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

• AcceptedJan 14, 2019
• PublishedOct 8, 2019
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### 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

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• 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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