Analysis of the Effect of Nonplanarity on Ground Deformation

Authors

  • Piu Kundu

    Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati 522241, Andhra Pradesh, India

DOI:

https://doi.org/10.30564/jbms.v7i4.10418
Received: 25 June 2025 | Revised: 3 September 2025 | Accepted: 16 September 2025 | Published Online: 28 November 2025

Abstract

The movement of interacting faults within the Earth's crust during earthquakes may cause significant structural damage. Large earthquake fault surfaces are often planar or a combination of several planar fault segments. This study analyses the interaction between a non-planar and a planar fault, where the faults are inclined, buried, creeping and strike-slip in nature. The non-planar fault is infinite and formed by two interconnected planar segments, while the planar fault is finite. The present analysis adduces the movement of interacting faults in a composite structure comprised of an elastic layer nested on a visco-elastic substrate of Maxwell medium. The significant effect of various affecting parameters viz. inclination of the faults, velocity of the fault movement, depth of the faults from the free surface, distance between the faults and the non-planarity of the fault has been discussed and also compared. The amount of stress and surface shear strain is restored after the creeping movement. The graphical representation of the effect of non-planarity of the fault on stress-strain accumulation has been established. Analytical solutions are obtained using Laplace transform and Green’s function techniques, supported by numerical simulations. The obtained results provide insights into fault interaction process and have important implications for assessing seismic hazard potential in viscoelastic media. The study of such earthquake fault dynamical models may give some ideas about the nature of stress-strain accumulation or release in the system and help us to observe the mechanism of lithosphere-asthenosphere boundary.

Keywords:

Interaction Between Nonplanar and Planar Fault; Creeping Movement; Aseismic Period; Integral Transform; Green's Function Technique

References

[1] Gabbianelli, G., Rapone, A., Milanesi, R.R., et al., 2025. Impact of Far- and Near-Field Records on the Seismic Fragility of Steel Storage Tanks. Applied Mechanics. 6(2), 24. DOI: https://doi.org/10.3390/applmech6020024

[2] Liu, Y., Erten, E. & Gonzalez-Ortega, A., et al., 2025. Shear-strain evolution in the East Anatolian Fault Zone revealed by InSAR phase gradients after the 2020 Elazig and 2023 kahramanmaras earthquakes. Geophysical Research Letters, 52(4). DOI: 10.1029/2024GL114033

[3] Mahato, P., Sarkar Mondal, S., 2025. Effect on surface deformation due to interacting fault in fractional standard linear solid. GEM—International Journal on Geomathematics. 16(1), 5. DOI: https://doi.org/10.1007/s13137-025-00264-5

[4] Kundu, P., 2024. On the Investigation of Interacting Fault Movement in a Viscoelastic Structure. In: Saha, A., Banerjee, S. (eds.). Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 2. Springer Nature: Cham, Switzerland; pp. 560–575. DOI: https://doi.org/10.1007/978-3-031-69134-8_39

[5] Kundu, P., Sarkar, S., 2020. Deformation analysis of a viscoelastic half-space due to a finite and an infinite interacting faults. Physica Scripta. 95(5), 055004. DOI: https://doi.org/10.1088/1402-4896/ab6f94

[6] Mondal, D., Kundu, P., Sarkar, S., 2020. Accumulation of Stress and Strain due to an Infinite Strike-Slip Fault in an Elastic Layer Overlying a Viscoelastic Half Space of Standard Linear Solid (SLS). Pure and Applied Geophysics. 177(10), 4643–4656. DOI: https://doi.org/10.1007/s00024-020-02536-7

[7] Muir, C., Cortez, J., Grigolini, P., 2020. Interacting faults in california and hindu kush. Chaos, Solitons & Fractals. 139, 110070. DOI: https://doi.org/10.1016/j.chaos.2020.110070

[8] Dutta, R., Jónsson, S., Vasyura‐Bathke, H., 2021. Simultaneous Bayesian Estimation of Non‐Planar Fault Geometry and Spatially‐Variable Slip. Journal of Geophysical Research: Solid Earth. 126(7), e2020JB020441. DOI: https://doi.org/10.1029/2020JB020441

[9] Li, D., Liu, Y., 2016. Spatiotemporal evolution of slow slip events in a nonplanar fault model for northern Cascadia subduction zone. Journal of Geophysical Research: Solid Earth. 121(9), 6828–6845. DOI: https://doi.org/10.1002/2016JB012857

[10] Sen, S., Karmakar, A., Mondal, B., 2012. A nonplanar surface breaking strike slip fault in a viscoelastic half space model of the lithosphere. IOSR Journal Of Mathematics. 2, 32–46, DOI: https://doi.org/10.9790/5728-0253246

[11] Marshall, S.T., Cooke, M.L., Owen, S.E., 2008. Effects of Nonplanar Fault Topology and Mechanical Interaction on Fault-Slip Distributions in the Ventura Basin, California. Bulletin of the Seismological Society of America. 98(3), 1113–1127. DOI: https://doi.org/10.1785/0120070159

[12] Mitsui, N., Hirahara, K., 2006. Slow slip events controlled by the slab dip and its lateral change along a trench. Earth and Planetary Science Letters. 245(1–2), 344–358. DOI: https://doi.org/10.1016/j.epsl.2006.03.001

[13] Rani, S., Singh, S.J., 1992. Static deformation of a uniform half-space due to a long dip-slip fault. Geophysical Journal International. 109(2), 469–476. DOI: https://doi.org/10.1111/j.1365-246X.1992.tb00108.x

[14] Rani, S., Singh, S.J., Garg, N.R., 1991. Displacements and stresses at any point of a uniform half-space due to two-dimensional buried sources. Physics of the Earth and Planetary Interiors. 65(3–5), 276–282. DOI: https://doi.org/10.1016/0031-9201(91)90134-4

[15] Rybicki, K., 1971. The elastic residual field of a very long strike-slip fault in the presence of a discontinuity. Bulletin of the Seismological Society of America. 61(1), 79–92. DOI: https://doi.org/10.1785/BSSA0610010079

[16] Maruyam, T., 1966. On two-dimensional dislocation in an infinite and semi-infinite medium. Bull. Earthquake Research Institute. 44, 811–871.

[17] Maruyama, T., 1964. Static elastic dislocations in an infinite and semi-infinite medium. Bull. Earthquake Research Institute. 42, 289–368.

[18] Chinnery, M.A., 1963. The stress changes that accompany strike-slip faulting. Bulletin of the Seismological Society of America. 53(5), 921–932. DOI: https://doi.org/10.1785/BSSA0530050921

[19] Chinnery, M.A., 1961. The deformation of the ground around surface faults. Bulletin of the Seismological Society of America. 51(3), 355–372. DOI: https://doi.org/10.1785/BSSA0510030355

[20] Steketee, J.A., 1958. SOME GEOPHYSICAL APPLICATIONS OF THE ELASTICITY THEORY OF DISLOCATIONS. Canadian Journal of Physics. 36(9), 1168–1198. DOI: https://doi.org/10.1139/p58-123

[21] Duan, B., Oglesby, D.D., 2005. Multicycle dynamics of nonplanar strike‐slip faults. Journal of Geophysical Research: Solid Earth. 110(B3), 2004JB003298. DOI: https://doi.org/10.1029/2004JB003298

[22] Ghosh, U., Mukhopadhyay, A., Sen, S., 1992. On two interacting creeping vertical surface-breaking strike-slip faults in a two-layer model of the lithosphere. Physics of the Earth and Planetary Interiors. 70(1–2), 119–129. DOI: https://doi.org/10.1016/0031-9201(92)90166-S

[23] Cathles, L.M., 1975. The visco-elasticity of the earth’s mantle. Princeton University Press: Princeton, NJ, USA.

[24] Aki, K., Richards, P.G., 1980. Quantitative seismology: Theory and methods. WH Freeman: New York, NY, USA.

[25] Clift, P., Lin, J., Barckhausen, U., 2002. Evidence of low flexural rigidity and low viscosity lower continental crust during continental break-up in the South China Sea. Marine and Petroleum Geology. 19(8), 951–970. DOI: https://doi.org/10.1016/S0264-8172(02)00108-3

[26] Karato, S., 2010. Rheology of the Earth’s mantle: A historical review. Gondwana Research. 18(1), 17–45. DOI: https://doi.org/10.1016/j.gr.2010.03.004

[27] Savage, J.C., Burford, R.O., 1970. Accumulation of tectonic strain in California. Bulletin of the Seismological Society of America. 60(6), 1877–1896. DOI: https://doi.org/10.1785/BSSA0600061877

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How to Cite

Kundu, P. (2025). Analysis of the Effect of Nonplanarity on Ground Deformation. Journal of Building Material Science, 7(4), 84–111. https://doi.org/10.30564/jbms.v7i4.10418

Issue

Vol. 7 , Iss. 4 (December 2025): In Progress

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Article

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Copyright © 2025 Piu Kundu

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This is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.

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