Analysis Method for Laterally Loaded Pile Groups Using an Advanced Modeling of Reinforced Concrete Sections
Abstract
:1. Introduction
2. Proposed ‘BEM-Based’ Method
2.1. Key Features of the Proposed Method
- a)
- pile-soil, pile-pile interactions are considered using the Mindlin’s solution;
- b)
- horizontally layered elastic soil;
- c)
- non-linear behavior for the reinforced concrete pile section;
- d)
- non-linear soil behavior (incremental analysis);
- e)
- the so-called shadowing effect, has been implemented in the code using an approach similar to that described in [35];
- f)
2.2. Pile Modelling
- 20 blocks with a thickness Δ = D/8, starting from the ground level up to a depth of 2.5D;
- 10 blocks with a thickness Δ = D/4, starting from a depth of 2.5D up to a depth of 5D;
- 10 blocks with a thickness Δ = D/2, starting from a depth of 5D up to a depth of 10D;
- 10 blocks with a thickness Δ = D, starting from a depth of 10D up to a depth of 20D;
- 10 blocks with a thickness Δ = (L − 20D)/10, starting from a depth of 20D up to the pile base depth.
2.3. Soil Modelling
Soil Non-Linear Behavior
2.4. Influence of Suction on Pile Group Response to Horizontal Loading
2.5. Group Effects Modelling
2.6. Solution System
- the km × km pile flexibility matrix [FP], composed of the aij coefficients;
- the km × km flexibility matrix [FS], composed of the bij coefficients that represent the displacements induced by a load acting at the pile-soil interface j to the pile-soil interface i.
3. Validation of the Proposed Method
3.1. Analysis Results with the Proposed BEM Method for a Specific Lateral Load Test on a Bored Pile Group
3.1.1. Soil and Pile Properties Description
3.1.2. Single Bored Pile B7 (Free-Head) and Pile Group (Fixed-Head): Analysis Results
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Case Reference | Pile Material | Pile Diameter (m) | Pile Length (m) | Soil Type | Hmax (kN) |
---|---|---|---|---|---|
[51] 3 × 3; s = 3D | Steel with Grout-fill | 0.273 | 13.11 | OC Clay | 695 |
[5] 3 × 3; s = 3D | Steel with Grout-fill | 0.273 | 13.11 | Sand | 808.5 |
[4] 3 × 2; s = 3D | Bored RC | 1.5 | 34.9 | Silty Sand | 11043 |
[8] ϕ’ = 34°; 3 × 3; s =3D | Aluminum | 0.43 | 13.3 | Sand | 761.2 |
[8] ϕ’ = 39°; 3 × 3; s = 3D | Aluminum | 0.43 | 13.3 | Sand | 1508.2 |
[8] ϕ’ = 34°; 3 × 3; s = 5D | Aluminum | 0.43 | 13.3 | Sand | 1110.5 |
[8] ϕ’ = 39°; 3 × 3; s = 5D | Aluminum | 0.43 | 13.3 | Sand | 1424 |
[52] 2 × 1; s = 2D | Aluminum | 0.72 | 12 | Sand | 1183 |
[52] 2 × 1; s = 4D | Aluminum | 0.72 | 12 | Sand | 1220.1 |
[52] 2 × 1; s = 6D | Aluminum | 0.72 | 12 | Sand | 1030.72 |
[53] 3 × 3; s = 3D | Steel with Grout-fill | 0.305 | 8.7 | Clay | 927.05 |
[11] 3 × 3; s = 3D | Steel pipe | 0.324 | 11.5 | Sand | 488.6 |
[54] 3 × 3; s = 5.65D | Steel pipe | 0.324 | 11.9 | Clay | 1407 |
[54] 3 × 4; s = 4.4D | Steel pipe | 0.324 | 11.9 | Clay | 1353.8 |
[54] 3 × 5; s = 3.3D | Steel pipe | 0.324 | 11.9 | Clay | 1942.5 |
Case | EpIp (MNm2) | γ (kN/m3) | ϕ (°) | DR (%) | cu (kPa) | Emax (Linear Increasing with Depth) (MPa) | G (-) | F (m) | W.T. (m) | Head B.C. |
---|---|---|---|---|---|---|---|---|---|---|
[51] | 16.0 | 19.0 | - | - | 58–145 (0–5.5 m) | 70–200 (0–5.5 m) | 0.25 | 0.305 | 0.0 | Free |
[5] | 16.0 | 19.5 | 47 | 90 | - | 35–100 (0–2.0 m) | 1.0 | 0.305 | 0.0 | Free |
[4] | variable | 18.5 | 34 | 50 | - | 40–400 (0–34.9 m) | 0.5 | 1.0 | 1.0 | Fixed |
[8] | 72.1 | 14.51 | 34 | 33 | - | 60–300 (0–13.3 m) | 0.25 | 1.68 | - | Free |
[8] | 72.1 | 15.18 | 39 | 55 | - | 50–260 (0–13.3 m) | 0.5 | 1.68 | - | Free |
[52] | 514.0 | 16.3 | 40 | 89 | - | 40–200 (0–12.0 m) | 1.0 | 1.6 | - | Free |
[53] | 26.91 | 19.0 | - | - | 50–75 (0–2.9 m) | 60–170 (0–8.7 m) | 0.25 | 0.4 | 0.0 | Free |
[11] | 30.03 | 19.5 | 40 | 44 | - | 20–150 (0–11.5 m) | 0.25 | 0.86 | 0.0 | Free |
[54] | 30.03 | 19.0 | - | - | 60 (0–1 m)120 (1.0–4.0 m) | 50–60 (0–4.0 m) | 0.25 | 0.48 | 1.0 | Free |
Pile Diameter D (mm) | Pile Length (m) | Cross Sectional Area (cm2) | Concrete Compressive Strength f’c (MPa) | Reinforcement Yield Stress fy (MPa) | Steel Ratio ρs | Intact Flexural Rigidity EI (GNm2) |
---|---|---|---|---|---|---|
1500 | 34.9 | 17672 | 27.5 | 471 | 0.025 | 6.86 |
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Stacul, S.; Squeglia, N. Analysis Method for Laterally Loaded Pile Groups Using an Advanced Modeling of Reinforced Concrete Sections. Materials 2018, 11, 300. https://doi.org/10.3390/ma11020300
Stacul S, Squeglia N. Analysis Method for Laterally Loaded Pile Groups Using an Advanced Modeling of Reinforced Concrete Sections. Materials. 2018; 11(2):300. https://doi.org/10.3390/ma11020300
Chicago/Turabian StyleStacul, Stefano, and Nunziante Squeglia. 2018. "Analysis Method for Laterally Loaded Pile Groups Using an Advanced Modeling of Reinforced Concrete Sections" Materials 11, no. 2: 300. https://doi.org/10.3390/ma11020300