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Rashid Mangushev
Ivan Bashmakov
Daria Paskacheva
Alina Kvashuk


Mathematical modeling of the undrained behavior of soils is carried out on the basis of theoretical paths of effective stresses under undrained deviatory loading in a triaxial compression chamber. The recommendations of normative sources and scientific papers on the application of undrained calculations in practice are analyzed. The basic laws of soil mechanics are considered in calculations taking into account the formation of excess pore pressures in the base. Theoretical calculations obtained by A. Skempton for the law of effective stresses of C. Terzaghi are applied for mathematical modeling of paths. Based on the results of mathematical modeling of an ideal elastic-plastic body it is shown that an accurate description of the paths of effective soil stresses using the elastic theory does not correspond to real soil tests. The influence of the law of volumetric plastic deformation on the paths of effective stresses and on the undrained shear strength is analyzed. The formula for determining the undrained strength parameter for the Modified Cam Clay model is presented. Attention is drawn to the fact that in addition to volumetric plastic deformation which affects the undrained calculation it is necessary to take into account the shear component of plastic deformation which is decisive for the calculations of excavations. Simulation of laboratory tests of soils in the Soil Test for the Mohr-Coulomb, Modified Cam Clay and Hardening Soil Models was carried out. A comparison of the obtained results with the data of laboratory tests is presented. The influence of the choice of soil model on the value of resistance to undrained shear is shown. Recommendations are given for choosing a soil model for numerical simulation based on the results of laboratory triaxial consolidated undrained tests.


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Mangushev, R., Bashmakov, I., Paskacheva, D., & Kvashuk, A. (2023). MATHEMATICAL MODELING OF UNDRAINED BEHAVIOR OF SOILS. International Journal for Computational Civil and Structural Engineering, 19(1), 97–111.


Mangushev, R.A., Osokin, A.I. (2020). The experience of the underground construction for the complex of buildings on a soft soil in the center of St. Petersburg. International Journal for Computational Civil and Structural Engineering, vol. 16, no. 3, pp. 47-53.doi:10.22337/2587-9618-2020-16-3-47-53 DOI:

Dashko, R.E., Aleksandrova, O.Y., Kotyukov, P.V., Shidlovskaya, A.V. (2011). Osobennosti inzhenerno-geologicheskih uslovij Sankt-Peterburga [Features of engineering and geological conditions of St. Petersburg], Urban development and geotechnical construction, vol. 1, pp. 1-47.

Ulickiy, V.M., Shashkin, A.G., Shashkin, K.G., Shashkin, V.A. (2014). Osnovy sovmestnyh raschetov zdanij i osnovanij [Fundamentals of joint calculations of buildings and foundations]. St. Petersburg: Publishing House of the Institute "Georeconstruction". (in Russian)

Skempton, A. W. (1954). The Pore-Pressure Coefficients A and B. Geotechnique, vol. 4, no. 4, pp. 143–147. doi:10.1680/geot.1954.4.4.143 DOI:

Schanz, T., Vermeer, P. A., Bonnier, P. G. (2019). The hardening soil model: formulation and verification. In Beyond 2000 in computational geotechnics, Routledge, pp. 281-296. DOI:

Shashkin, A.G. (2011). Vyazko-uprugo-plasticheskaya model' povedeniya glinistogo grunta [Visco-elastic-plastic model of clay soil behavior], Urban development and geotechnical construction, vol. 2, pp. 1-32.

Roscoe, K. H., Schofield, A. N., Wroth, C. P. (1958). On The Yielding of Soils. Geotechnique, vol. 8, no. 1, pp. 22–53. doi:10.1680/geot.1958.8.1.22 DOI:

Burland, J. B. (1965). The yieding and dilation of clay. Géotechnique, vol. 15, no. 1, pp. 211-214. DOI:

Puller, M. (2003). Deep Excavations: A Practical Manual, Thomas Telford Ltd.

Vermeer, P. A. (1999). Column Vermeer. Plaxis Bulletin, Delpth: Plaxis, pp. 2-3.

Kolybin, I.V. (2008). Uroki avarijnyh situacij pri stroitel'stve kotlovanov v gorodskih usloviyah [Lessons of emergency situations during the construction of pits in urban conditions], Urban development and geotechnical construction, vol. 12, pp. 90-124.

Yannie, J. (2012). Change of shear strength in soft soil excavations. Paper presented at the 22nd European Young Geotechnical Engineers Conference in Gothenburg, 26-29 August, 2012.

Solov`yov, Y.I., Karaulov, A.M., Vaganov, P.S. (1980). The theory of instantaneous strength and its application in the calculations of the stability of consolidating soil arrays. Proceedings of the Design and study of the foundations of hydraulic structures: Materials of conferences and meetings on hydraulic engineering. Leningrad: Energy, pp. 104-105.

Paramonov, V.N. (2012). Metod konechnyh elementov pri reshenii nelinejnyh zadach geotekhniki [Finite element method for solving nonlinear geotechnical problems]. St. Petersburg: Georeconstruction Group of Companies. (in Russian)

Yang, Y., Kou, H., Li, Z., Jia, Y., Zhu, C. (2022). Normalized Stress–Strain Behavior of Deep-Sea Soft Soils in the Northern South China Sea. Journal of Marine Science and Engineering, vol. 10, no. 8, pp. 1142. doi:10.3390/jmse10081142 DOI:

Yin, J., Zhang, K., Geng, W., Gaamom, A., Xiao, J. (2021). Effect of initial water content on undrained shear strength of K0 consolidated clay. Soils and Foundations, vol. 61, no. 5, pp. 1453-1463. doi:10.1016/j.sandf.2021.08.010 DOI:

Wroth, C. P. (1984). The interpretation of in situ soil tests. Geotechnique, vol. 34, no. 4, pp. 449–489. doi:10.1680/geot.1984.34.4.449 DOI:

Mayne, P. W., Coop, M. R., Springman, S. M., Huang, A. B., Zornberg, J. G. (2009). Geomaterial behavior and testing. In Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering (Volumes 1, 2, 3 and 4), 5-9 October 2009, Alexandria: IOS Press., pp. 2777-2872.

Iovlev, G.A., Piskunov, N.S., Bahvalov, E.D., Ochkurov, V.I. (2022). Metody optimizacii parametrov nelinejnyh gruntovyh modelej dlya inzhenerno-geologicheskih uslovij Sankt-Peterburga [Methods of optimization of parameters of nonlinear soil models for engineering and geological conditions of St. Petersburg]. Mining Information and Analytical Bulletin (scientific and technical journal), vol. 7, pp. 148-163. DOI:

Alekseev, A.V., Iovlev, G.A. (2019). Adaptaciya modeli uprochnyayushchegosya grunta (hardening soil) dlya inzhenerno-geologicheskih uslovij Sankt-Peterburga [Adaptation of the hardening soil model for the engineering and geological conditions of St. Petersburg]. Mining Information and Analytical Bulletin (scientific and technical journal), vol. 4, pp. 75-87. DOI:

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