Improved prediction of pile bending moment and deflection due to adjacent braced excavation

doi:10.1007/s11709-023-0961-2

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (11) : 1739-1759 https://doi.org/10.1007/s11709-023-0961-2

Improved prediction of pile bending moment and deflection due to adjacent braced excavation

Chana PHUTTHANANON¹, Pornkasem JONGPRADIST¹(

), Duangkamol SIRIRAK², Prateep LUEPRASERT², Pitthaya JAMSAWANG³

¹. Construction Innovations and Future Infrastructures Research Center, Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
². Department of Civil Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
³. Soil Engineering Research Center, Department of Civil Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

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Abstract

Deep excavations in dense urban areas have caused damage to nearby existing structures in numerous past construction cases. Proper assessment is crucial in the initial design stages. This study develops equations to predict the existing pile bending moment and deflection produced by adjacent braced excavations. Influential parameters (i.e., the excavation geometry, diaphragm wall thickness, pile geometry, strength and small-strain stiffness of the soil, and soft clay thickness) were considered and employed in the developed equations. It is practically unfeasible to obtain measurement data; hence, artificial data for the bending moment and deflection of existing piles were produced from well-calibrated numerical analyses of hypothetical cases, using the three-dimensional finite element method. The developed equations were established through a multiple linear regression analysis of the artificial data, using the transformation technique. In addition, the three-dimensional nature of the excavation work was characterized by considering the excavation corner effect, using the plane strain ratio parameter. The estimation results of the developed equations can provide satisfactory pile bending moment and deflection data and are more accurate than those found in previous studies.

Keywords pile responses excavation prediction deflection bending moments

Corresponding Author(s): Pornkasem JONGPRADIST

Just Accepted Date: 31 July 2023 Online First Date: 27 December 2023 Issue Date: 24 January 2024

Cite this article:

Chana PHUTTHANANON,Pornkasem JONGPRADIST,Duangkamol SIRIRAK, et al. Improved prediction of pile bending moment and deflection due to adjacent braced excavation[J]. Front. Struct. Civ. Eng., 2023, 17(11): 1739-1759.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0961-2
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I11/1739

Fig.1 Considered configuration of hypothetical excavation adjacent to an existing pile.

parameter	symbol	unit	sedimentary crust	soft clay	stiff clay	sand
constitutive soil model	?	?	MC	HSS	HSS	MC
unit weight	$γ$	kN/m³	17	16	18	20
Young’s modulus	$E ′$	kPa	6000	?	?	80000
Poisson’s ratio	$ν ′$	(?)	0.32	?	?	0.30
secant stiffness in standard drained TX test	$E 50 ref$	kPa	?	4000?9000	34000?53000	?
tangent stiffness for primary oedometer loading	$E oed ref$	kPa	?	4000?9000	34000?53000	?
unloading/reloading stiffness from drained TX test	$E ur ref$	kPa	?	12000?27000	104000?158000	?
reference shear stiffness at very small strains	$G 0 ref$	kPa	?	9000?20300	78300?118800	?
threshold shear strain at which $G S = 0.7 G 0$	$γ 0.7$	(?)	?	0.0001	0.0001	?
Poisson’s ratio for unloading/reloading	$ν ur$	(?)	?	0.33	0.33	?
power of the stress level dependency of stiffness	$m$	(?)	?	1	1	?
effective cohesion	$c ′$	kPa	8	?	?	0
soil undrained shear strength	$s u$	kPa	?	15?34	87?132	?
effective friction angle	$? ′$	°	22	0	0	36
dilatancy angle	$ψ$	°	0	0	0	0
failure ratio	$R f$	(?)	?	0.9	0.9	?
reference stress for stiffnesses	$p ref$	kPa	?	100	95	?
$K 0$ -value for normally consolidated soils	$K 0 nc$	(?)	0.625	0.625	0.625	0.412

Tab.1 Constitutive model parameters for soils (MC and HSS models)

Fig.2 Finite element mesh for hypothetical excavation adjacent to an existing pile for the case of

H e

= 11 m, B = 60 m,

X p

= 5 m, and

T s

= 14 m.

Fig.3 Simulated and measured horizontal displacement profiles of the braced wall for a basement excavation in Bangkok subsoil.

parameter	symbol	unit	range	normalized parameter (dimensionless)
excavation depth	$H e$	m	2, 5, 8, 11	$H e / B ref$
excavation width	$B$	m	20, 40, 60, 80	$B / B ref$
thickness of diaphragm wall	$t w$	m	0.6, 0.8, 1.0, 1.2	$ln ? (E w I w / (B ref γ w h avg 4))$
pile diameter	$D p$	m	0.50, 0.75, 1.00, 1.25	$ln ? (E p I p / (γ w D p 5))$
pile length	$L p$	m	15, 18, 23	$L p / B ref$
pile distance from primary wall	$X p$	m	0.6, 1, 3, 5, 10	$X p / B ref$
pile distance from complementary wall	$X p cn$	m	10, 20, 30	$X p cn / B ref$
relative undrained shear strength ratio for soft clay	$s u-soft / σ v ′$	(?)	0.27, 0.30, 0.35, 0.38, 0.40	$s u-soft / σ v ′$
relative undrained shear strength ratio for stiff clay	$s u-stiff / σ v ′$	(?)	0.45, 0.60, 0.75, 0.90, 1.05	$s u-stiff / σ v ′$
relative shear stiffness ratio for soft clay	$G 0-soft ref / σ v ′$	(?)	123, 158, 210, 263, 315	$G 0-soft ref / σ v ′$
relative shear stiffness ratio for stiff clay	$G 0-stiff ref / σ v ′$	(?)	375, 525, 675, 825, 975	$G 0-stiff ref / σ v ′$
thickness of soft clay layer	$T s$	m	11, 14, 16.5	$T s / B ref$

Tab.2 Summary of input parameters with their variations used for establishing hypothetic cases and normalized parameters used in regression analysis for establishing the predicted equations

Fig.4 Excavation-induced pile responses with respect to pile-head conditions: (a) pile bending moment and (b) pile deflection along depth.

Fig.5 Percentage contribution for all considered factors upon the variations of maximum pile bending moments (both positive and negative values) and maximum pile deflection.

design parameters included in predicted equations	symbols	Poulos and Chen [7]^?	Liyanapathirana and Nishanthan [38]^?	Zhang et al. [31]^?	this study^?
excavation depth	$H e$	√	√	√	√
excavation width	$B$	×	×	√	√
wall thickness	$t w$	√^*	×	×	√^***
strut stiffness	$s k$	√	√	×	×
strut spacing (average value)	$h avg$	√	√	×	√^***
unsupported depth of excavation	$h un$	×	√	×	×
pile diameter (or width)	$D p$	√	√	√	√
pile length	$L p$	×	×	√	√
pile distance from excavation	$X p$	√	√	√	√
pile-head fixity	$F p$	×	×	√	√
axial load exerted on pile head	$P p$	×	×	√	×
undrained shear strength of soft clay	$s u-soft$	√^**	√^**	×	√
undrained shear strength of stiff clay	$s u-stiff$	√^**	√^**	×	√
shear stiffness of soft clay	$G 0-soft ref$	×	×	×	√
shear stiffness of stiff clay	$G 0-stiff ref$	×	×	×	√
thickness of soft clay layer	$T s$	×	×	×	√

Tab.3 Summary of the design parameters included in the semi-empirical equations for predicting maximum pile bending moment and deflection used in the existing methods and this study

Fig.6 Prediction performance of pile responses caused by adjacent excavation using existing methods: (a) predicted bending moment under ZZG method and (b) predicted pile deflection under PC, LN, and ZZG methods.

No.	input variables, $t [X]$	coefficients of Eqs. (2), (5?7)
		model A1 for predicting $M n max (+)$				model A2 for predicting $M n max (?)$				model B for predicting $d n max$
		β	a	b	c	α	a	b	c	η	a	b	c
0	?	?32.456	?	?	?	?14.613	?	?	?	?0.215	?	?	?
1	$H e / B ref$	0.889	?83.340	70.909	4.864	1.067	?19.837	18.690	1.225	0.016	?	?	?
2	$B / B ref$	1.735	?	?	?	1.673	?0.066	0.465	2.262	0.726	?0.00019	0.00213	0.00999
3	$ln ? (E w I w / (B ref γ w h avg 4))$	0.717	0.318	?4.506	32.106	0.638	0.447	?6.839	28.132	0.614	0.00049	?0.00745	0.03876
4	$ln ? (E p I p / γ w D p 5)$	0.509	3.793	?77.632	401.420	0.266	2.135	?53.457	338.350	1.079	0.00677	?0.14466	0.77826
5	$L p / B ref$	?0.398	?	?	?	?0.174	?	?	?	?0.001	?	?	?
6	$X p / B ref$	0.772	60.353	?56.828	24.013	0.912	?8.160	?0.463	6.021	0.819	?0.00788	?0.00916	0.01616
7	$s u-soft / σ v ′$	?5.396	?	?	?	?3.558	?	?	?	0.974	0.03095	?0.02983	0.01732
8	$s u-stiff / σ v ′$	?1.255	?	?	?	?0.142	?	?	?	11.985	3.14 × 10^?4	?6.71 × 10^?4	0.00854
9	$G 0-soft ref / σ v ′$	?0.038	?	?	?	?0.017	?	?	?	1.328	2.14 × 10^?8	?4.60 × 10^?5	0.02855
10	$G 0-stiff ref / σ v ′$	?0.007	?	?	?	?0.001	?	?	?	3.601	1.81 × 10^?9	?5.00 × 10^?6	0.01097
11	$T s / B ref$	17.998	?	?	?	6.254	?	?	?	0.021	?	?	?

Tab.4 Coefficients for predicting the normalized values of maximum pile bending moments and pile deflection

Fig.7 Performance of Eqs. (5) and (6) for predicting the normalized values of maximum positive and negative pile bending moments, compared to 136 FE hypothetical case results.

Fig.8 Performance of Eq. (7) for the normalized maximum pile deflection prediction under plane strain conditions, as compared against 136 FE hypothetical case results.

No.	input variables, $t [X]$	coefficients of Eqs. (2) and (8)
		ω	a	b	c
0	?	?2.702	?	?	?
1	$H e / B ref$	0.992	?0.03238	0.03900	0.84641
2	$B / L$	0.982	0.12381	?0.17917	0.91069
3	$L p / B ref$	0.189	?0.15261	0.26377	0.74332
4	$X p / B ref$	0.996	0.08356	?0.14026	0.87659
5	$X p cn / B ref$	1.001	?0.37632	1.06570	0.22809

Tab.5 Coefficients for predicting the PSR

Fig.9 Performance of Eq. (8) for predicting PSR according to the 360 FE hypothetical case analyses.

Fig.10 Performance of Eq. (9) for predicting maximum pile deflection under 3D condition according to the 360 FE hypothetical case analyses.

input variable, $t [X]$	value	remark
$H e / B ref$	0.325	data from Goh et al. [8]: $H e$ = 6.5 m
$B / B ref$	1	data from Goh et al. [8]: B = 20 m
$ln ? (E w I w / B ref γ w h avg 4)$	4.761	data from Goh et al. [8] and Zhang et al. [31]: $t w$ = 0.8 m, $h avg$ = 2.5 m and $E w$ = $2.1 × 107$ kPa
$ln ? (E p I p / γ w D p 5)$	11.562	data from Goh et al. [8]: $D p$ = 1 m and assuming $E p$ = $E w$
$L p / B ref$	2.3	data from Goh et al. [8]: $L p$ = 46 m
$X p / B ref$	0.15	data from Goh et al. [8]: $X p$ = 3 m
$s u-soft / σ v ′$	0.2825^*	data from Zhang et al. [31]: $? ′$ = 25°
$s u-stiff / σ v ′$	0.4698^*	data from Zhang et al. [31]: $? ′$ = 40°
$G 0-soft ref / σ v ′$	268^**	data from Xuan [64]: $I R$ = 700 and assuming $p ref$ = 100 kPa, $K 0 = 1 ? sin ? ? ′$ , and $σ 1 ′ = σ v ′$
$G 0-stiff ref / σ v ′$	431^**	data from Xuan [64]: $I R$ = 700 and assuming $p ref$ = 100 kPa, $K 0 = 1 ? sin ? ? ′$ , and $σ 1 ′ = σ v ′$
$T s / B ref$	0.9	data from Zhang et al. [31]: $T s$ = 18 m (base level of soft marine clay layer)

Tab.6 Summary of input parameters used for estimating maximum pile deflection based on specific information of case history

estimation method	observed and estimated values of $d max$ (mm) at $H e$ = 6.5 m
estimation method	observed	estimated	error
proposed method of this study	15	14.84	1.05%
PC method	15	9.49	36.7%
LN method	15	65.52	336.8%
ZZG method	15	12.70	15.3%

Tab.7 Comparison between observed and estimated results for case history

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