Vacuum preloading and PVDs in soft soils beneath embankments: 3D coupled analysis incorporating overall stability study

Borges, José Leitão

doi:10.28927/SR.2022.072821

José Leitão Borges ^##Corresponding author. E-mail address: leitao@fe.up.pt

Universidade do Porto, Construct, Faculdade de Engenharia, Porto, Portugal

https://orcid.org/0000-0003-3851-7489

#Corresponding author. E-mail address: leitao@fe.up.pt

Declaration of interest

The author has no conflicts of interest to declare.

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Figure 1
Yield and critical state surfaces of the p-q-θ critical state model in (a) principal effective stress space and (b) p-q space.

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Figure 2
20-noded brick element: (a) coupled element, with 60 displacement degrees of freedom and 8 excess pore pressure degrees of freedom; (b) non-coupled element, with 60 displacement degrees of freedom.

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Figure 3
3D scheme of a potential slip cylindrical surface.

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Figure 4
Quadrilateral of the slip surface within a 20-noded brick element.

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Figure 5
Slip surface of a symmetric problem that does not include the entire domain.

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Figure 6
Vertical cross section of the problem.

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Figure 7
Staged construction and vacuum pressure: (a) cases C1 (without vacuum) and C2; (b) cases C3, C4 and C5 (without vacuum).

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Figure 8
3D finite element mesh of the problem.

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Figure 9
Overall safety factor versus time, for cases C1-C5.

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Figure 10
Critical slip surfaces for cases C1-C5: (a) end of construction; (b) end of consolidation.

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Figure 11
Excess pore pressure (u) for case C1 (without vacuum pressure; u_min = 0): (a) end of construction (t = 11 days) (u_max = 67.64 kPa); (b) 1 month after the end of construction (u_max = 47.72 kPa).

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Figure 12
Excess pore pressure (u) for case C2 (vacuum pressure =-60 kPa; u_min =-60 kPa): (a) end of construction (t = 11 days) (u_max = 64.22 kPa); (b) 1 month after the end of construction (u_max = 40.47 kPa).

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Figure 13
Excess pore pressure (u) for case C3 (vacuum pressure=-60 kPa; u_min =-60 kPa): (a) end of construction (t = 50 days) (u_max = 49.29 kPa); (b) 1 month after the end of construction (u_max = 25.31 kPa).

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Figure 14
Excess pore pressure (u) for case C4 (vacuum pressure=-90 kPa; u_min =-90 kPa): (a) end of construction (t = 50 days; u_max = 42.27 kPa); (b) 1 month after the end of construction (u_max = 17.25 kPa).

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Figure 15
Excess pore pressure (u) for case C5 (without vacuum pressure; u_min = 0): (a) end of construction (t = 50 days; u_max = 64.63 kPa); (b) 1 month after the end of construction (u_max = 48.94 kPa).

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Figure 16
Settlement versus time at midpoint of the embankment base (co-ordinates: x = 0; y = 9 m; z = 0).

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Figure 17
Vertical displacements on the soft soil surface (y = 9 m; z = 0): (a) end of construction; (b) end of consolidation.

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Figure 18
Horizontal displacements under the embankment toe (x = 12 m; z = 0).

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Figure 19
Yield and critical state surfaces of the p-q-θ critical state model in the p-q plane.

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Figure 20
Stress level (SL) at the end of construction and end of consolidation, for cases C1-C5: (a) case C1 (end of construction); (b) case C1 (end of consolidation); (c) case C2 (end of construction); (d) case C2 (end of consolidation); (e) case C3 (end of construction); (f) case C3 (end of consolidation); (g) case C4 (end of construction); (h) case C4 (end of consolidation); (i) case C5 (end of construction); (j) Case C5 (end of consolidation).

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Table 1
Parameters related to the PVDs.

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Table 2
Geotechnical properties of the clay and embankment soil.

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Table 3
At rest earth pressure coefficient, K₀, and undrained shear strength, c_u, of the clay.

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Table 4
Critical slip surfaces at the end of construction for cases C1-C5: overall safety factor (F) and sums of acting and resisting forces.

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Table 5
Critical slip surfaces at the end of consolidation for cases C1-C5: overall safety factor (F) and sums of acting and resisting forces.

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(2)

(3)

(4)

(5)

(6)

Spacing	1.5 m
Vertical length	9.0 m
Cross-section of PVD	100 × 5 mm2
Discharge capacity, qw	130 m3 / year (per drain)
Cross-section of mandrel	120 × 60 mm2
Cross-section of smear zone	240 × 120 mm2

	γ (kN/m³)	ν'	ϕ' (º)	c' (kPa)	k_h (m/ s)	k_v (m / s)	p-q-θ critical state model
							λ	k	Γ	N
Clay	16	0.25	26	0	10^-9	10^-9	0.18	0.025	3.05	3.158
Embankment	20	0.30	35	0	-	-	0.03	0.005	1.80	1.817

Depth (m)	K₀	c_u (kPa)
0 - 3	0.9 – 0.5	13.0 – 4.9
≥ 3	0.5	0.272σ′_v0

	X₀ (m)	Y₀ (m)	R (m)	Sum of acting forces (kN)			Sum of resisting forces (kN)			F
	X₀ (m)	Y₀ (m)	R (m)	Total $\sum_{i = 1}^{N} τ_{i} A_{i}$	Foundation $\sum_{i = 1}^{N 1} τ_{i} A_{i}$	Embankment $\sum_{i = 1}^{N 2} τ_{i} A_{i}$	Total $\sum_{i = 1}^{N} τ_{f i} A_{i}$	Foundation $\sum_{i = 1}^{N 1} τ_{f i} A_{i}$	Embankment $\sum_{i = 1}^{N 2} τ_{f i} A_{i}$	$\frac{\sum_{i = 1}^{N} τ_{f i} A_{i}}{\sum_{i = 1}^{N} τ_{i} A_{i}}$
Case C1	10.0	12.5	8.53	138.67	126.91	11.76	151.06	135.20	15.86	1.09
Case C2	10.0	14.5	11.35	177.83	166.35	11.48	207.01	190.25	16.76	1.16
Case C3	9.5	18.0	15.34	230.52	220.22	10.30	311.20	294.37	16.83	1.35
Case C4	10.0	18.0	15.72	242.93	234.96	7.97	354.92	339.68	15.24	1.46
Case C5	9.5	12.5	8.80	145.39	136.04	9.35	164.36	149.17	15.19	1.13

	X₀ (m)	Y₀ (m)	R (m)	Sum of acting forces (kN)			Sum of resisting forces (kN)			F
	X₀ (m)	Y₀ (m)	R (m)	Total $\sum_{i = 1}^{N} τ_{i} A_{i}$	Foundation $\sum_{i = 1}^{N 1} τ_{i} A_{i}$	Embankment $\sum_{i = 1}^{N 2} τ_{i} A_{i}$	Total $\sum_{i = 1}^{N} τ_{f i} A_{i}$	Foundation $\sum_{i = 1}^{N 1} τ_{f i} A_{i}$	Embankment $\sum_{i = 1}^{N 2} τ_{f i} A_{i}$	$\frac{\sum_{i = 1}^{N} τ_{f i} A_{i}}{\sum_{i = 1}^{N} τ_{i} A_{i}}$
Case C1	10.0	20.0	18.68	291.62	293.38	-1.76	470.55	452.23	18.32	1.61
Case C2	10.5	15.0	13.68	259.47	256.25	3.22	446.59	425.03	21.56	1.72
Case C3	10.0	16.0	14.78	280.09	277.12	2.97	506.21	478.78	27.43	1.81
Case C4	11.0	17.5	16.06	291.66	289.88	1.78	505.18	480.43	24.75	1.73
Case C5	10.0	20.0	18.68	289.41	289.78	-0.37	460.64	441.21	19.43	1.59

[1] #Corresponding author. E-mail address: leitao@fe.up.pt

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Vacuum preloading and PVDs in soft soils beneath embankments: 3D coupled analysis incorporating overall stability study

Abstract