Stable expression and control parameters in the numerical simulation of unsaturated flow

doi:10.1007/s11709-022-0893-2

Frontiers of Structural and Civil Engineering

2022, Vol. 16

Issue (12): 1501-1514 https://doi.org/10.1007/s11709-022-0893-2

本期目录

Stable expression and control parameters in the numerical simulation of unsaturated flow

Zhiyuan ZHANG, Xu LI, Yongkang WU(

), Xiaokang LI

Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China

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Abstract：

The Richards’ equation describes the flow phenomenon in unsaturated porous media and is essential to hydrology and environmental science. This study evaluated the numerical stability of two different forms of the Richards’ equation. Sensitivity analyses were performed to investigate the control parameters of the equation. The results show that the h-form Richards’ equation has better applicability for calculating variable saturation flows than the θ-form Richards’ equation. For the h-form Richards’ equation, the hydraulic conductivity of the soil in the low-suction range and the specific moisture capacity in the high-suction range primarily influenced the solution. In addition, sensitivity analyses indicated that the saturated hydraulic conductivity, initial condition, and air-entry pressure have a higher sensitivity to the simulation results than the saturated water content, rainfall intensity, and decline rate of hydraulic conductivity. Moreover, their correctness needs to be guaranteed first in numerical simulations. The research findings can provide a helpful reference for improving the reliability of numerical simulations of unsaturated flows.

Key words： Richards’ equation sensitivity analysis unsaturated soil hydraulic diffusivity seepage simulation

收稿日期: 2022-05-03 出版日期: 2023-01-16

Corresponding Author(s): Yongkang WU

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2022, 16(12): 1501-1514.
Zhiyuan ZHANG, Xu LI, Yongkang WU, Xiaokang LI. Stable expression and control parameters in the numerical simulation of unsaturated flow. Front. Struct. Civ. Eng., 2022, 16(12): 1501-1514.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-022-0893-2
https://academic.hep.com.cn/fsce/CN/Y2022/V16/I12/1501

Fig.1

Tab.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

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Fig.10

test No.	$D ¯ (m 2 / s)$	Q (m)	numerical results L (m)
T1	8.66e–5	0.038	0.039
T2	5.97e–5	0.032	0.031
T3	1.82e–4	0.055	0.056
T4	8.63e–5	0.038	0.039
T5	8.68e–5	0.038	0.039

Tab.2

Fig.11

Tab.3

soil type	parameter	unit	benchmark value	disturbance value	range
clay	θ_s	−	0.5	0.42, 0.46, 0.54, 0.58	0.4−0.6
	k_s	m/s	3e−9	2e−10, 8e−10, 1e−8, 5e−8	1e−10−1e−7
	ψ₀	kPa	1000	158, 398, 2512, 6310	100−10000
	ψ_b	kPa	316	126, 200, 501, 794	100−1000
	$n ¯$	−	1.80	1.24, 1.52, 2.08, 2.36	1.1−2.5
silt	θ_s	−	0.45	0.37, 0.41, 0.49, 0.53	0.35−0.55
	k_s	m/s	3e−7	2e−8, 8e−8, 1e−6, 5e−6	1e−8−1e−5
	ψ₀	kPa	100	16, 40, 251, 631	10−1000
	ψ_b	kPa	32	13, 20, 50, 79	10−100
	$n ¯$	−	3.00	2.20, 2.60, 3.40, 3.80	2−4
sand	θ_s	−	0.4	0.32, 0.36, 0.44, 0.48	0.3−0.5
	k_s	m/s	3e−5	2e−6, 8e−6, 1e−4, 5e−4	1e−6−1e−3
	ψ₀	kPa	6	3, 4, 10, 16	1−20
	ψ_b	kPa	4.5	2.4, 3.2, 6.2, 8.5	2−10
	$n ¯$	−	6.25	4.45, 5.35, 7.15, 8.05	4−8.5

Tab.4

Fig.12

Fig.13

Fig.14

Fig.15

data type	saturated water content θ_s	saturated hydraulic conductivity k_s	initial condition ψ₀	air-entry value ψ_b	hydraulic conductivity decline rate $n ¯$	rainfall intensity v
geological prospecting value	0.43	4.0e−6 m/s	6 m	50 kPa	2.30	38 mm/h
adjusted value	0.47	1.6e−5 m/s	9 m	79 kPa	2.70	43 mm/h

Tab.5

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Fig.17

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