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Frontiers of Structural and Civil Engineering

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ISSN 2095-2449(Online)

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Front. Struct. Civ. Eng.    2021, Vol. 15 Issue (6) : 1480-1493    https://doi.org/10.1007/s11709-021-0776-y
RESEARCH ARTICLE
Upper bound solution to seismic active earth pressure of submerged backfill subjected to partial drainage
Zhengqiang ZENG1, Shengzhi WU2, Cheng LYU3
1. State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
2. School of Civil Engineering, Shandong Jianzhu University, Jinan 250000, China
3. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China
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Abstract

In waterfront geotechnical engineering, seismic and drainage conditions must be considered in the design of retaining structures. This paper proposes a general analytical method to evaluate the seismic active earth pressure on a retaining wall with backfill subjected to partial steady seepage flow under seismic conditions. The method comprises the following steps: i) determination of the total head, ii) upper bound solution of seismic active earth thrust, and iii) deduction for the earth pressure distribution. The determination of total head h(x,z) relies on the Fourier series expansions, and the expressions of the seismic active earth thrust and pressure are derived by using the upper bound theorem. Parametric studies reveal that insufficient drainage and earthquakes are crucial factors that cause unfavorable earth pressure. The numerical results confirm the validity of the total head distribution. Comparisons indicate that the proposed method is consistent with other relevant existing methods in terms of predicting seismic active earth pressure. The method can be applied to the seismic design of waterfront retaining walls.

Keywords seismic active earth pressure      partial seepage flow      pore pressure      anisotropy      upper bound theorem     
Corresponding Author(s): Cheng LYU   
Just Accepted Date: 29 October 2021   Online First Date: 01 December 2021    Issue Date: 21 January 2022
 Cite this article:   
Zhengqiang ZENG,Shengzhi WU,Cheng LYU. Upper bound solution to seismic active earth pressure of submerged backfill subjected to partial drainage[J]. Front. Struct. Civ. Eng., 2021, 15(6): 1480-1493.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0776-y
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I6/1480
Fig.1  Vertical wall supporting a backfill subjected to complete seepage flow.
Fig.2  Vertical wall supporting a backfill subjected to partial seepage flow: (a) partial seepage flow and the phreatic surface (based on the impervious layer); (b) decomposed total seepage field and hydrostatic field.
Fig.3  FDM model: (a) diagrammatic sketch and three hypothetical failure surfaces; (b) contours of grid point pore pressure in the numerical model when d = 0.4 m.
Fig.4  Comparison of results between proposed analytical method and FDM when d = 0, 0.4, and 0.8 m, respectively.
Fig.5  Distribution of total head in planar seepage state: (a) differing partial drainage condition d; (b) differing anisotropy index ξ.
Fig.6  Present active failure mechanism in limit analysis accounting for seismic forces.
φ δ/φ kh kv proposed method complete drainage(d = 0) [16] undrained(d = 5 m)
d = 1 m d = 2 m d = 3 m d = 4 m
25° 1/3 0.0 0.00 124.6 137.8 151.0 160.9 114.6 164.5
0.1 0.00 161.9 176.3 188.8 197.0 149.6 199.8
0.1 0.05 157.6 172.2 184.7 192.7 144.8 195.4
0.1 0.10 153.7 168.6 181.1 188.9 140.4 191.5
1/2 0.0 0.00 122.9 136.1 149.0 158.4 112.8 161.8
0.1 0.00 162.4 177.1 189.6 197.7 149.6 200.4
0.1 0.05 158.4 173.4 186.0 193.9 145.1 196.6
0.1 0.10 155.0 170.4 182.9 190.7 141.0 193.4
2/3 0.0 0.00 122.1 135.4 148.2 157.3 111.9 160.5
0.1 0.00 164.1 179.3 192.0 200.0 150.7 202.7
0.1 0.05 160.5 176.0 188.8 196.8 146.5 199.4
0.1 0.10 157.6 173.5 186.4 194.3 142.8 196.9
30° 1/3 0.0 0.00 109.1 124.3 139.6 151.5 98.1 155.9
0.1 0.00 144.4 160.8 175.8 185.9 131.1 189.4
0.1 0.05 140.5 157.2 172.2 182.1 126.8 185.5
0.1 0.10 136.9 154.0 168.9 178.7 122.7 182.0
1/2 0.0 0.00 108.1 123.3 138.5 149.8 96.9 153.9
0.1 0.00 145.5 162.4 177.6 187.6 131.5 190.9
0.1 0.05 141.9 159.2 174.4 184.2 127.5 187.6
0.1 0.10 138.8 156.5 171.7 181.4 123.7 184.7
2/3 0.0 0.00 108.2 123.6 138.8 149.9 96.7 153.8
0.1 0.00 148.2 165.9 181.4 191.5 133.4 194.9
0.1 0.05 145.0 163.1 178.7 188.7 129.6 192.1
0.1 0.10 142.2 160.8 176.6 186.5 126.1 189.9
35° 1/3 0.0 0.00 95.5 112.4 129.9 143.7 83.7 149.0
0.1 0.00 129.3 147.7 165.0 177.1 115.1 181.3
0.1 0.05 125.9 144.5 161.9 173.8 111.3 177.9
0.1 0.10 122.7 141.7 159.1 170.8 107.6 174.8
1/2 0.0 0.00 95.3 112.4 129.9 143.2 83.1 148.1
0.1 0.00 131.3 150.4 168.2 180.2 116.2 184.3
0.1 0.05 128.1 147.6 165.5 177.4 112.6 181.4
0.1 0.10 125.3 145.3 163.2 175.0 109.2 179.0
2/3 0.0 0.00 96.3 113.9 131.6 144.8 83.7 149.6
0.1 0.00 135.2 155.5 174.1 186.4 119.1 190.5
0.1 0.05 132.4 153.2 171.9 184.1 115.6 188.3
0.1 0.10 129.9 151.3 170.3 182.5 112.4 186.6
Tab.1  Variation of seismic active earth thrust with drainage conditions (kN·m)
φ δ/φ presented method reference
d/H = 0.2 d/H = 0.4 d/H = 0.6 d/H = 0.8 undrained (d/H = 1) fw = 0 [16] (d = 0) [3] [1,35,41]
20° 0 0.743 0.791 0.832 0.860 0.869 0.569 0.701 0.567 0.573
1/2 0.732 0.782 0.822 0.846 0.855 0.532 0.686 0.522 0.536
1 0.757 0.810 0.852 0.877 0.886 0.520 0.704 0.491 0.524
30° 0 0.588 0.653 0.715 0.760 0.776 0.397 0.538 0.395 0.400
1/2 0.582 0.650 0.710 0.750 0.764 0.368 0.526 0.353 0.371
1 0.637 0.717 0.786 0.829 0.844 0.372 0.568 0.325 0.376
40° 0 0.466 0.544 0.623 0.686 0.710 0.268 0.411 0.266 0.271
1/2 0.476 0.561 0.643 0.700 0.720 0.253 0.412 0.235 0.255
1 0.583 0.704 0.816 0.889 0.913 0.275 0.491 0.211 0.278
Tab.2  Comparisons of Kas with other theoretical results
Fig.7  Variations of θcr and Kas with drainage efficiency d/H for different soils: (a) θcr?d/H; (b) Kas?d/H.
Fig.8  Variations of θcr and Kas with internal friction angle under different seismic coefficients: (a) θcr?φ; (b) Kas?φ.
Fig.9  Variations of θcr and Kas with internal friction angle under different wall-soil friction conditions and drainage rate: (a) θcr?φ; (b) Kas?φ.
Fig.10  Partial seismic active earth thrust evaluation. (a) Case I; (b) Case II.
Fig.11  Variation of earth pressure distribution with drainage efficiency.
Fig.12  Seismic active earth pressure coefficient using different methods.
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