Skip to main content
SpringerLink
Log in

Generating Stochastic Structural Planes by Considering Parameter Correlations Using Deep Generative Adversarial Networks

  • Technical Note
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Highlights

  • Stochastic structural planes are generated by considering parameter correlations.

  • The probability distributions of the inclination and the dip angle of stochastic structural planes can be learned using deep neural networks.

  • The correction between the inclination and the dip angle can be automatically captured via deep learning.

  • The generated stochastic structural planes are consistent with the measured factual structural planes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Data availability

Not applicable.

References

  • Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks. In: 34th international conference on machine learning, proceedings of machine learning research, vol 70

  • Baghbanan A, Jing L (2008) Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min 45(8):1320–1334. https://doi.org/10.1016/j.ijrmms.2008.01.015

    Article  Google Scholar 

  • Benton DJ, Iverson SR, Martin LA, Johnson JC, Raffaldi MJ (2016) Volumetric measurement of rock movement using photogrammetry. Int J Min Sci Technol 26(1):123–130

    Article  Google Scholar 

  • Elmouttie MK, Poropat GV (2012) A method to estimate in situ block size distribution. Rock Mech Rock Eng 45(3):401–407. https://doi.org/10.1007/s00603-011-0175-0

    Article  Google Scholar 

  • Fu GY, Ma GW, Qu XL, Huang D (2016) Stochastic analysis of progressive failure of fractured rock masses containing non-persistent joint sets using key block analysis. Tunn Undergr Space Technol 51:258–269. https://doi.org/10.1016/j.tust.2015.10.013

    Article  Google Scholar 

  • Gabbiani F, Cox SJ (2017) Mathematics for neuroscientists. Academic Press, New York

    Google Scholar 

  • Ge Y, Cao B, Tang H (2022) Rock discontinuities identification from 3d point clouds using artificial neural network. Rock Mech Rock Eng 55(3):1705–1720. https://doi.org/10.1007/s00603-021-02748-w

    Article  Google Scholar 

  • Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2020) Generative adversarial networks. Commun ACM 63(11):139–144. https://doi.org/10.1145/3422622

    Article  Google Scholar 

  • Goodman RE, Shi Gh (1985) Block theory and its application to rock engineering. Prentice Hall, New York

    Google Scholar 

  • Han X, Chen J, Wang Q, Li Y, Zhang W, Yu T (2016) A 3d fracture network model for the undisturbed rock mass at the songta dam site based on small samples. Rock Mech Rock Eng 49(2):611–619. https://doi.org/10.1007/s00603-015-0747-5

    Article  Google Scholar 

  • Hong Y, Hwang U, Yoo J, Yoon S (2019) How generative adversarial networks and their variants work: an overview. ACM Comput Surv. https://doi.org/10.1145/3301282

  • Huang L, Tang H, Wang L, Juang CH (2019) Minimum scanline-to-fracture angle and sample size required to produce a highly accurate estimate of the 3-d fracture orientation distribution. Rock Mech Rock Eng 52(3):803–825. https://doi.org/10.1007/s00603-018-1621-z

    Article  Google Scholar 

  • Janeczek D, Meyer R, Cai M, Srivastava RM, Munier R (2018) Efficient application of geostatistics-based rules to surface fracture modelling. In: ARMA international discrete fracture network engineering conference, ARMA, p D033S016R004

  • Junkin W, Janeczek D, Bastola S, Wang X, Cai M, Fava L, Sykes E, Munier R, Srivastava R (2017) Discrete fracture network generation for the Äspö tas08 tunnel using mofrac. In: 51st US rock mechanics/geomechanics symposium, OnePetro

  • Junkin W, Fava L, Ben-Awuah E, Srivastava M (2018) Analysis of mofrac-generated deterministic and stochastic discrete fracture network models. In: ARMA international discrete fracture network engineering conference, ARMA, p D033S016R005

  • Karras T, Aittala M, Hellsten J, Laine S, Lehtinen J, Aila T (2020) Training generative adversarial networks with limited data. arXiv:2006.06676

  • Keskar NS, Mudigere D, Nocedal J, Smelyanskiy M, Tang PTP (2017) On large-batch training for deep learning: generalization gap and sharp minima. arXiv:1609.04836

  • Kilkenny MF, Robinson KM (2018) Data quality: garbage in-garbage out. Health Inf Manag J 47(3):103–105

    Google Scholar 

  • Kulatilake PH (1985) Fitting fisher distributions to discontinuity orientation data. J Geol Educ 33(5):266–269

    Google Scholar 

  • Lecun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324. https://doi.org/10.1109/5.726791

    Article  Google Scholar 

  • Lecun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444. https://doi.org/10.1038/nature14539

    Article  Google Scholar 

  • Li HB, Li XW, Li WZ, Zhang Sl, Zhou JW (2019) Quantitative assessment for the rockfall hazard in a post-earthquake high rock slope using terrestrial laser scanning. Eng Geol 248:1–13. https://doi.org/10.1016/j.enggeo.2018.11.003

    Article  Google Scholar 

  • Li Z, Zheng T, Wang Y, Cao Z, Guo Z, Fu H (2021) A novel method for imbalanced fault diagnosis of rotating machinery based on generative adversarial networks. IEEE Trans Instrum Meas. https://doi.org/10.1109/tim.2020.3009343

  • Lin K, Li D, He X, Zhang Z, Sun MT (2017) Adversarial ranking for language generation. In: 31st annual conference on neural information processing systems (NIPS), advances in neural information processing systems, vol 30

  • Liu Y, Chen J, Tan C, Zhan J, Song S, Xu W, Yan J, Zhang Y, Zhao M, Wang Q (2022) Intelligent scanning for optimal rock discontinuity sets considering multiple parameters based on manifold learning combined with uav photogrammetry. Eng Geol. https://doi.org/10.1016/j.enggeo.2022.106851

  • Lyu Y, Gu G, Wang Z, Leng Y, Ma P, Peng J (2022) Study on the structural plane characteristics and disaster-induced mechanism of the yellow river Jingtai stone forest, northwestern loess plateau, china. Front Earth Sci 9:1461

    Article  Google Scholar 

  • Ma L, Gao D, Qian J, Han D, Xing K, Ma H, Deng Y (2023) Multiscale fractures integrated equivalent porous media method for simulating flow and solute transport in fracture-matrix system. J Hydrol. https://doi.org/10.1016/j.jhydrol.2022.128845

  • Miyoshi T, Elmo D, Rogers S (2018) Influence of data analysis when exploiting dfn model representation in the application of rock mass classification systems. J Rock Mech Geotech Eng 10(6):1046–1062. https://doi.org/10.1016/j.jrmge.2018.08.003

    Article  Google Scholar 

  • Priest SD (2004) Determination of discontinuity size distributions from scanline data. Rock Mech Rock Eng 37(5):347–368. https://doi.org/10.1007/s00603-004-0035-2

    Article  Google Scholar 

  • Rafiee A, Vinches M (2008) Application of geostatistical characteristics of rock mass fracture systems in 3d model generation. Int J Rock Mech Min 45(4):644–652. https://doi.org/10.1016/j.ijrmms.2007.09.009

    Article  Google Scholar 

  • Robinson P (1983) Connectivity of fracture systems—a percolation theory approach. J Phys A Math Gen 16(3):605

    Article  Google Scholar 

  • Rose LT, Fischer KW (2011) Garbage in, garbage out: having useful data is everything. Meas Interdiscip Res Perspect 9(4):222–226

  • Salvini R, Mastrorocco G, Seddaiu M, Rossi D, Vanneschi C (2017) The use of an unmanned aerial vehicle for fracture mapping within a marble quarry (Carrara, Italy): photogrammetry and discrete fracture network modelling. Geomat Nat Hazards Risk 8(1):34–52. https://doi.org/10.1080/19475705.2016.1199053

    Article  Google Scholar 

  • Salvini R, Vanneschi C, Coggan JS, Mastrorocco G (2020) Evaluation of the use of uav photogrammetry for rock discontinuity roughness characterization. Rock Mech Rock Eng 53(8):3699–3720. https://doi.org/10.1007/s00603-020-02130-2

    Article  Google Scholar 

  • Samaniego J, Priest S (1984) 19 the prediction of water flows through discontinuity networks into underground excavations. In: Design and performance of underground excavations: ISRM symposium—Cambridge, UK, 3–6 September 1984, Thomas Telford Publishing, pp 157–164

  • Schultz RA, Soliva R, Fossen H, Okubo CH, Reeves DM (2008) Dependence of displacement-length scaling relations for fractures and deformation bands on the volumetric changes across them. J Struct Geol 30(11):1405–1411. https://doi.org/10.1016/j.jsg.2008.08.001

    Article  Google Scholar 

  • Shi Gh, Goodman RE (1989) The key blocks of unrolled joint traces in developed maps of tunnel walls. Int J Numer Anal Methods 13(2):131–158. https://doi.org/10.1002/nag.1610130203

    Article  Google Scholar 

  • Singh J, Pradhan SP, Vishal V, Singh M (2023) Characterization of a fractured rock mass using geological strength index: A discrete fracture network approach. Transport Geotech. https://doi.org/10.1016/j.trgeo.2023.100984

  • Tariq W, Rehman G, Gardezi SAH, Ikram N (2023) Impact of fractures and diagenesis on reservoir potential of inner ramp paleocene carbonates exposed in western part of the lesser himalayas of pakistan. J Earth Sci 34(2):536–555. https://doi.org/10.1007/s12583-021-1559-z

    Article  Google Scholar 

  • Tomczak JM (2022) Deep generative modeling. Springer, Berlin

    Book  Google Scholar 

  • Vermilye JM, Scholz CH (1995) Relation between vein length and aperture. J Struct Geol 17(3):423–434

    Article  Google Scholar 

  • Wang S, Ni P, Guo M (2013) Spatial characterization of joint planes and stability analysis of tunnel blocks. Tunn Undergr Space Technol 38:357–367. https://doi.org/10.1016/j.tust.2013.07.017

    Article  Google Scholar 

  • Wang C, Xu C, Wang C, Tao D (2018) Perceptual adversarial networks for image-to-image transformation. IEEE T Image Process 27(8):4066–4079. https://doi.org/10.1109/tip.2018.2836316

    Article  Google Scholar 

  • Wang S, Zhang Z, Wang C, Zhu C, Ren Y (2019) Multistep rocky slope stability analysis based on unmanned aerial vehicle photogrammetry. Environ Earth Sci. https://doi.org/10.1007/s12665-019-8145-z

  • Wang Z, Li W, Qiao L, Liu J, Yang J (2018) Hydraulic properties of fractured rock mass with correlated fracture length and aperture in both radial and unidirectional flow configurations. Comput Geotech 104:167–184. https://doi.org/10.1016/j.compgeo.2018.08.017

    Article  Google Scholar 

  • Warburton P (1985) A computer program for reconstructing blocky rock geometry and analyzing single block stability. Comput Geosci 11(6):707–712

    Article  Google Scholar 

  • Wong YJ, Yeganeh A, Chia MY, Shiu HY, Ooi MCG, Chang JHW, Shimizu Y, Ryosuke H, Try S, Elbeltagi A (2023) Quantification of covid-19 impacts on no2 and o3: systematic model selection and hyperparameter optimization on ai-based meteorological-normalization methods. Atmos Environ. https://doi.org/10.1016/j.atmosenv.2023.119677

  • Xing L, Gong W, Li B, Zhao C, Tang H, Wang L (2023) Probabilistic analysis of earthquake-induced failure and runout behaviors of rock slopes with discrete fracture network. Comput Geotech 159:105487. https://doi.org/10.1016/j.compgeo.2023.105487

    Article  Google Scholar 

  • Yan B, Mi L, Chai Z, Wang Y, Killough JE (2018) An enhanced discrete fracture network model for multiphase flow in fractured reservoirs. J Pet Sci Eng 161:667–682. https://doi.org/10.1016/j.petrol.2017.12.016

    Article  Google Scholar 

  • Yu L, Zhang W, Wang J, Yu Y, Aaai (2017) Seqgan: sequence generative adversarial nets with policy gradient. In: 31st AAAI conference on artificial intelligence, AAAI conference on artificial intelligence, pp 2852–2858

  • Yu Y, Si X, Hu C, Zhang J (2019) A review of recurrent neural networks: Lstm cells and network architectures. Neural Comput 31(7):1235–1270. https://doi.org/10.1162/neco_a_01199

    Article  Google Scholar 

  • Zanbak C (1977) Statistical interpretation of discontinuity contour diagrams. Int J Rock Mech Min Sci Geomech Abstr Elsevier 14:111–120

    Article  Google Scholar 

  • Zhang QH, Liu QB (2022) Semi-stochastic generation of rock discontinuity networks based on traces exposed on cavern roof. Int J Rock Mech Min. https://doi.org/10.1016/j.ijrmms.2021.104978

  • Zhang W, Jp Chen, Liu C, Huang R, Li M, Zhang Y (2012) Determination of geometrical and structural representative volume elements at the Baihetan dam site. Rock Mech Rock Eng 45(3):409–419. https://doi.org/10.1007/s00603-011-0191-0

    Article  Google Scholar 

  • Zhang F, Damjanac B, Maxwell S (2019) Investigating hydraulic fracturing complexity in naturally fractured rock masses using fully coupled multiscale numerical modeling. Rock Mech Rock Eng 52(12):5137–5160. https://doi.org/10.1007/s00603-019-01851-3

    Article  Google Scholar 

  • Zhang Q, Wang X, He L, Tian L (2021) Estimation of fracture orientation distributions from a sampling window based on geometric probabilistic method. Rock Mech Rock Eng 54(6):3051–3075. https://doi.org/10.1007/s00603-021-02431-0

    Article  Google Scholar 

  • Zhao X, Liu L, Qi S, Teng Y, Li J, Qian W (2018) Agile convolutional neural network for pulmonary nodule classification using ct images. Int J Comput Assist Radiol Surg 13(4):585–595. https://doi.org/10.1007/s11548-017-1696-0

    Article  Google Scholar 

  • Zhu GL, Sousa RL, He MC, Zhou P, Yang J (2020) Stability analysis of a non-pillar-mining approach using a combination of discrete fracture network and discrete-element method modeling. Rock Mech Rock Eng 53(1):269–289. https://doi.org/10.1007/s00603-019-01901-w

    Article  Google Scholar 

Download references

Acknowledgements

We thank JMX analyst Demo software for providing data for slope structural plane data. This work was supported by the National Natural Science Foundation of China (Grant No.42277161, No.42230709).

Author information

Authors and Affiliations

  1. School of Engineering and Technolgy, China University of Geosciences, Beijing, 100083, China

    Han Meng, Gang Mei, Xiaoyu Qi, Nengxiong Xu & Jianbing Peng

  2. School of Geological Engineering and Geomatics, Chang’an University, Xi’an, 710064, China

    Jianbing Peng

Authors
  1. Han Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gang Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoyu Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nengxiong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianbing Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Mei.

Ethics declarations

Conflict of Interest

All authors declare that there are no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, H., Mei, G., Qi, X. et al. Generating Stochastic Structural Planes by Considering Parameter Correlations Using Deep Generative Adversarial Networks. Rock Mech Rock Eng 56, 9215–9230 (2023). https://doi.org/10.1007/s00603-023-03553-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-023-03553-3

Search

Navigation