在大地工程相關的數值模擬分析研究中，大部分都是將同一地層之土壤或岩石參數視為常數來進行分析。然而，這麼做可能無法完全體現土壤和岩石的真實特性。由於土壤和岩體受到複雜且漫長的地質過程作用，例如沉積、變質、風化和生物效應，使其在同一地層的兩個不同位置之物理及力學特性可能有明顯之不同，這種現象在地質與大地工程中稱為「空間變異性」。本論文主要嘗試將地質不確定性方法應用於大地工程之數值模擬，模擬分析的對象包含「在具空間變異性之岩體中隧道開挖之地拱效應」、「耦合馬可夫鏈於土壤液化潛能評估之應用」、「地錨鏽蝕和土壤強度參數之不確定性對邊坡穩定之影響」，其中將運用到隨機場、自關連方法、條件機率等地質不確定性方法。根據本論文研究，可發現傳統的數值模擬分析方法為單一方案對應單一模擬分析結果；而考慮地質不確定性方法之數值模擬結果會形成一個區間。因此，未來若要在工程實務上考慮地質不確定性所帶來的影響，可以妥善利用兩者之比例關係，作為未來相關工程在設計、施工、監測、維護等之參考，例如調整設計時的安全係數，至於如何訂定此比例，尚需更多現場案例與數值分析的結果進行分析。

Numerical simulation analysis of geotechnical engineering mostly regards soil or rock mass parameters of a single layer as constants. However, this approach does not fully reflect the actual characteristics of soil and rock mass. Soil and rock mass undergo long periods of complex geological processes such as sedimentation, metamorphism, weathering, and biological effects. As a result, the physical and mechanical properties of soil and rock mass at two different points within the same stratum could have overt differences. In geological and geotechnical engineering, this phenomenon is known as “spatial variability”. This study mainly attempts to apply the geological uncertainty method to the numerical simulation analysis of geotechnical engineering, including “Ground arch effect of tunnel excavation when considering spatial variability in rock masses”, “Application of the coupled Markov chain in soil liquefaction potential evaluation”, and “Influence of Ground Anchors Corrosion and Uncertainty Strength Parameters”. The geological uncertainty methods it uses include random fields, autocorrelation methods, conditional probability. According to the results of this dissertation, a single scheme corresponds to a single result in the traditional simulation analysis method. If we consider the geological uncertainty method applied to the numerical simulation, the result will be a range. Therefore, if we want to consider the effects of geological uncertainty in geotechnical engineering, we can use the ratio between the traditional method and the geological uncertainty method. As a reference for engineering design, construction, monitoring, maintenance, etc., such as adjusting the factor of safety during design. However, how to determine this ratio still needs to be analyzed with more field cases and numerical analysis results.

中華民國大地工程學會，2011，「國道3號3.1公里崩塌事件原因調查工作」調查報告。
Baecher, G. B., and Christian, J. T. 2003. “Reliability and statistics in geotechnical engineering.” Wiley, London.
Baise, L.G. and Lenz, J.A., 2006. “Guidelines for Regional Liquefaction Hazard Mapping”; Tufts University, Department of Civil and Environmental Engineering: Medford, MA, USA
Batistuta, V.H., 2022. “Influence of Uncertainty Strength Parameters and Anchor Stresses: A Case Study of Landslide in Northern Taiwan.” Thesis, National Taiwan University of Science and Technology.
Bolton Seed, H., Tokimatsu, K., Harder, L. and Chung, R.M, 1985. “Influence of SPT procedures in soil liquefaction resistance evaluations.” Journal of Geotechnical Engineering, 111, 1425–1445.
Cami, B., Javankhoshdel, S., Phoon, K. K., and Ching, J., 2020. Scale of Fluctuation for Spatially Varying Soils: Estimation Methods and Values. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 6(4), 03120002.
Cao, W., Zhou, A. and Shen, S.-L, 2021. “An analytical method for estimating horizontal transition probability matrix of coupled Markov chain for simulating geological uncertainty.” Computers and Geotechnics, 129, 103871.
Cao, Z., and Wang, Y., 2014. Bayesian model comparison and selection of spatial correlation functions for soil parameters. Structural Safety, 49, 10–17.
Carle, S.F., Labolle, E.M., Weissmann, G.S., Van Brocklin, D. and Fogg, G.E, 1998. “Conditional simulation of hydrofacies architecture: A transition probability/Markov approach.” Hydrogeologic Models of Sedimentary Aquifers, Concepts in Hydrogeology and Environmental Geology, 1, 147–170.
Cetin, K.; Seed, R.; Der Kiureghian, A., Tokimatsu, K., Harder, L. and Kayen, R, 2000. “SPT-Based probabilistic and deterministic assessment of seismic soil liquefaction initiation hazard.” Pacific Earthquake Engineering Research Report No. PEER-2000/05, Pacific Gas and Electric Company (PG&E): San Francisco, CA, USA.
Chang, C. T., Sun, C. W., Duann, S. W., and Hwang, R. N., 2001. Response of a Taipei Rapid Transit System (TRTS) tunnel to adjacent excavation. Tunnelling and Underground Space Technology, 16(3), 151–158.
Chappell, B. A., 1979. Deformational Response in discontinua. International Journal of Rock Mechanics and Mining Sciences And, 16(6), 377–390.
Chelapati, C. V., 1964. Arching in Soil Due to the Deflection of a Rigid Horizontal Strip. Proceedings of the Symposium on Soil-Structure Interaction, 356–377.
Chen, C. C., Li, H. H., Chiu, Y. C., and Tsai, Y. K., 2020. Dynamic response of a physical anti-dip rock slope model revealed by shaking table tests. Engineering Geology, 277, 105772.
Chen, C. N., Huang, W. Y., and Tseng, C. T., 2011. Stress redistribution and ground arch development during tunneling. Tunnelling and Underground Space Technology, 26(1), 228–235.
Chen, F., Wang, L. and Zhang, W, 2019. “Reliability assessment on stability of tunnelling perpendicularly beneath an existing tunnel considering spatial variabilities of rock mass properties.” Tunnelling and Underground Space Technology, 88, 276–289.
Cheng, H., Chen, J., and Li, J., 2019a. Probabilistic Analysis of Ground Movements Caused by Tunneling in a Spatially Variable Soil. International Journal of Geomechanics, 19(12), 04019125.
Cheng, H., Chen, J., Chen, R., and Chen, G., 2019b. Comparison of Modeling Soil Parameters Using Random Variables and Random Fields in Reliability Analysis of Tunnel Face. International Journal of Geomechanics, 19(1), 04018184.
Cheng, H., Chen, J., Chen, R., Huang, J., and Li, J., 2019c. Three-dimensional analysis of tunnel face stability in spatially variable soils. Computers and Geotechnics, 111(February), 76–88.
Cheng, H., Chen, J., Huang, Z., and Huang, J., 2018. Face stability analysis for a shield tunnel considering spatial variability of shear strength in sand. Rock and Soil Mechanics, 39(8), 3047–3054.
Cheng, Y.M., Lansivaara, T., and Wei, W.B., 2007. Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Computers and Geotechnics 34:137-150.
Chien, W.-Y., Lu, Y.-C., Juang, C.H., Dong, J.-J. and Hung, W.-Y, 2022. “Effect of stratigraphic model uncertainty at a given site on its liquefaction potential index: Comparing two random field approaches.” Engineering Geology, 309, 106838.
Chiles, J.-P. and Delfiner, P. Geostatistics, 2009. “Modeling Spatial Uncertainty”; John Wiley & Sons: New York, NY, USA; Volume 497.
Ching, J., Yang, Z.Y., Shiau, J.Q., and Chen, C.J., 2012. Estimation of rock pressure during an excavation/cut in sedimentary rocks with inclined bedding planes. Structural Safety 41,11-19.
Ching, J.Y., and Liao, H.J., 2013. A Spatial Variability View of Freeway-3 Dip Slope Failure in Taiwan. Journal of GeoEngineering 8:1-10.
Cho, S.E., 2007. Effects of Spatial Variability of Soil Properties on Slope Stability. Engineering Geology 92 (3): 97–109.
Chung, J.-W. and Rogers, J.D, 2011. “Simplified method for spatial evaluation of liquefaction potential in the St. Louis area.” Journal of Geotechnical and Geoenvironmental Engineering. 137, 505–515.
Cross, G.R. and Jain, A.K, 1983. “Markov random field texture models.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 1, 25–39.
Dalong, J., Zhichao, S. and Dajun, Y, 2020. “Effect of spatial variability on disc cutters failure during TBM tunneling in hard rock.” Rock Mechanics and Rock Engineering, 53, 4609–4621.
Dawson, E. M., Roth, W. H., and Drescher, A., 1999. Slope stability analysis by strength reduction. Geotechnique 49: 835-40.
De Marsily, G., Delay, F., Gonçalvès, J., Renard, P., Teles, V. and Violette, S, 2005. “Dealing with spatial heterogeneity.” Hydrogeology Journal, 13, 161–183.
Deng, Z.-P., Jiang, S.-H., Niu, J.-T., Pan, M. and Liu, L.-L, 2020. “Stratigraphic uncertainty characterization using generalized coupled Markov chain.” Bulletin of Engineering Geology and the Environment, 79, 5061–5078.
Deng, Z.-P., Li, D.-Q., Qi, X.-H., Cao, Z.-J. and Phoon, K.-K, 2017. “Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters.” Computers and Geotechnics, 92, 121–131.
Doveton, J.H, 1994. “Theory and Applications of Vertical Variability Measures from Markov Chain Analysis.” AAPG: Tulsa, OK, USA.
Elfeki, A and Dekking, F, 2005. “Modelling subsurface heterogeneity by coupled Markov chains: Directional dependency, Walther’s law and entropy.” Geotechnical & Geological Engineering, 23, 721–756.
Elfeki, A. and Dekking, M, 2001. “A Markov chain model for subsurface characterization: Theory and applications.” Mathematical Geology, 33, 569–589.
Elfeki, A.M, 2006. “Reducing concentration uncertainty using the coupled Markov chain approach.” Journal of Hydrology, 317, 1–16.
Elkateb, T., Chalaturnyk, R. and Robertson, P.K, 2003. “An overview of soil heterogeneity: Quantification and implications on geotechnical field problems.” Canadian Geotechnical Journal, 40, 1–15.
Evans, C. H., 1984. An examination of arching in granular soils. In Science. Massachusetts Institute of Technology.
Fenton, G. A., Griffiths, D. V., 2008. Risk Assessment in Geotechnical Engineering. In Risk Assessment in Geotechnical Engineering.
Gholampour, A, 2022. “Site-scale liquefaction potential analysis using a sectional random field model.” Engineering Geology, 297, 106485.
Goldsworthy, J. S., Jaksa, M. B., Fenton, G. A., Kaggwa, W. S., Griffiths, D. V., and Poulos, H. G. 2007. Effect of sample location on the reliability based design of pad foundations. GeoRisk, 1(3), 155–166.
Gong, W., Juang, C. H., Martin, J. R., Tang, H., Wang, Q., Huang, H., 2018. Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties. Tunnelling and Underground Space Technology, 73(November 2017), 1–14.
Gong, W., Juang, C.H., Martin II, J.R., Tang, H., Wang, Q. and Huang, H, 2018. “Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties.” Tunnelling and Underground Space Technology, 73, 1–14.
Gong, W., Tang, H., Wang, H., Wang, X. and Juang, C.H, 2019. “Probabilistic analysis and design of stabilizing piles in slope considering stratigraphic uncertainty.” Engineering Geology, 259, 105162.
Gong, W., Zhao, C., Juang, C.H., Zhang, Y., Tang, H. and Lu, Y, 2021. “Coupled characterization of stratigraphic and geo-properties uncertainties–A conditional random field approach.” Engineering Geology, 294, 106348.
Goodman, R.E. (1989). “Introduction to Rock Mechanics.” John Wiley and Sons, New York.
Grasmick, J. G. and Mooney, M. A., 2017. A Probabilistic Approach for Predicting Settlement Due to Tunneling in Spatially Varying Glacial Till. Geo-Risk 2017, 300–309.
Griffiths D.V., Huang, J., and Fenton, G.A., 2009. Influence of spatial variability on slope reliability using 2-D random fields. J. Geotech. Geoenvironm. Eng. 135(10):1367–78.
Griffiths, D. V. and Lane, P. A., 1999. Slope stability analysis by finite elements. Geotechnique 49: 387-403.
Griffiths, D.V., Szynakiewicz, T., and Fenton, G.A., 2002. A probabilistic investigation of c', φ' slope stability. In: Proc. 6th Int. Cong. Numerical Methods in Engineering and Scientific Applications 2002 p. 25–36.
Grifths, D. and Fenton, G., 2004. Probabilistic slope stability analysis by finite elements. J. Geotech. Geoenvironm. Eng. 130(5):507–518.
Gu, X., Wang, L., Chen, F., Li, H., and Zhang, W., 2020. Reliability analysis of slope stability considering temporal variations of rock mass properties. Computers, Materials and Continua, 63(1), 263–281.
Guan, Z. and Wang, Y, 2022. “CPT-based probabilistic liquefaction assessment considering soil spatial variability, interpolation uncertainty and model uncertainty.” Computers and Geotechnics, 141, 104504.
Guan, Z., Jiang, Y., and Tanabasi, Y., 2007. Ground reaction analyses in conventional tunnelling excavation. Tunnelling and Underground Space Technology, 22(2), 230–237.
Hoek, E., 1998. Reliability of Hoek-Brown estimates of rock mass properties and their impact on design. International Journal of Rock Mechanics and Mining Sciences, 35(1), 63–68.
Hoek, E., Carranza, C., and Corkum, B., 2002. Hoek-brown failure criterion – 2002 edition. Narms-Tac, 267–273.
Hogg, R.V., Tanis, E.A., and Zimmerman, D. 2013. 'Probability and Statistical Inference: 9th Edition', Pearson.
Hu, B. and Wang, C., 2019. Ground surface settlement analysis of shield tunneling under spatial variability of multiple geotechnical parameters. Heliyon, 5(9), e02495.
Hu, Q, 2006. “Risk Analysis and Its Application for Tunnel Works Based on Research of Stratum and Soil Spatial Variability.” Ph.D. Thesis, Tongji University.
Huang, H., Gong, W., Khoshnevisan, S., Juang, C. H., Zhang, D., and Wang, L., 2015. Simplified procedure for finite element analysis of the longitudinal performance of shield tunnels considering spatial soil variability in longitudinal direction. Computers and Geotechnics, 64, 132–145.
Huang, X., Schweiger, H. F., and Huang, H., 2013. Influence of Deep Excavations on Nearby Existing Tunnels. International Journal of Geomechanics, 13(2), 170–180.
Hwang, J. H., Khoshnevisan, S., Juang, C. H., and Lu, C. C., 2021. “Soil liquefaction potential evaluation–An update of the HBF method focusing on research and practice in Taiwan. Eng. Geol., 280, 105926.
Itasca. 2014. '3DEC - Three-Dimensional Distinct Element Code, User's Manual', Itasca Consulting Group Inc.
Itasca. 2014. 'UDEC - universal distinct element code, version 6.0, User's Manual', Itasca Consulting Group Inc.
Iwasaki, T., Arakawa, T. and Tokida, K.-I, 1984. “Simplified procedures for assessing soil liquefaction during earthquakes.” International Journal of Soil Dynamics and Earthquake Engineering, 3, 49–58.
Iwasaki, T., Tokida, K., Tatsuoka, F., Watanabe, S., Yasuda, S. and Sato, H, 1982, “Microzonation for soil liquefaction potential using simplified methods.” Proceedings of the 3rd International Conference on Microzonation, Seattle, WA, USA, pp. 1310–1330.
Japan Road Association, 1996. “Design code and explanations for roadway bridges.”
Karakus, M. and Fowell, R. J., 2003. Effects of different tunnel face advance excavation on the settlement by FEM. Tunnelling and Underground Space Technology, 18(5), 513–523.
Kawa, M. and Puła, W, 2020. “3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil.” Acta Geotech, 15, 1453–1466.
Kelesoglu, M. K., 2016. The evaluation of three-dimensional effects on slope stability by the strength reduction method. KSCE Journal of Civil Engineering 20(1):229-242.
Krumbein, W, 1968. “Statistical models in sedimentology 1.” Sedimentology, 10, 7–23.
Lee, W. F., Liao, H.J., Chang, M.H., Wang, C.W., Chi, S.Y., and Lin, C.C., 2013. Failure Analysis of a Highway Dip Slope Slide. Journal of Performance of Constructed Facilities 27.1 (2013): 116- 31.
Li, A. J., Merifield, R. S., and Lyamin, A. V., 2010. Three-dimensional stability charts for slopes based on limit analysis methods. Canadian Geotechnical Journal, 47(12), 1316-1334.
Li, A. J., Wen, H. C., Batistuta, V. H., & Cheng, S. H., 2023. Influence of ground anchors corrosion and uncertainty strength parameters: A case study slope failure in northern Taiwan. Soils and Foundations, 63(3), 101316.
Li, A.J., Mburu, J.W., Chen, C.W., and Yang, K.H., 2022. Investigations of Silty Soil Slopes under Unsaturated Conditions Based on Strength Reduction Finite Element and Limit Analysis. KSCE Journal of Civil Engineering, 26 (3), 1095-1110.
Li, A.J., Wang, W.C., and Lin, H.D., 2022. Investigation of slope reinforcement with drilled shafts in colluvium soils. Geomechanics and Engineering, 31(1), 71-86.
Li, J., Cai, Y., Li, X. and Zhang, L, 2019. “Simulating realistic geological stratigraphy using direction-dependent coupled Markov chain model.” Computers and Geotechnics, 115, 103147.
Li, K. S. and Lumb, P., 1987. Probabilistic design of slopes. Canadian Geotechnical Journal. 24, 520-531.
Li, W.; Zhang, C., Burt, J.E., Zhu, A.-X. and Feyen, J, 2004. “Two-dimensional Markov chain simulation of soil type spatial distribution.” Soil Science Society of America Journal, 68, 1479–1490.
Li, Z., Wang, X., Wang, H. and Liang, R.Y, 2016. “Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field.” Engineering Geology, 201, 106–122.
Liao, H.J., Lee, Wei, F., and Wang, C.W., 2013. A tale of twin cut slopes in Taiwan. Proceedings of the Institution of Civil Engineers-Forensic Engineering 2013, 166:2, 72-80.
Lin, H.D., Wang, W.C., and Li, A.J., 2020. Investigation of dilatancy angle effects on slope stability using the 3D finite element method strength reduction technique. Computers and Geotechnics, 118: 103295.
Liu, B., Zhang, D. W., Yang, C., and Zhang, Q. B., 2020. Long-term performance of metro tunnels induced by adjacent large deep excavation and protective measures in Nanjing silty clay. Tunnelling and Underground Space Technology, 95(May 2019), 103147.
Lloret-Cabot, M., Fenton, G.A. and Hicks, M.A, 2014. “On the estimation of scale of fluctuation in geostatistics.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazard, 8, 129–140.
Low, B. K., Lacasse, S., and Nadim, F., 2007. Slope reliability analysis accounting for spatial variation. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 1:4, 177-189.
Low, B.K. and Tang, W.H., 1997. Reliability analysis of reinforced embankments on soft ground. Canadian Geotechnical Journal, 34(5), 672-685.
Matsui, T. and San, K.C., 1992. Finite Element Slope Stability Analysis by Shear Strength Reduction Technique. Soils and Foundations, 32: 59-70.
Mollon, G., Phoon, K. K., Dias, D., and Soubra, A. H., 2011. Validation of a New 2D Failure Mechanism for the Stability Analysis of a Pressurized Tunnel Face in a Spatially Varying Sand. Journal of Engineering Mechanics, 137(1), 8–21.
P.W.R. Public Works Research Institute: Ibaraki, Japan, 2017. “Evaluation Method for Liquefaction Strength of Fine-Grained Sand.”
Pan, Q. and Dias, D, 2017. “Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis.” Acta Geotechnica, 12, 1415–1429.
Pan, Y., Yao, K., Phoon, K.K. and Lee, F.H, 2019. “Analysis of tunnelling through spatially-variable improved surrounding–A simplified approach.” Tunnelling and Underground Space Technology, 93, 103102.
Phoon, K. K., Kulhawy, F. H., 1999a. Characterization of geotechnical variability. Canadian Geotechnical Journal, 36(4), 612–624.
Phoon, K. K., Kulhawy, F. H., 1999b. Evaluation of geotechnical property variability. Canadian Geotechnical Journal, 36(4), 625–639.
Pokhrel, R.M., Kuwano, J. and Tachibana, S, 2012. “Geostatistical analysis for spatial evaluation of liquefaction potential in Saitama City.” LOWLAND TECHNOLOGY INTERNATIONAL, 14, 45–51.
Pokhrel, R.M., Kuwano, J. and Tachibana, S, 2013. “A kriging method of interpolation used to map liquefaction potential over alluvial ground.” Engineering Geology ,152, 26–37.
Qi, X.-H., Li, D.-Q. and Phoon, K.-K, 2016a. “Estimation of horizontal transition probability matrix for coupled Markov chain.” Japanese Geotechnical Society Special Publication, 2, 2423–2428.
Qi, X.-H., Li, D.-Q., Phoon, K.-K., Cao, Z.-J. and Tang, X.-S, 2016b. “Simulation of geologic uncertainty using coupled Markov chain.” Engineering Geology, 207, 129–140.
Ritter, W., 1879. Die statik der tunnelgewölbe. J. Springer.
Shi, C. and Wang, Y, 2021. “Nonparametric and data-driven interpolation of subsurface soil stratigraphy from limited data using multiple point statistics.” Canadian Geotechnical Journal, 58, 261–280.
Tatsuoka, F., Iwasaki, T., Tokida, K.-I., Yasuda, S., Hirose, M., Imai, T. and Kon-No, M, 1980. “Standard penetration tests and soil liquefaction potential evaluation.” Soils and Foundations, 20, 95–111.
Terzaghi, K., 1946. Rock Defects and Loads on Tunnel Supports. Rock Tunneling with Steel Supports, ed. R. V. Proctor and T. White, Commercial Shearing Co., Youngstown, 15–99.
Thompson, E., Wald, D.J. and Worden, C, 2014. “A VS30 Map for California with Geologic and Topographic Constraints.” Bulletin of the Seismological Society of America ,104, 2313–2321.
Thompson, E.M., Baise, L.G., Kayen, R.E., Tanaka, Y. and Tanaka, H, 2010. “A geostatistical approach to mapping site response spectral amplifications.” Engineering Geology, 114, 330–342.
Tokimatsu, K. and Yoshimi, Y, 1983. “Empirical correlation of soil liquefaction based on SPT N-value and fines content.” Soils and Foundations, 23, 56–74.
Tschuchnigg, F., Schweiger, H.,F., Sloan, S., W., Lyamin, A., V., and Raissakis, I., 2015. Comparison of finite-element limit analysis and strength reduction techniques. Géotechnique 65:249-257.
Tsinidis, G., DiSarno, L., Sextos, A., and Furtner, P., 2019. A critical review on the vulnerability assessment of natural gas pipelines subjected to seismic wave propagation. Part 2: Pipe analysis aspects. Tunnelling and Underground Space Technology, 92(December 2018), 103056.
Wang, H., Wellmann, J.F., Li, Z., Wang, X. and Liang, R.Y, 2017. “A segmentation approach for stochastic geological modeling using hidden Markov random fields.” Mathematical Geosciences, 49, 145–177.
Wang, L., Wu, C., Gu, X., Liu, H., Mei, G. and Zhang, W, 2020. “Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines.” Bulletin of Engineering Geology and the Environment, 79, 2763–2775.
Wang, X, 2020. “Uncertainty quantification and reduction in the characterization of subsurface stratigraphy using limited geotechnical investigation data.” Underground Space, 5, 125–143.
Wang, X., Wang, H. and Liang, R.Y, 2018a. “A method for slope stability analysis considering subsurface stratigraphic uncertainty.” Landslides, 15, 925–936.
Wang, X., Wang, H., Liang, R.Y., Zhu, H. and Di, H, 2018b. “A hidden Markov random field model based approach for probabilistic site characterization using multiple cone penetration test data.” Structural Safety, 70, 128–138.
Wang, X.; Li, Z., Wang, H., Rong, Q. and Liang, R.Y, 2016. “Probabilistic analysis of shield-driven tunnel in multiple strata considering stratigraphic uncertainty.” Structural Safety, 62, 88–100.
Wang, Y., Cao, Z., and Li, D., 2016. Bayesian perspective on geotechnical variability and site characterization. Engineering Geology, 203, 117–125.
Wang, Y., Shu, S. and Wu, Y, 2022. “Reliability analysis of soil liquefaction considering spatial variability of soil property.” J. Journal of Earthquake and Tsunami, 16, 2250002.
Wen, H. C., Li, A. J., Lu, C. W., and Chen, C. N, 2022. Application of the Coupled Markov Chain in Soil Liquefaction Potential Evaluation. Buildings, 12(12), 2095.
Weng, M. C., Chang, C. Y., Jeng, F. S., and Li, H. H., 2020. Evaluating the stability of anti-dip slate slope using an innovative failure criterion for foliation. Engineering Geology, 275, 105737.
Weng, M. C., Lin, C. H., Shiu, W. J., Chao, W. A., Chiu, C. C., Lee, C. F., Huang, W. K., and Yang, C. M., 2022. Towards a rapid assessment of highway slope disasters by using multidisciplinary techniques. Landslides, 19(3), 687-701.
Wengang, Z., Liang, H., Zixu, Z., and Yanmei, Z., 2020. Digitalization of mechanical and physical properties of Singapore Bukit Timah granite rocks based on borehole data from four sites. Underground Space (China).
Wu, J. H. and Hsieh, P. H., 2021. Simulating the postfailure behavior of the seismically-triggered Chiu-fen-erh-shan landslide using 3DEC. Engineering Geology, 287, 106113.
Xiang, Y., Liu, H., Zhang, W., Chu, J., Zhou, D., and Xiao, Y., 2018. Application of transparent soil model test and DEM simulation in study of tunnel failure mechanism. Tunnelling and Underground Space Technology, 74(August 2017), 178–184.
Xiao, L., Huang, H., and Zhang, J., 2017. Effect of Soil Spatial Variability on Ground Settlement Induced by Shield Tunnelling. June, 330–339.
Youd, T.L. and Idriss, I.M, 2001. “Liquefaction resistance of soils: Summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils.” Journal of Geotechnical and Geoenvironmental Engineering, 127, 297–313.
Yue, Q., and Ang, A. H. S., 2016. Nonlinear response and reliability analysis of tunnels under strong earthquakes. Structure and Infrastructure Engineering, 12(5), 618–630.
Yue, Q., and Ang, A. H. S., 2017. 3D reliability evaluation of tunnels under strong-motion earthquakes considering spatial randomness. Structure and Infrastructure Engineering, 13(7), 882–893.
Zhang, D.-M., Zhang, J.-Z., Huang, H.-W., Qi, C.-C. and Chang, C.-Y, 2020. “Machine learning-based prediction of soil compression modulus with application of 1D settlement.” Journal of Zhejiang University-SCIENCE A, 21, 430–444.
Zhang, J.-Z., Huang, H.-W., Zhang, D.-M., Phoon, K.K., Liu, Z.-Q. and Tang, C, 2021a. “Quantitative evaluation of geological uncertainty and its influence on tunnel structural performance using improved coupled Markov chain.” Acta Geotech, 16, 3709–3724.
Zhang, J.-Z., Huang, H.-W., Zhang, D.-M., Zhou, M.-L., Tang, C. and Liu, D.-J, 2021b. “Effect of ground surface surcharge on deformational performance of tunnel in spatially variable soil.” Computers and Geotechnics, 136, 104229.
Zhang, J.-Z., Liu, Z.-Q., Zhang, D.-M., Huang, H.-W., Phoon, K.-K. and Xue, Y.-D, 2022. “Improved coupled Markov chain method for simulating geological uncertainty.” Engineering Geology, 298, 106539.
Zhang, W., Han, L., Gu, X., Wang, L., Chen, and F., Liu, H., 2020. Tunneling and deep excavations in spatially variable soil and rock masses: A short review. Underground Space (China).
Zhang, W., Han, L., Gu, X.; Wang, L., Chen, F. and Liu, H, 2020. “Tunneling and deep excavations in spatially variable soil and rock masses: A short review.” Underground Space, 7, 380–407.
Zhao, C., Gong, W., Li, T., Juang, C.H., Tang, H. and Wang, H, 2021. “Probabilistic characterization of subsurface stratigraphic configuration with modified random field approach.” Engineering Geology, 288, 106138.
Zhao, J., 2007. Tunnelling in Rocks – Present Technology and Future Challenges. In ITA-AITES World Tunnel Congress and 33rd ITA General Assembly, May, 22–32.
Zhu, H. and Zhang, L.M. 2013. 'Characterizing geotechnical anisotropic spatial variations using random field theory', Canadian Geotechnical Journal. 50(7): 723-734.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W., 1975. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 25: 671-89.