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SCIENCE CHINA Technological Sciences, Volume 63 , Issue 2 : 341-356(2020) https://doi.org/10.1007/S11431-018-9452-X

General axisymmetric active earth pressure obtained by the characteristics method based on circumferential geometric condition

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  • ReceivedJul 25, 2018
  • AcceptedJan 14, 2019
  • PublishedOct 8, 2019

Abstract

Existing solutions for axisymmetric active earth pressure are based on certain hypotheses of the circumferential stress, lacking of strict basis. This article presents a technique for deriving the actual circumferential stress according to the circumferential geometric condition, the Drucker-Prager criterion and incremental theory. Based on the actual circumferential stress, a new characteristics method for determining the axisymmetric active earth pressure in plastic flow is developed in this article. In this new method, the inclined angle of boundaries, interface friction of contact interface, dilatation effect and flow velocity of soil are considered at the same time. The validity of the new method is confirmed using several sets of experimental data from the literature. The pressure coefficients are investigated individually in detail, and some different conclusions are found. Finally, a practical formula for calculating axisymmetric active earth pressure is presented based on the linear superposition principle, and related tables of coefficients are also provided for engineering application.


Funded by

the National Natural Science Foundation of China(Grant,No.,51678360)

the Shanghai Science and Technology Commission Project(Grant,No.,19QC1400800)

and the National Basic Research Program of China(Grant,No.,2014CB046302)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant No. 51678360), the Shanghai Science and Technology Commission Project (Grant No. 19QC1400800), and the National Basic Research Program of China (Grant No. 2014CB046302).


References

[1] Qu J T Zhou J. 3-Dimensional numerical analysis in a very deep circle pit. J Kunming Univ Sci Tech (Sci Tech), 2004, 29: 96–99. Google Scholar

[2] Kumagai T, Ariizumi K, Kashiwagi A. Behaavior large-scale cylindrical earth retaining structure. Stions, 2005, 39: 13–26. Google Scholar

[3] Zhu S Q. Calculation of ground pressure on shaft due to deep overburden. J China Univ Mining Tech, 1981, 1: 6. Google Scholar

[4] Zhang M J. Earth pressure on shaft sunk in thick overburden. J China Univ Mining Tech, 1983, 2: 7. Google Scholar

[5] Ma Y M. Theory and practice of ground pressure on shaft due to thick overburden. J China Univ Mining Tech, 1979, 1: 3. Google Scholar

[6] Haar A, Kármán T V. Zur Theorie der Spannungszustände in plastischen und sandartigen Medien. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse, 1909, 1909: 204–218. Google Scholar

[7] Berezantzev V G. Earth pressure on the cylindrical retaining wall. In: Proceedings of the International Society of Soil Mechanics and foundation Engineerin (ISSMFE) Conference on Earth Pressure Problems. London: Butterworths, 1958. 21–27. Google Scholar

[8] Cox A D, Eason G, Hopkins H G. Axially symmetric plastic deformations in soils. Philos Trans R Soc A-Math Phys Eng Sci, 1961, 254: 1-45 CrossRef ADS Google Scholar

[9] Cox A D. Axially-symmetric plastic deformation in soils—II. Indentation of ponderable soils. Int J Mech Sci, 1962, 4: 371-380 CrossRef Google Scholar

[10] Jenike A W, Yen B C. Slope Stability in Axial Symmetry. Proa. 5th Rock Mechanics Symposium. University of Minnesota. Pergamon Press, 1962. Google Scholar

[11] Hill J M, Cox G M. Rat-hole stress profiles for shear-index granular materials. Acta Mech, 2002, 155: 157-172 CrossRef Google Scholar

[12] Cox G M, Hill J M. Some exact velocity profiles for granular flow in converging hoppers. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 2005, 56: 92–106. Google Scholar

[13] Houlsby G T, Wroth C P. Direct solution of plasticity problems in soils by the method of characteristics. NASA STI/Recon Technical Report. 1982. Google Scholar

[14] Drescher A. Limit plasticity approach to piping in bins. J Appl Mech, 1983, 50: 549-553 CrossRef ADS Google Scholar

[15] Drescher A. Kinematics of axisymmetric vertical slopes at collapse. Int J Numer Anal Methods Geomech, 1986, 10: 431-441 CrossRef ADS Google Scholar

[16] Cheng Y M, Hu Y Y. Active earth pressure on circular shaft lining obtained by simplified slip line solution with general tangential stress coefficient. Chin J Geotech Eng, 2005, 27: 110–115. Google Scholar

[17] Prater E G. An examination of some theories of earth pressure on shaft linings. Can Geotech J, 1977, 14: 91-106 CrossRef Google Scholar

[18] Cheng Y M, Hu Y Y, Wei W B. General axisymmetric active earth pressure by method of characteristics—Theory and numerical formulation. Int J Geomech, 2007, 7: 1-15 CrossRef Google Scholar

[19] Cheng Y M, Au S K, Hu Y Y, et al. Active pressure for circular cut with berezantzev’s and prater’s theories, numerical modeling and field measurements. Soils Found, 2008, 48: 621-631 CrossRef Google Scholar

[20] Liu F Q, Wang J H. A generalized slip line solution to the active earth pressure on circular retaining walls. Comput Geotech, 2008, 35: 155-164 CrossRef Google Scholar

[21] Liu F Q, Wang J H, Zhang L L. Discussion of “General axisymmetric active earth pressure by method of characteristics—Theory and numerical formulation” by Y. M. Cheng, Y. Y. Hu, and W. B. Wei. Int J Geomech, 2008, 8: 325-326 CrossRef Google Scholar

[22] Liu F Q, Wang J H, Zhang L L. Axi-symmetric active earth pressure obtained by the slip line method with a general tangential stress coefficient. Comput Geotech, 2009, 36: 352-358 CrossRef Google Scholar

[23] Liu F Q. Lateral earth pressures acting on circular retaining walls. Int J Geomech, 2014, 14: 04014002 CrossRef Google Scholar

[24] Chen J J, Li M G, Wang J H. Active earth pressure against rigid retaining walls subjected to confined cohesionless soil. Int J Geomech, 2017, 17: 06016041 CrossRef Google Scholar

[25] Li M G, Chen J J, Wang J H. Arching effect on lateral pressure of confined granular material: numerical and theoretical analysis. Granular Matter, 2017, 19: 20 CrossRef Google Scholar

[26] Yu M H, Li J H, Zhang Y Q. Unified characteristics line theory of spacial axisymmetric plastic problem. Sci China Series E: Tech Sci, 2001, 44: 207–215. Google Scholar

[27] Hu X R. Calculation method of pressures acting on shaft wall based on twin shear unified spatially axisymmetric characteristics line theory. Rock Soil Mech, 2007, 28: 2083–2086. Google Scholar

[28] Hill R. The Mathematical Theory of Plasticity. Oxford: Oxford University Press, 1950. Google Scholar

[29] Chen W F. Limit Analysis and Soil Plasticity. New York: Elsevier, 1975. Google Scholar

[30] Xiong G J, Wang J H. A rigorous characteristic line theory for axisymmetric problems and its application in circular excavations. Acta Geotech, 2018, 35: 1-15 CrossRef Google Scholar

[31] Xiong G J, Wang J H, Chen J J. Theory and practical calculation method for axisymmetric active earth pressure based on the characteristics method considering the compatibility condition. Appl Math Model, 2019, 68: 563-582 CrossRef Google Scholar

[32] Tobar T, Meguid M A. Experimental study of the earth pressure distribution on cylindrical shafts. J Geotech Geoenviron Eng, 2011, 137: 1121-1125 CrossRef Google Scholar

[33] Terzaghi K. Theoretical Soil Mechanics. New York: Wiley, 1943. Google Scholar

[34] Kerisel J, Absi E. Active and Passive Earth Pressure Tables. Rotterdam: Balkema, 1973. Google Scholar

  • Figure 1

    (Color online) General analysis model of a circular excavation.

  • Figure 2

    (Color online) The Limit Mohr circle of Mohr-Coulomb criterion and Drucker-Prager criterion

  • Figure 3

    (Color online) The equivalent friction angle φe of Drucker-Prager criterion. (a) The 3D diagram of φe; (b) the 2D diagram of φe.

  • Figure 4

    (Color online) Velocity fields. (a) The actual velocity field; (b) the ideal velocity field.

  • Figure 5

    (Color online) The polar diameters ρ and ρC in ACD zone.

  • Figure 6

    (Color online) The direction of the two clusters slip lines. (a) The slip line; (b) the failure surface.

  • Figure 7

    (Color online) Diagram of the differential calculation.

  • Figure 8

    (Color online) The stress boundary condition.

  • Figure 9

    (Color online) Limit state of the contact boundary. (a) Direction of the major principal stress; (b) limit Mohr’s circle of the contact interface; (c) the differential iteration diagram.

  • Figure 10

    (Color online) Comparison between the solutions for the axisymmetric active pressure and the experimental data. (a) S=3 mm; (b) S=4 mm.

  • Figure 11

    (Color online) Comparison between the solutions from this paper and those from Cheng. (a) Pressure due to the weight; (b) pressure due to the surcharge; (c) pressure due to cohesion.

  • Figure 12

    (Color online) Influences of various factors on the earth pressure coefficient due to the weight. (a) k(rA); (b) k(μθA); (c) k(α); (d) k(φ); (e) k(ψ); (f) k(δ).

  • Figure 13

    (Color online) Influences of various factors on the earth pressure coefficient due to the surcharge. (a) kaq(rA); (b) kaq(μθA); (c) kaq(α); (d) kaq(φ); (e) kaq(ψ); (f) kaq(δ).

  • Figure 14

    (Color online) Influences of various factors on the earth pressure coefficient due to the cohesive strength. (a) kac(rA); (b) kac(μθA); (c) kac(α); (d) kac(φ); (e) kac(ψ); (f) kac(δ).

  • Figure 15

    (Color online) Results for kaq, kac and Cost.

  • Figure 16

    (Color online) Numerical results and fitting results of the pressure coefficients. (a) kaγKa; (b) kaqKa.

  • Figure 17

    (Color online) Comparison of the practical and numerical solutions.

  • Table 1   Basic experimental parameters from the literature

    Property

    Experimental unit weight (γ)

    Internal friction angle (φ)

    Cohesion (C)

    Radius (R)

    Depth (H)

    Value

    14.7 kN/m3

    41°

    0

    75 mm

    1000 mm

    Test number

    Radial displacement

    Estimated limit displacement

    4, 8, 11

    3 mm

    Sa≥max{0.2%·H, 2.5%·rA}=2 mm

    1, 2, 3

    4 mm

  • Table 2   Fitting parameters (), (), () and (), (), ()

    φ

    aγ

    bγ

    cγ

    aq

    bq

    cq

    0

    –0.0344

    –0.0344

    0

    2.0592

    2.0764

    0.0003

    2.5

    0.1517

    0.1711

    0.0002

    0.2433

    0.2868

    0.0004

    5

    0.1329

    0.1712

    0.0004

    0.2048

    0.2868

    0.0008

    7.5

    0.1199

    0.1775

    0.0007

    0.1771

    0.2992

    0.0014

    10

    0.1085

    0.1859

    0.001

    0.1521

    0.316

    0.002

    12.5

    0.0981

    0.196

    0.0014

    0.1279

    0.3358

    0.0028

    15

    0.0884

    0.2075

    0.002

    0.1036

    0.3578

    0.0036

    17.5

    0.0791

    0.2203

    0.0026

    0.0782

    0.3814

    0.0042

    20

    0.0701

    0.2344

    0.0034

    0.0498

    0.4054

    0.0039

    22.5

    0.0608

    0.2493

    0.0043

    0.0143

    0.4275

    –0.0002

    25

    0.0503

    0.2641

    0.0052

    1.5755

    2.0436

    0.7737

    27.5

    0.0348

    0.2753

    0.0049

    0.1247

    0.6398

    0.1063

    30

    0.0023

    0.2717

    –0.0003

    0.042

    0.6202

    0.0895

    32.5

    0.6807

    0.9687

    0.2157

    0.0024

    0.6456

    0.1012

    35

    0.2064

    0.5258

    0.0837

    –0.0286

    0.682

    0.1259

    37.5

    0.168

    0.5162

    0.0864

    –0.0572

    0.724

    0.163

    40

    0.1647

    0.5414

    0.105

    –0.0857

    0.7703

    0.2148

    42.5

    0.1683

    0.5741

    0.1311

    –0.1147

    0.8198

    0.2882

    45

    0.1657

    0.6032

    0.1583

    –0.1466

    0.8759

    0.3828

  • Table 3   Basic parameters of the six examples used for validation

    Example

    γ (kN/m3)

    q (kPa)

    c (kPa)

    φ

    1

    15

    50

    45

    18

    2

    17

    75

    35

    22

    3

    19

    100

    25

    27

    4

    21

    125

    15

    33

    5

    23

    150

    0

    38

    6

    25

    175

    0

    43

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