Infiltration Grouting Mechanism in Porous Media Based on Fractal Theory

doi:10.11988/ckyyb.20230536

Abstract

Abstract:

To investigate the infiltration grouting mechanism of Bingham fluid in porous media, we derived formulas for calculating the apparent velocity of infiltration diffusion and the spherical infiltration grouting diffusion distance of Bingham fluid in porous media based on the fractal theory, the capillary model, and the rheological equation of Bingham fluid. We compared and validated the theoretical formulas against existing models and laboratory grouting tests. The results indicate that the diffusion radius of the grout calculated using the fractal theory-based formulas aligns more closely with experimental data compared to conventional Bingham fluid infiltration grouting formulas. These findings offer valuable theoretical support for practical grouting applications in porous media strata.

Key words: porous media, Bingham fluid, fractal theory, infiltration grouting, apparent velocity, diffusion distance

CLC Number:

TU451

HOU Xiao-ping, MO Hao, ZHAO Wei-quan, HUANG Yong. Infiltration Grouting Mechanism in Porous Media Based on Fractal Theory[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(9): 106-113.

Figures/Tables 7

Fig.1 Spherical infiltration diffusion model of Bingham fluid in porous media

Fig.2 Fractal capillary bundle model of porous media

Fig.3 Diagram of the penetrometer

Fig.4 Comparison of velocity vs. pressure drop of Bingham fluid between the present model equation (41) with different ratios of λmin/λmax in porous media and equation (49) (k=7.61×10-9 m2, φ=0.404, μp=0.01 Pa·s, τ0=2 Pa)

Table 1 Parameters of grouting tests for different sand layers

编号	m	流变方程	ϕ	K/ (cm·s^-1)	Δp/ MPa
1	1.2	$τ = 0.1922 + 0.0118 γ$	0.325	0.008 4	0.20
2	1.6	$τ = 0.1480 + 0.0087 γ$	0.402	0.01	0.32
3	2.0	$τ = 0.1448 + 0.0081 γ$	0.369	0.108	0.16
4	1.0	$τ = 0.3219 + 0.0166 γ$	0.358	0.123	0.28
5	1.4	$τ = 0.1574 + 0.0097 γ$	0.331	0.267	0.12
6	1.8	$τ = 0.1455 + 0.0083 γ$	0.374	0.754	0.24

Table 1 Parameters of grouting tests for different sand layers

编号	m	流变方程	ϕ	K/ (cm·s^-1)	Δp/ MPa
1	1.2	$τ = 0.1922 + 0.0118 γ$	0.325	0.008 4	0.20
2	1.6	$τ = 0.1480 + 0.0087 γ$	0.402	0.01	0.32
3	2.0	$τ = 0.1448 + 0.0081 γ$	0.369	0.108	0.16
4	1.0	$τ = 0.3219 + 0.0166 γ$	0.358	0.123	0.28
5	1.4	$τ = 0.1574 + 0.0097 γ$	0.331	0.267	0.12
6	1.8	$τ = 0.1455 + 0.0083 γ$	0.374	0.754	0.24

Table 2 Comparison of experimental values of diffusion radius with theoretical values for different sand layers

编号	实测值/cm	考虑扩散路径法^[11]/cm	考虑扩散路径法的误差^[11]/%	本文方法/cm	本文方法的误差/%
1	19	3.35	-82.37	14.20	-25.26
2	24	4.83	-79.88	18.09	-24.63
3	39	11.10	-71.54	33.14	-15.03
4	38	10.68	-71.89	33.14	-12.79
5	41	14.64	-64.29	39.68	-3.22
6	73	32.14	-55.97	71.33	-2.29

Fig.5 Comparison of relative errors for different sand layers

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[9]	LEI Jin-sheng, LIU Fei, PENG Gang, WANG Qian-feng, XIA Lei. Diffusion Range of Grout in Consideration of Dynamic Change and Correlation of Parameters [J]. Journal of Changjiang River Scientific Research Institute, 2016, 33(2): 57-61.
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[11]	QIN Peng, ZHANG Zhe-Yu, QIN Zhi-Hai, WANG Wei-Han. IVDF-ANN Prediction Model for Monitoring Data of Landslide Deformation [J]. Journal of Changjiang River Scientific Research Institute, 2012, 29(3): 29-34.
[12]	ZHANG Jia-fa ，JIAO Jiu-jiu. Influence of Grain Shape on Characteristics of Pores and Seepage in Porous Media [J]. Journal of Changjiang River Scientific Research Institute, 2011, 28(3): 39-44.