Mathematical Problems in Engineering

Research Article

An Improved Prediction Method of Soil-Water Characteristic Curve by Geometrical Derivation and Empirical Equation

Table 1

The parameters of 45 SWCC datasets fitting to Gardner equation.


Type	Data resource		Gardner equation			VG equation				FX equation
Type	Data resource

Sand	[38]	0.2106	0.0339	7.50	3.14	0.0360	4.51	100.56	0.01	0.0347	45.52	5.09	12.82	0.40	0.0349
	[38]	0.4246	0.0153	1.11	6.79	0.0142	1.00	8.18	0.59	0.0110	1.21	1.10	32.79	0.80	0.0135
	[26]	0.3884	0.0735	22.14	4.12	0.1044	58.69	3.37	21.24	0.1043	30.72	18.64	5.12	0.95	0.0941
	[39]	0.3464	0.0655	2.86	3.02	0.0559	1.64	196.12	0.01	0.0607	6.62 10⁷	1.92	5.48	0.65	0.0607
	[40]	0.3263	0.0802	23.71	4.47	0.0678	20.26	5.20	0.56	0.0340	77.34	18.96	5.91	0.74	0.0607
	[40]	0.2656	0.0862	1.71	4.35	0.0568	1.23	6.50	0.26	0.0656	6.67 10¹⁰	1.29	5.46	0.62	0.0695
	[41]	0.3418	0.0860	2.17	7.86	0.0741	1.68	282.43	0.01	0.0901	7.31 10¹⁰	1.80	20.32	0.44	0.0834
	[42]	0.2959	0.0854	0.51	0.43	0.0740	0.03	17.09	0.01	0.0756	3.02	0.07	32.04	0.12	0.0783	0.054082
	[20]	0.2499	0.1109	5.88	4.52	0.0829	3.76	35.21	0.04	0.0987	23.37	4.35	10.78	0.29	0.0975
	[20]	0.3448	0.1004	4.30	1.77	0.0842	1.71	26.44	0.03	0.0623	7.68 10¹⁰	2.16	4.25	0.46	0.0823
	[43]	0.4527	0.0263	2.51	1.14	0.0193	1.40	25.11	0.03	0.0123	7.27 10⁷	1.54	1.69	1.28	0.0193
	[44]	0.3523	0.0437	180.15	2.17	0.0406	76.67	115.40	0.01	0.0367	104.89	109.29	10.40	0.33	0.0403
	[44]	0.3598	0.0447	183.69	2.33	0.0377	104.53	3.99	0.30	0.0110	88.64	120.65	6.06	0.53	0.0311
	[45]	0.1838	0.0192	2.96	1.03	0.0146	0.86	69.99	0.01	0.0172	6.42	1.30	4.31	0.55	0.0170
	[45]	0.2444	0.0356	3.64	1.55	0.0283	1.48	37.79	0.02	0.0219	17.68	3.07	15.09	0.41	0.0286
	[34]	0.4028	0.0377	1769.98	0.91	0.0404	2.75 10⁴	0.84	9.86	0.0362	333.00	5152.19	0.90	4.27	0.0381
	[34]	0.4078	0.0391	1280.15	1.22	0.0694	1.32 10⁷	0.98	6488.41	0.0694	165.45	867.80	2.35	0.65	0.0593
	[7]	0.4226	0.0769	742.25	1.94	0.0754	541.70	2.21	0.64	0.0710	259.60	611.82	99.27	0.14	0.0744
	[7]	0.3841	0.0340	1993.11	0.64	0.0928	2.32 10⁸	0.60	1034.88	0.0461	5.27 10⁵	250.67	0.86	0.97	0.0576
	[38]	0.3300	0.0156	3927.64	0.63	0.0382	9117.25	0.59	1.52	0.0196	1415.78	1329.20	0.57	1.10	0.0245
	[38]	0.3041	0.0017	6104.89	0.50	0.0127	101.35	0.96	0.07	0.0076	47.28	1.13 10⁴	7.62	0.13	0.0073
	[46]	0.4804	0.1186	6.08	2.82	0.1218	7.78	2.50	1.61	0.1198	0.74	4.82	7.90	0.39	0.1201

Silt	[47]	0.4556	0.0341	514.29	0.65	0.0788	53.34	1.51	0.38	0.0511	8532.04	36.42	2.02	0.50	0.0547	0.062445
	[47]	0.4417	0.0141	877.77	0.57	0.0207	33.60	1.58	0.20	0.0179	1823.62	33.72	1.79	0.45	0.0176
	[48]	0.3794	0.0361	70.11	0.91	0.0397	61.19	0.95	0.94	0.0387	213.49	29.23	1.01	1.18	0.0382
	[44]	0.3220	0.0325	513.71	0.75	0.0397	847.53	0.72	1.35	0.0252	14.16	317.82	1.99	0.39	0.0325
	[45]s	0.3456	0.0456	63.62	1.27	0.0165	21.19	2.05	0.28	0.0681	191.38	28.54	1.64	0.92	0.0434
	[45]s	0.4371	0.0923	23.36	1.22	0.0964	44.96	1.10	1.70	0.0949	1.64	28.09	62.51	0.16	0.0945
	[49]	0.3991	0.1160	21.97	3.11	0.1992	12.96	161.64	0.01	0.1136	2146.41	14.03	8.07	0.23	0.1429
	[50]	0.4368	0.1273	25.97	1.16	0.1339	5.62	1.83	0.15	0.1336	1.81 10⁸	7.45	1.53	0.35	0.1316
	[42]	0.4956	0.0498	302.63	0.96	0.0532	281.19	0.99	0.97	0.0665	37.96	183.24	1.25	0.85	0.0565
	[42]	0.4364	0.0662	945.31	0.52	0.0445	2741.66	0.52	2.22	0.0796	4.08	641.51	1.73	0.97	0.0634
	[51]	0.6945	0.0102	2477.66	0.62	0.0039	4397.95	0.59	1.32	0.0080	33.37	3141.60	1.50	0.61	0.0074

Clay	[7]	0.6018	0.0343	2363.76	0.34	0.0373	4.80 10⁵	0.39	3.71	0.0338	1.72 10⁵	122.36	1.05	0.48	0.0351	0.079245
	[7]	0.4482	0.0737	7430.10	0.67	0.0647	2858.87	0.77	0.62	0.0835	235.38	3.83 10⁵	2.02	−2.62	0.0740
	[14]	0.5204	0.0108	2961.29	0.88	0.0132	3007.03	0.89	1.02	0.0143	297.14	2599.03	1.12	1.07	0.0128
	[43]	0.4913	0.2434	66.27	0.62	0.2762	2.14 10⁶	0.53	210.14	0.2926	2.68	1017.68	135.80	−0.03	0.2707
	[44]	0.4405	0.1567	256.59	1.01	0.0854	34.76	69.13	0.00	0.1480	4702.93	53.19	2.83	0.30	0.1300
	[44]	0.5530	0.1594	432.81	0.72	0.1179	153.42	0.83	0.50	0.1725	16.30	226.37	17.84	0.05	0.1499
	[52]	0.4600	0.1647	11.42	1.56	0.0989	4.62	2.30	0.25	0.1209	96.73	5.19	1.95	0.56	0.1282
	[53]	0.3781	0.0915	2916.26	1.31	0.0432	981.45	1.18	0.48	0.0616	5925.74	1024.26	2.71	0.40	0.0654
	[53]	0.4888	0.1196	2569.65	1.32	0.0841	758.27	3.39	0.17	0.0728	3787.67	866.21	3.43	0.33	0.0922
	[54]	0.9031	0.0620	3535.16	0.73	0.0537	1463.29	0.87	0.61	0.0613	7600.92	492.90	1.10	0.65	0.0590
	[54]	0.6467	0.0294	8007.59	0.74	0.0288	4786.72	0.81	0.76	0.0249	1.91 10⁴	1268.51	0.94	0.76	0.0277
	[55]	0.4702	0.0159	1757.23	0.77	0.0171	1909.35	0.76	1.05	0.0161	60.42	1264.73	1.66	0.57	0.0164