Laboratory study and predictive modeling for thaw subsidence in deep permafrost

doi:10.3724/SP.J.1226.2021.20087

Abstract

Abstract:

Oil wells on the North Slope of Alaska pass through deep deposits of permafrost. The heat transferred during their operation causes localized thawing, resulting in ground subsidence adjacent to the well casings. This subsidence has a damaging effect, causing the casings to compress, deform, and potentially fail. This paper presents the results of a laboratory study of the thaw consolidation strain of deep permafrost and its predictive modeling. Tests were performed to determine strains due to thaw and post-thaw loading, as well as soil index properties. Results, together with data from an earlier testing program, were used to produce empirical models for predicting strains and ground subsidence. Four distinct strain cases were analyzed with three models by multiple regression analyses, and the best-fitting model was selected for each case. Models were further compared in a ground subsidence prediction using a shared subsurface profile. Laboratory results indicate that strains due to thaw and post-thaw testing in deep core permafrost are insensitive to depth and are more strongly influenced by stress redistributions and the presence of ice lenses and inclusions. Modeling results show that the most statistically valid and useful models were those constructed using moisture content, porosity, and degree of saturation. The applicability of these models was validated by comparison with results from Finite Element modeling.

Key words: deep permafrost, thaw consolidation strain, predictive models, multiple regression analysis

ZhaoHui Joey Yang,Gabriel T. Pierce. Laboratory study and predictive modeling for thaw subsidence in deep permafrost[J].Sciences in Cold and Arid Regions, 2021, 13(2): 95-106.

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Table 4

Selected best regression model for each case"

Case	Best model	Regression equation	Correlation coefficient, R
1	1	ε_T $= - 113 + 458 S - 71.7 S 2 + 770 n ω + 69.0 n S - 612 ω n$	0.82
2	1	ε_TC $= - 158 + 596 S - 102 S 2 + 946 n ω + 94.3 n S - 758 ω n$	0.90
3	2	ε_T $= - 83.6 + 182 S - 31.0 S 2 + 186 n 3 + 53.8 n S - 159 ω n$	0.84
4	2	ε_TC $= - 61.1 + 163 S - 7.58 S 2 + 294 n 3 + 39.0 n S - 203 ω n$	0.84

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References 0

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Sample number	Depth (m)	USCS class	Moisture content, ω	Salinity (ppt)	Specific gravity, G_s	Atterberg limits			Dry density, ρ_d (kg/m³)
Sample number	Depth (m)	USCS class	Moisture content, ω	Salinity (ppt)	Specific gravity, G_s	LL	PL	PI	Dry density, ρ_d (kg/m³)
2M89	2.7	SM	163.0%	0.68	-	Non-plastic			369
2M118T	3.6	CL-ML	37.4%	1.04	-	18	13	5	1,465
2M229	6.9	SM	6.8%	19.60	-	Non-plastic			1,767
2M290	8.8	SM	17.3%	3.60	2.67	Non-plastic			1,452
2M636	19.4	SM	21.3%	9.40	-	Non-plastic			1,355
2M960	29.3	CL	10.6%	11.60	2.85	32	22	10	1,655
2M1110	33.8	CL	13.1%	21.00	-	36	20	16	1,686
2M1334	40.6	SC	19.0%	5.30	2.67	24	14	10	1,491
2M1856	56.5	CH	16.5%	58.90	2.82	55	27	28	1,567
2M2760	84.1	CL	21.3%	1.27	2.78	29	17	12	1,683
2M3108	94.7	CL	17.5%	26.70	-	38	21	17	1,698
2M3836	116.9	CL	14.6%	2.70	-	31	16	15	1,805
2M4634	141.2	CL	22.7%	0.28	-	35	18	17	1,481
2M5080	154.8	CH	22.8%	1.70	2.79	58	24	34	1,590

Borehole	Sample number	Soil class	100% σ_v (kPa)	Strain ε_T	Strain ε_TC	Degree of saturation S	Porosity, n	Moisture content
1H Perm2	23	SM	415.5	3.6%	3.9%	95.8%	0.515	37.3%
	30	SM	510.4	0.7%	0.7%	99.7%	0.407	25.2%
	83	SM	1,207	3.0%	3.1%	92.7%	0.341	17.7%
	86	SM	1,258	1.3%	1.3%	85.7%	0.367	18.3%
	111	Fine	1,670	2.2%	2.8%	89.5%	0.452	27.2%
	134	Fine	2,104	7.2%	8.3%	92.8%	0.409	23.6%
	167	Fine	2,774	4.5%	6.2%	84.3%	0.377	18.6%
2M Perm1	26	SM	346.5	8.5%	9.6%	72.2%	0.487	25.2%
	55	Fine	778.7	1.8%	2.1%	89.1%	0.404	22.2%
	57	Fine	1,601	4.0%	4.3%	91.4%	0.437	26.1%
	116	Fine	2,023	1.6%	3.6%	99.3%	0.388	23.1%
	153	Fine	2,888	2.1%	4.5%	92.5%	0.421	24.7%
	2M229	SM	127	7.1%	7.5%	34.3%	0.350	6.8%
	2M290	SM	162	11.7%	12.3%	53.9%	0.466	17.3%
	2M636	SM	356	17.4%	18.1%	57.5%	0.502	21.3%
	2M960	CL	540	5.3%	6.4%	44.9%	0.392	10.6%
	2M1110	CL	626	2.4%	5.1%	58.2%	0.380	13.1%
	2M1334	SC	754	5.9%	7.8%	62.8%	0.452	19.0%
	2M1856	CH	1,057	3.5%	7.6%	61.0%	0.424	16.5%
	2M2760	CL	1,592	4.5%	8.7%	94.1%	0.381	21.3%
	2M3108	CL	1,801	3.8%	8.5%	79.2%	0.376	17.5%
	2M3836	CL	2,245	3.6%	6.6%	78.5%	0.336	14.6%
	2M4634	CL	2,741	9.8%	17.5%	71.2%	0.465	22.7%
	2M5080	CH	3,023	3.7%	10.2%	87.0%	0.416	22.8%
2A Perm1	27	Fine	284.7	1.2%	1.9%	81.6%	0.509	31.2%
	52	Fine	711.8	1.5%	1.9%	246.0%	0.199	22.5%
	90	SM	1,331	2.4%	2.7%	78.9%	0.490	27.9%
	115	Fine	1,785	3.3%	5.0%	96.3%	0.438	27.5%
	164	Fine	2,850	2.0%	3.3%	88.8%	0.446	26.3%
	184	SM	3,020	2.0%	2.4%	102.0%	0.490	27.1%
2X Perm1	26	SM	389.6	6.6%	14.4%	63.9%	0.485	22.1%
	59	Fine	858.5	1.3%	1.5%	91.3%	0.424	24.7%
	137	Fine	2,010	2.6%	3.9%	59.7%	0.369	12.9%
	205	SM	3,374	2.4%	3.2%	89.5%	0.450	27.0%
1Y Perm1	30	Fine	429.8	3.6%	5.3%	94.2%	0.434	26.5%

Case	Model	Sample number	R²	R²_a	S_e	F-Test	P-Value
1-ε_T at 20% σ_v	1	19	0.669	0.542	1.30%	5.26	0.0074
	2	19	0.608	0.457	1.41%	4.03	0.0198
	3	19	0.639	0.501	1.36%	4.61	0.0122
2-ε_TC at 20% σ_v	1	20	0.815	0.748	1.11%	12.3	0.0001
	2	20	0.698	0.590	1.41%	6.48	0.0026
	3	20	0.772	0.691	1.23%	9.48	0.0004
3-ε_T at 100% σ_v	1	27	0.628	0.540	2.52%	7.10	0.0005
	2	27	0.711	0.642	2.23%	10.3	0.0000
	3	27	0.668	0.589	2.39%	8.45	0.0002
4-ε_TC at 100% σ_v	1	27	0.566	0.462	3.02%	5.47	0.0022
	2	27	0.712	0.643	2.46%	10.4	0.0000
	3	27	0.682	0.606	2.59%	9.01	0.0001

method Prediction	Predicted subsidence at ground surface (m)
method Prediction	Case 1: thaw strain at 20% σ_v	Case 2: total strain at 20% σ_v	Case 3: thaw strain at 100% σ_v	Case 4: total strain at 100% σ_v
Model 1	0.53	1.67	1.32	3.44
Model 2	2.76	4.24	4.51	4.55
Model 3	4.93	8.77	7.11	9.21