Automated inverse analysis of a deep excavation in Ankara clay using finite element analysis

Abstract

The objective of this study is to find out the constant that shows a linear relationship between the deformation modulus parameter of Ankara clay and SPT N₆₀ values by using Plaxis 2D software. During analyses, three constitutive models are used, those are Mohr-Coulomb (MC), hardening soil model (HS), and hardening soil model with small strain stiffness (HSsmall). For that purpose, reverse analysis of a 25.0-m deep excavation was done by comparing results with displacements taken from inclinometer measurements. Instead of using an idealized soil profile, soil layers are divided into 1.5-m thicknesses according to SPT N measurement depths; and for each interval, soil parameter correlation is performed. To minimize time loss, analyses were performed by writing a Python code. Finally, results were evaluated by comparing soil models with each other, and it is found out that displacement curves of the MC model could not converge to the actual displacements. Analyses results of the HSsmall model are the closest displacements to the measured values on the site. Also, displacement curves of the hardening models (HS and HSsmall) are almost similar, and the linear correlation constant is found as E₅₀^ref ~780×N₆₀ kPa for this excavation of the case study in Ankara clay in HS and HSsmall models.

Appendices

Appendix A

Fig. 12

Inclinometer measurement result. The altitude of 886.0m is defined as zero elevation (±0.00) in the project

Appendix B

Table 1 Plaxis parameters used in parametrized study

Table 2 Obtained γ_0.7 values for HSsmall model

Appendix C

For pile;

$$ {\displaystyle \begin{array}{c}E=285\times {10}^5\ \mathrm{kPa}\ \left(\mathrm{C}25\ \mathrm{concrete}\ \mathrm{class}\right)\\ {}A=\pi \times {d}^2/4=\pi \times {0.8}^2/4=0.5\ {\mathrm{m}}^2\\ {}I=\pi \times {d}^4/64=\pi \times {0.8}^4/64=0.02\ {\mathrm{m}}^4\end{array}} $$

Table 3 Plate element input data

For anchorages;

$$ {\displaystyle \begin{array}{c}{E}_{\mathrm{anchor}}=195\ \mathrm{kN}/\mathrm{m}{\mathrm{m}}^2\left(\mathrm{BS}8081\right)\\ {}{A}_{\mathrm{anchor}}=139\times 4=556\ \mathrm{m}{\mathrm{m}}^2\\ {}\begin{array}{c}\mathrm{EA}=\mathrm{108,420}.\mathrm{0}/2.0=\mathrm{54,210}\ \mathrm{kN}/\mathrm{m}\ \mathrm{for}\ 2.0-\mathrm{m}\ \mathrm{anchor}\ \mathrm{spacing}\\ {}\mathrm{EA}=\mathrm{108,420}/1.5=\mathrm{72,280}\ \mathrm{kN}/\mathrm{m}\ \mathrm{for}\ 1.5-\mathrm{m}\ \mathrm{anchor}\ \mathrm{spacing}\end{array}\end{array}} $$

Table 4 Seven-wire strand specific characteristic strengths (BS8081)

For geogrids;

$$ {\displaystyle \begin{array}{c}E=285\times {10}^5\ \mathrm{kPa}\\ {}\mathrm{EA}=285\times {10}^5\times 0.017/2.0=\mathrm{251,818.0}\ \mathrm{for}\ 2.0-\mathrm{m}\ \mathrm{anchor}\ \mathrm{spacing}\\ {}\mathrm{EA}=285\times {10}^5\times 0.017/1.5=\mathrm{335,785}\ \mathrm{for}\ 1.5-\mathrm{m}\ \mathrm{anchor}\ \mathrm{spacing}\end{array}} $$

Appendix D

Fig. 13

Horizontal displacement of the pile (MC model)

Fig. 14

Vertical displacement of the soil at final excavation level (MC model)

Fig. 15

Horizontal displacement of the pile (HS Model)

Fig. 16

Vertical displacement of the soil at final excavation level (HS model)

Fig. 17

Horizontal displacement of the pile (HSsmall model)

Fig. 18

Vertical displacement of the pile (HSsmall model)