An elastoplastic constitutive model for assessing ground settlements induced by deep excavations

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Reference parameters (calibrated on the triaxial tests) for the Hochstetten sand_

HSM	Eurref=63 MPa, E50ref=21 MPa, ν=0.1, m=0.5, pref=100 kPa, c=5 kPa, φ=43°, ψ=14°, Rf=0.9
HCD model	E=75 MPa, ν=0.3, Ro=0, pc=2 kPa, φult=43°, φc=29°, αo=3, b=0.0025

HCD model parameters_

	E	v	φo	pc	φult	αo	φc	b
	MPa		°	kPa	deg		deg
Monotonic test (confining pressure 175 kPa)	57	0.4	φmin	0	37	8	27	0.001
Cyclic test (confining pressure 157 kPa)	57	0.4	φmin	0	37	20	31	0.003

Parameters of the reaction wall and the sheet pile wall_

Wall	E(MPa)	I(cm4/m)	A(cm2/m)	Eeq (MPa)	teq (cm)
Reaction wall	210,000	968	106	24,400	10
Sheet pile wall	210,000	11,610	116	6800	35

Results obtained with HSM (displacements in mm)_

	Measures	HSM (ref.)	HSM (adj.)
Max horizontal displacement – 4 m	1.83	1.34 (−27%)	0.91 (−50%)
Max horizontal displacement – 5 m	2.95	4.49 (+52%)	2.56 (−13%)
Max horizontal displacement –surcharge	3.36	5.80 (+73%)	3.28 (−2%)
Settlement 1 m behind the wall – 5 m	2.17	1.21 (−44%)	0.80 (−63%)
Settlement 1 m behind the wall – surcharge	2.80	4.18 (+49%)	2.26 (−19%)

Summary of the triaxial tests considered in this study_

Test	Depth	Type of soil	Type of test
B	6.5–7	Very fine silty sand	Consolidated drained CD
C	8.5–9.5	Slightly sandy pebbles and gravel	Consolidated drained CD
E	13.7–14	Silty clay	Consolidated drained CD

Parameters of the HCD model for tests B, C, and E (σc denotes the confining pressure)_

		σc	E	v	φo	pc	φult	αo	φc	b
		kPa	MPa	-	°	kPa	°	-	°	-
Test B	1	150	45	0.2	7	10	35	1	31	0.005
	2	250	70	0.2	7	10	35	1	32	0.008
Test C	3	400	107	0.2	7	10	35	1	33	0.009
	2	200	133	0.1	15	15	41	1	38	0.002
	3	350	233	0.127	15	15	41	1	39	0.005
Test E	1	200	16	0.12	1.2	60	23	1	20	0.004
	2	350	45	0.12	2.2	60	23	1	20	0.005
	3	550	112	0.14	4.2	60	23	1	21	0.015

Results obtained with the HCD model (displacements in mm)_

	Measures	HCD (ref.)	HCD (adj.)
Max. horizontal displacement – 4 m	1.83	0.86 (−53%)	1.37 (−25%)
Max. horizontal displacement – 5 m	2.95	2.53 (−14%)	2.99 (+1%)
Max. horizontal displacement – surcharge	3.36	2.86 (−14%)	3.51 (+4%)
Settlement 1 m behind the wall – 5 m	2.17	1.81 (−17%)	1.81 (−17%)
Settlement 1 m behind the wall – surcharge	2.80	2.65 (−5%)	3.04 (+8%)