Seismic codes based equivalent nonlinear and stochastic soil structure interaction analysis

Mohamed Elhebib Guellil; Zamila Harichane; Erkan Çelebi

doi:10.2478/sgem-2020-0007

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Seismic codes based equivalent nonlinear and stochastic soil structure interaction analysis

Studia Geotechnica et Mechanica

Volume 43 (2021): Issue 1 (April 2021)

By: Mohamed Elhebib Guellil, Zamila Harichane and Erkan Çelebi

Open Access

|Oct 2020

Figures & Tables

Modelling of SSI: (a) schematic view of SSI system, (b) equivalent SDOF system.

Model of a rigid circular footing on a soil layer underlain by elastic half-space.

Impedance functions obtained before and after the correction of shear modulus and damping coefficient: (a) and (b) for horizontal motion, (c) and (d) for rotational motion.

SSI response with respect to the free field before and after the correction of shear modulus and damping coefficients: (a) displacement of the structure, (b) displacement of the mass and (c) total displacement of the base.

Comparison between stochastic (random G) and nonlinear (corrected G and ξ) SSI responses: (a) structure displacement, (b) mass displacement, (c) base displacement.

Table 1

Error margin (%) in displacements and frequency SSI system due to random G and corrected (G and ξ).

SSI response	Deterministic	Stochastic (20% COV of G)	Nonlinear	Error margin (%)

				20% COV of G vs. initial G	Corrected (G & ξ) vs initial G
\|u\|/\|ug\|	1.81	1.51	1.21	− 16.6%	− 33.1%
\|u₀+hθ₀+u\|/\|ug	7.35	6.07	7.37	− 17.4%	+ 0.3%
\|u₀+ug\|/\|ug\|	0.86	0.86	0.95	±00.0%	+ 10.4%
Frequency (ω/ω_s)	0.5	0.5	0.41	±00.0%	−18.0%

Design response spectrum: (a) RPA99-2003, (b) EC8-2004, (c) IBC-2015 and (d) IS-1893-2002.

Base shear forces: (a) RPA99-2003, (b) EC8-2004, (c) IBC-2015 and (d) IS-1893-2002.

Table 2

Ordinate of elastic and inelastic design spectra for RPA99-2003, EC8-2004, IBC-2015 and IS-1893-2002.

	T ≤ T_B	T_B ≤ T ≤ TC	T ≥ T_C	Seismic base shear
RPA99v2003	$\begin{array}{l} \frac{S_{a}}{g} = 1, 25 . A . ⌊ 1 + \frac{T}{T_{1}} (2.5 η \frac{Q}{R} - 1) ⌋ & (T_{1} = T_{B}) \end{array}$	$\begin{array}{l} \begin{array}{l} \frac{S_{a}}{g} = 1, 25 . A . 2, 5 . η . (\frac{Q}{R}) & (T_{1} \leq T \leq T_{2}) \end{array} \end{array}$	$\begin{array}{l} \frac{S_{a}}{g} = 1, 25 . A . 2, 5 . η . (\frac{Q}{R}) {(\frac{T_{2}}{T})}^{2 / 3} & (T_{2} \leq T \leq T_{3}) \end{array}$	$V = \frac{A . D . Q}{R} . W {\begin{array}{l} A : area acceleration coefficient, \\ D : average dynamic amplification factor \\ Q : quality factor \\ R : overall behavior coefficient of the structure \\ W : The effective seismic weight of the structure \end{array}$
RPA99v2003			$\begin{array}{l} \frac{S_{a}}{g} = 1, 25 . A . 2, 5 . η . (\frac{Q}{R}) {(\frac{T_{2}}{3})}^{2 / 3} {(\frac{T}{3})}^{5 / 3} & (T_{2} \leq T \leq T_{3}) \end{array}$
EC8-2004	$S_{e} = a_{g} . S . ⌊ 1 + \frac{T}{T_{B}} (η 2.5 - 1) ⌋$	S_e=2.5.a_g.S.η	$T_{C} \leq T \leq T_{D} \to S_{e} = 2.5 . a_{g} . S . η . [\frac{T_{C}}{T}]$	$F_{b} = S_{d} (T) \frac{W}{g} . λ {\begin{array}{l} λ = 0.85 if T_{1} \leq 2 T_{C} & or \\ λ = 1.00 otherwise \end{array}$
	$S_{d} = a_{g} . S . [\frac{2}{3} + \frac{T}{T_{B}} (\frac{2.5}{q} - \frac{2}{3})]$	S_d = 2.5.a_g.S.η	$T_{C} \leq T \leq T_{D} \to S_{d} {\begin{matrix} = \frac{2.5}{q} . a_{g} . S . [\frac{T_{C}}{T}] \\ \geq β . a_{g} \end{matrix}$
			$T_{D} \leq T \leq 4 s \to S_{e} = 2.5 . a_{g} . S . η . ⌊ \frac{T_{C} T_{D}}{T^{2}} ⌋$
			$T \geq T_{D} \to S_{d} = \frac{2.5}{q} . a_{g} . S . ⌊ \frac{T_{C} T_{D}}{T^{2}} ⌋ \geq β . a_{g}$
IBC-2015	$\begin{matrix} \frac{S_{a}}{g} = 1 + 15 T & (0.00 \leq T \leq 0.10) \end{matrix}$	S_a = S_DS (T₀≤T≤T_S)	$\begin{matrix} S_{a} = \frac{S_{DS}}{T} & (T > T_{s}) \end{matrix}$	$V = C_{s} . W {\begin{array}{l} C_{s} : The seismic response coefficient \\ W : The effective seismic weight of the structure \end{array}$
IS-1893-2002	$\begin{matrix} \frac{S_{a}}{g} = 1 + 15 T & (0.00 \leq T \leq 0.10) \end{matrix}$	$\begin{matrix} \frac{S_{a}}{g} = 2.50 & (0.10 \leq T \leq 0.40) \end{matrix}$	$\begin{matrix} \frac{S_{a}}{g} = 1.00 / T & (0.40 \leq T \leq 4.00) \end{matrix}$	$V = \frac{Z . I . S_{a}}{2 . R . g} . W {\begin{array}{l} Z : zone factor \\ I : importance factor \\ S_{a} : average response acceleration coefficient \\ R : response reduction factor \\ g:acceleration due to gravity \\ W : Seismic weight of the structure \end{array}$

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DOI: https://doi.org/10.2478/sgem-2020-0007 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 1 - 14

Submitted on: Mar 31, 2020

Accepted on: Aug 29, 2020

Published on: Oct 23, 2020

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

Shear modulus,

damping,

uncertainties,

linear iterative method,

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2020 Mohamed Elhebib Guellil, Zamila Harichane, Erkan Çelebi, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 43 (2021): Issue 1 (April 2021)

Seismic codes based equivalent nonlinear and stochastic soil structure interaction analysis

Figures & Tables

Figure 1

Figure 2

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Figure 5

Table 1

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Figure 8

Table 2

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