and lowering, respectively, neglecting the role of the water pressure in the overall stress field acting in the saturated rock mass. In this study, the Skempton generalization of Terzaghi’s effective stress principle and the laws of linear elasticity were combined to explain the detected hydrological deformation of karst mountains, providing new analytical solutions. The water pressure variation associated with the water table rising and lowering is the main driver of the observed hydrological deformation, controlled by the elastic properties of the rock mass and the coefficient of earth pressure at rest, K0. The phenomenon of the hydrological deformation could be assimilated to the thermal expansion of solids, whose magnitude depends on the physical and geometric characteristics of the material and the temperature increase. Similarly, the hydrologically induced ground displacements measured by GNSS stations depend on the deformation of a specific aquifer portion caused by variations in the groundwater pressure.
Highlights
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Karst aquifers of Apennines are affected by ground displacements, observable by GNSS stations, clearly associated with the hydrological stage of the water table.
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Hydrological stages mainly affect the horizontal ground displacements, revealing that rock masses undergo hydrological deformation; this phenomenon, however, does not find a simple interpretation in literature.
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A physically-based model has been introduced to explain the observed hydrological deformations, joining Terzaghi’s effective stress principle (generalized by Skempton) and elastic theory.
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The equations found are based on the coefficient of earth pressure at rest, K0, and relate the strain of a saturated karst rock mass to pore water pressure variations; in karst aquifers, the latter are due to water table rising and lowering.
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(modified from Leone et al. 2023)
(modified from Leone et al. 2023)
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Data availability
GNSS data measured at the VAGA, LNGN, PTRJ and ALIF stations are available at: http://geodesy.unr.edu/. Spring discharge data were provided by Acquedotto Campano.
References
Amadei B, Stephansson O (1997) Rock stress and its measurement. Springer, Netherlands, Dordrecht
Ascione A, Ciotoli G, Bigi S, Buscher J, Mazzoli S, Ruggiero L, Sciarra A, Tartarello MC, Valente E (2018) Assessing mantle versus crustal sources for non-volcanic degassing along fault zones in the actively extending southern Apennines mountain belt (Italy). GSA Bull 130(9–10):1697–1722. https://doi.org/10.1130/B31869.1
Barton CA, Zoback MD, Burns KL (1988) In-situ stress orientation and magnitude at the Fenton Geothermal Site, New Mexico, determined from wellbore breakouts. Geophys Res Lett 15(5):467–470. https://doi.org/10.1029/GL015i005p00467
Bawden GW, Thatcher W, Stein RS, Hudnut KW, Peltzer G (2001) Tectonic contraction across Los Angeles after removal of groundwater pumping effects. Nature 412(6849):812–815. https://doi.org/10.1038/35090558
Bell JW, Amelung F, Ramelli AR, Blewitt G (2002) Land subsidence in Las Vegas, Nevada, 1935–2000: new geodetic data show evolution, revised spatial patterns, and reduced rates. Environ Eng Geosci 8(3):155–174. https://doi.org/10.2113/8.3.155
Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12(2):155–164. https://doi.org/10.1063/1.1712886
Biot MA, Willis DG (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24(4):594–601. https://doi.org/10.1115/1.4011606
Blewitt G, Hammond W, Kreemer C (2018) Harnessing the GPS data explosion for interdisciplinary science. Eos. https://doi.org/10.1029/2018EO104623
Blewitt G (2015) GPS and space-based geodetic methods. In: Treatise on Geophysics. Elsevier, pp 307–338
Bonacci O (1995) Ground water behaviour in karst: example of the Ombla Spring (Croatia). J Hydrol 165(1–4):113–134. https://doi.org/10.1016/0022-1694(94)02577-X
Boncio P, Auciello E, Amato V, Aucelli P, Petrosino P, Tangari AC, Jicha BR (2022) Late Quaternary faulting in the southern Matese (Italy): implications for earthquake potential and slip rate variability in the southern Apennines. Solid Earth 13(3):553–582. https://doi.org/10.5194/se-13-553-2022
Braitenberg C, Pivetta T, Barbolla DF, Gabrovšek F, Devoti R, Nagy I (2019) Terrain uplift due to natural hydrologic overpressure in karstic conduits. Sci Rep 9(1):3934. https://doi.org/10.1038/s41598-019-38814-1
Brooker EW, Ireland HO (1965) Earth pressures at rest related to stress history. Can Geotech J 2(1):1–15. https://doi.org/10.1139/t65-001
Brown ET, Hoek E (1978) Trends in relationships between measured in-situ stresses and depth. Int J Rock Mech Min Sci Geomech Abstr 15(4):211–215. https://doi.org/10.1016/0148-9062(78)91227-5
Chow VT, Maidment DR, Mays LW (2010) Applied hydrology, Tata McGraw-Hill ed. Tata McGraw-Hill Education, New Delhi
Civita M (1969) Valutazione analitica delle riserve in acque sotterranee alimentanti alcune tra le principali sorgenti del massiccio del Matese (Italia meridionale). Mem Della Soc Dei Nat Napoli 78:133–163
D’Agostino N (2014) Complete seismic release of tectonic strain and earthquake recurrence in the Apennines (Italy). Geophys Res Lett 41(4):1155–1162. https://doi.org/10.1002/2014GL059230
D’Agostino N, Silverii F, Amoroso O, Convertito V, Fiorillo F, Ventafridda G, Zollo A (2018) Crustal deformation and seismicity modulated by groundwater recharge of Karst aquifers. Geophys Res Lett 45(22):253–262. https://doi.org/10.1029/2018GL079794
Devoti R, Zuliani D, Braitenberg C, Fabris P, Grillo B (2015) Hydrologically induced slope deformations detected by GPS and clinometric surveys in the Cansiglio Plateau, southern Alps. Earth Planet Sci Lett 419:134–142. https://doi.org/10.1016/j.epsl.2015.03.023
Devoti R, Riguzzi F, Cinti FR, Ventura G (2018) Long-term strain oscillations related to the hydrological interaction between aquifers in intra-mountain basins: a case study from Apennines chain (Italy). Earth Planet Sci Lett 501:1–12. https://doi.org/10.1016/j.epsl.2018.08.014
Domenico PA, Schwartz FW (1998) Physical and chemical hydrogeology, 2nd edn. Wiley, New York
Engelder T (1993) Stress regimes in the lithosphere. Princeton University Press, Princeton, NJ, Course Book
Fiorillo F (2014) The recession of spring hydrographs, focused on Karst aquifers. Water Resour Manag 28(7):1781–1805. https://doi.org/10.1007/s11269-014-0597-z
Fiorillo F, Guadagno FM (2012) Long karst spring discharge time series and droughts occurrence in Southern Italy. Environ Earth Sci 65(8):2273–2283. https://doi.org/10.1007/s12665-011-1495-9
Fiorillo F, Pagnozzi M (2015) Recharge processes of Matese karst massif (southern Italy). Environ Earth Sci 74(12):7557–7570. https://doi.org/10.1007/s12665-015-4678-y
Fiorillo F, Pagnozzi M, Ventafridda G (2015) A model to simulate recharge processes of Karst massifs. Hydrol Process 29(10):2301–2314. https://doi.org/10.1002/hyp.10353
Fiorillo F, Esposito L, Testa G, Ciarcia S, Pagnozzi M (2018) The upwelling water flux feeding springs: hydrogeological and hydraulic features. Water 10(4):501. https://doi.org/10.3390/w10040501
Fiorillo F, Leone G, Pagnozzi M, Catani V, Testa G, Esposito L (2019) The upwelling groundwater flow in the Karst area of grassano-telese springs (Southern Italy). Water 11(5):872. https://doi.org/10.3390/w11050872
Fiorillo F, Leone G, Pagnozzi M, Esposito L (2021) Long-term trends in karst spring discharge and relation to climate factors and changes. Hydrogeol J 29(1):347–377. https://doi.org/10.1007/s10040-020-02265-0
Ford D, Williams P (2007) Karst hydrogeology and geomorphology. John Wiley & Sons Ltd, West Sussex, England
Geertsma J (1957) The effect of fluid pressure decline on volumetric changes of porous rocks. Trans AIME 210(01):331–340. https://doi.org/10.2118/728-G
Goodman RE (1989) Introduction to rock mechanics, 2nd edn. Wiley, New York
Herget G (1993) Rock stresses and rock stress monitoring in Canada. In: Rock Testing and Site Characterization. Elsevier, pp 473–496
Hoek E, Brown ET (1980) Underground excavations in rock. The Institution of Mining and Metallurgy, London
Jeannin P-Y (2001) Modeling flow in phreatic and epiphreatic karst conduits in the H/ffloch cave (Muotatal, Switzerland). Water Resour Res 37(2):191–200
King NE, Argus D, Langbein J, Agnew DC, Bawden G, Dollar RS, Liu Z, Galloway D, Reichard E, Yong A, Webb FH, Bock Y, Stark K, Barseghian D (2007) Space geodetic observation of expansion of the San Gabriel Valley, California, aquifer system, during heavy rainfall in winter 2004–2005. J Geophys Res 112(B3):B03409. https://doi.org/10.1029/2006JB004448
Lambe TW, Whitman RV (1969) Soil mechanics. Wiley, New York
Lancellotta R (2009) Geotechnical engineering. Taylor & Francis, New York, NY
Larochelle S, Chanard K, Fleitout L, Fortin J, Gualandi A, Longuevergne L, Rebischung P, Violette S, Avouac J (2022) Understanding the geodetic signature of large aquifer systems: example of the ozark plateaus in central United States. J Geophys Res Solid Earth 127(3):e2021JB023097. https://doi.org/10.1029/2021JB023097
Leone G, Catani V, Pagnozzi M, Ginolfi M, Testa G, Esposito L, Fiorillo F (2022) Hydrological features of Matese Karst Massif, focused on endorheic areas, dolines and hydroelectric exploitation. J Maps. https://doi.org/10.1080/17445647.2022.2144497
Leone G, D’Agostino N, Esposito L, Fiorillo F (2023) Hydrological deformation of karst aquifers detected by GPS measurements, Matese massif. Italy Environ Earth Sci 82(9):240. https://doi.org/10.1007/s12665-023-10905-3
Martens HR, Argus DF, Norberg C, Blewitt G, Herring TA, Moore AW, Hammond WC, Kreemer C (2020) Atmospheric pressure loading in GPS positions: dependency on GPS processing methods and effect on assessment of seasonal deformation in the contiguous USA and Alaska. J Geod 94(12):115. https://doi.org/10.1007/s00190-020-01445-w
McGarr A, Gay NC (1978) State of stress in the earth’s crust. Annu Rev Earth Planet Sci 6(1):405–436. https://doi.org/10.1146/annurev.ea.06.050178.002201
Means WD (1976) Stress and Strain. Springer, New York, New York, NY
Nur A, Byerlee JD (1971) An exact effective stress law for elastic deformation of rock with fluids. J Geophys Res 76(26):6414–6419. https://doi.org/10.1029/JB076i026p06414
Pan E, Amadei B, Savage WZ (1995) Gravitational and tectonic stresses in anisotropic rock with irregular topography. Int J Rock Mech Min Sci Geomech Abstr 32(3):201–214. https://doi.org/10.1016/0148-9062(94)00046-6
Petrella E, Celico F (2009) Heterogeneous aquitard properties in sedimentary successions in the Apennine chain: case studies in southern Italy. Hydrol Process 23(23):3365–3371. https://doi.org/10.1002/hyp.7441
Riel B, Simons M, Ponti D, Agram P, Jolivet R (2018) Quantifying ground deformation in the Los Angeles and santa ana coastal basins due to groundwater withdrawal. Water Resour Res 54(5):3557–3582. https://doi.org/10.1029/2017WR021978
Ruggero P (1926) Risultati di alcune indagini sul regime idrologico del Massiccio del Matese. Ann Dei Lav Pubblici 64(5):381–401
Savage WZ, Swolfs HS, Amadei B (1992) On the state of stress in the near-surface of the earth’s crust. Pure Appl Geophys PAGEOPH 138(2):207–228. https://doi.org/10.1007/BF00878896
Serpelloni E, Pintori F, Gualandi A, Scoccimarro E, Cavaliere A, Anderlini L, Belardinelli ME, Todesco M (2018) Hydrologically induced Karst deformation: insights from GPS measurements in the Adria-Eurasia plate boundary zone. J Geophys Res Solid Earth 123(5):4413–4430. https://doi.org/10.1002/2017JB015252
Silverii F, D’Agostino N, Métois M, Fiorillo F, Ventafridda G (2016) Transient deformation of karst aquifers due to seasonal and multiyear groundwater variations observed by GPS in southern Apennines (Italy). J Geophys Res Solid Earth 121(11):8315–8337. https://doi.org/10.1002/2016JB013361
Silverii F, D’Agostino N, Borsa AA, Calcaterra S, Gambino P, Giuliani R, Mattone M (2019) Transient crustal deformation from karst aquifers hydrology in the Apennines (Italy). Earth Planet Sci Lett 506:23–37. https://doi.org/10.1016/j.epsl.2018.10.019
Skempton AW (1961a) Effective Stress in Soils, Concrete and Rocks. In: Pore Pressure and Suction in Soils. Butterworths, London, England
Skempton AW (1961b) Horizontal Stresses in an Over-Consolidated Eocene Clay. In: Proc. 5th Int. Conf. Soil Mech. Dunod, Paris, France, pp 351–357
Smith MB, Montgomery CT (2015) Hydraulic fracturing. CRC Press, Taylor & Francis Group, Boca Raton
Terzaghi K (1923) Die Berechnung der Durchlassigkeitsziffer des Tones aus Dem Verlauf der Hidrodynamichen Span-nungserscheinungen Akademie der Wissenschaften in Wien. Math Nat Schaftiliche 132:105–124
Terzaghi K (1936) The shearing resistance of saturated soils. Proceedings in 1st International Conference on Soil Mechanics and Foundation Engineering. Massasuchets, United States, Cambridge, pp 54–56
Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice, 3rd edn. Wiley, New York
van Dam T, Wahr J, Milly PCD, Shmakin AB, Blewitt G, Lavallée D, Larson KM (2001) Crustal displacements due to continental water loading. Geophys Res Lett 28(4):651–654. https://doi.org/10.1029/2000GL012120
Voight B (1966) Interpretation of in-situ stress measurements. In: Proc. 1st Cong. Int. Soc. Rock Mech. (ISRM). Lab. Nac de Eng. Civil, Lisbon, Portugal, pp 332–348
Wahr J, Khan SA, van Dam T, Liu L, van Angelen JH, van den Broeke MR, Meertens CM (2013) The use of GPS horizontals for loading studies, with applications to northern California and southeast Greenland. J Geophys Res Solid Earth 118(4):1795–1806. https://doi.org/10.1002/jgrb.50104
Wang H (2000) Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press, Princeton, N.J.
White WB (2002) Karst hydrology: recent developments and open questions. Eng Geol 65(2–3):85–105. https://doi.org/10.1016/S0013-7952(01)00116-8
White AM, Gardner WP, Borsa AA, Argus DF, Martens HR (2022) A review of GNSS/GPS in hydrogeodesy: hydrologic loading applications and their implications for water resource research. Water Resour Res. https://doi.org/10.1029/2022WR032078
Wisely BA, Schmidt D (2010) Deciphering vertical deformation and poroelastic parameters in a tectonically active fault-bound aquifer using InSAR and well level data. Geophys J Int, San Bernardino basin, California. https://doi.org/10.1111/j.1365-246X.2010.04568.x
Worthington SRH (1999) A comprehensive strategy for understanding flow in carbonate aquifers. Karst Waters Inst Special Publ 5:30–37
Worthington SRH, Ford DC (2009) Self-organized permeability in carbonate aquifers. Groundwater 47(3):326–336. https://doi.org/10.1111/j.1745-6584.2009.00551.x
Worthington SRH, Smart CC, Ruland W (2012) Effective porosity of a carbonate aquifer with bacterial contamination: Walkerton, Ontario, Canada. J Hydrol 464–465:517–527. https://doi.org/10.1016/j.jhydrol.2012.07.046
Zang A, Stephansson O (2010) Stress field of the earth’s crust. Springer, Netherlands, Dordrecht
Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, Cambridge
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Guido, L., Libera, E. & Francesco, F. Terzaghi’s Effective Stress Principle and Hydrological Deformation of Karst Aquifers Detected by GNSS Measurements. Rock Mech Rock Eng 57, 2365–2383 (2024). https://doi.org/10.1007/s00603-023-03688-3
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DOI: https://doi.org/10.1007/s00603-023-03688-3