Prediction of yield shear strength of saturated sandy soils using artificial neural networks

Figures & data

Figure 1. Undrained behavior of sandy soil [1].

Figure 2. Triaxial Apparatus.

Table 1. Experimental database of the used sandy soils [1].

Sand No.		D50	FC	Void ratio
	Sand name	(mm)	(%)	e max	e min	References
1	Dune sand (DS)	0.21	3	0.91 (A)	0.54 (A)	Konrad 1990 [5]
2	Well-rounded silica sand (WA)	0.175	1	1.06 (A)	0.67 (A)	Konrad 1990 [5]
3	Fraser River Delta sand (FRD)	0.25	3–15	1.00 (A)	0.60 (A)	Chillarige et al. 1997 [6]
4	Duncan Dam sand (DD)	0.2	6.5	1.15 (-)	0.76 (-)	Pillai and Stewart 1994 [7]
5	Hostun RF sand (HRF)	0.38	0	1 (-)	0.656 (-)	Canou et al. 1994 [8]
6	Garnet tailings (GT)	0.17	20	1.52 (-)	0.53 (H)	Highter and Tobin 1980; Highter and Vallee 1980 [9,10]
7	Zinc tailings (ZT)	0.2	17	1.43 (-)	0.49 (H)	Highter and Tobin 1980; Highter and Vallee 1980 [9,10]
8	Natural silt (NS)	0.013	98	1.526 (-)	0.434 (-)	Dyvik and Hoeg 1999 [11]
9	Fine-coarse sand (FCS)	0.33	1	0.796 (-)	0.404 (-)	Dierichs and Forster 1985
10.1	Ottawa banding sand (OBS)^a	0.19	2	0.82 (-)	0.51 (-)	Dennis 1988 [12]
10.2	Ottawa banding sand (OBS)^b	0.19	2	0.82 (-)	0.51 (-)	Dennis 1988 [12]
10.3	Ottawa banding sand (OBS)^C	0.19	2	0.82 (-)	0.51 (-)	Dennis 1988 [12]
10.4	Ottawa banding sand (OBS)^d	0.19	2	0.82 (-)	0.51 (-)	Dennis 1988 [12]
11	Nevada fine sand (NFS)	0.12	—	0.87 (-)	0.57 (-)	Arulanandan et al. 1993 [13]
12.1	Nerlerk 0–2% (N2)	0.23–0.28	0–2	0.94 (C)	0.62 (C)	Sladen et aI. 1985 [14]
12.2	Nerlerk 12% (NI2)	0.28	12	0.96 (B)	0.43 (C)	Sladen et aI. 1985 [14]
13	Leighton Buzzard sand (LBS)	0.86	0	0.75 (C)	0.58 (C)	Sladen et aI. 1985 [14]
14	Syncrude tailings sand (STS)	0.17	10	0.93 (A)	0.55 (A)	Sladen and Handford 1987 [15]
15	Tottori sand (TS)	0.28	0	1.008 (D)	0.638 (D)	Takeshita et al. 1995 [16]
16	Monterey #9 sand (M9S)	0.35	0	0.86 (E)	0.53 (I)	Riemer et al. 1990; Riemer and Seed
						1992, 1997 [17]
17	Sydney sand (SS)	0.3	—	0.855 (-)	0.565 (-)	Chu 1995 [18]
18	Arabian Gulf sand (AGS)	—	40	—	—	Hanzawa 1980 [19]
19	Hostun RF sand (HRFS)	0.32	0	1 (-)	0.655 (-)	Konrad 1993 [20]
20	Tilt sand (TillS)	0.11	32	0.835 (-)	0.3625 (-)	Konrad 1993 [20]
21	Massey Tunnel sand (MTS)	0.25	3	1.102 (F)	0.712 (F)	Konrad and Pouliot 1997 [21]
22	Quebec sand (QS)	0.5	0	0.79 (B)	0.54 (F)	Konrad 1998 [22]
23	Erksak 330/0.7 (E330)	0.33	0.7	0.753 (-)	0.469 (-)	Been et aI. 1991 [23]
24	Ottawa sand (C109)	0.34	0	0.82 (A)	0.5 (A)	Sasitharan et al. 1993, 1994
25	Sand F	0.205	0	1.88 (G)	1.23 (G)	Castro and Poulos 1977; Castro 1969
26	Sand B	0.16	0	0.84 (G)	0.5 (G)	Castro and Poulos 1977; Castro 1969
27	Sand C	0.27	1	0.99 (G)	0.66 (G)	Castro and Poulos 1977; Castro 1969
28	Sand H	0.66	13	0.73 (G)	0.36 (G)	Castro and Poulos 1977; Castro 1969
29	Sand A	0.2	2	1.88 (G)	1.23 (G)	Castro 1969
30	Alcan tailings (AT)	0.002	99	—	—	Poulos et al. 1985b
31	Mai-Liao sand (MLS)	0.105	15	1.06 (-)	0.59 (-)	Huang et al. 1999
32	Star Morning tailings (SMT)	0.062	51	—	—	Bryant et aI. 1983 [24]
33	Bunker Hill tailings (BHT)	0.0097	87	—	—	Bryant et aI. 1983 [24]
34	Coeur Mine tailings (CMT)	0.06	54	—	—	Bryant et aI. 1983 [24]
35	Galena tailings (GT)	0.086	40	—	—	Bryant et aI. 1983 [24]
36	Lucky Friday tailings (LFT)	0.065	53	—	—	Bryant et aI. 1983 [24]
37	Mission tailings (MT)	0.04	60	—	—	Bryant et aI. 1983 [24]
38	Morenci tailings (MoT)	0.086	47	—	—	Bryant et aI. 1983 [24]
39	Climax tailings (CT)	0.026	67	—	—	Bryant et aI. 1983 [24]
40	Lornex Mine tailings (LMT)	0.256	7	—	—	Bryant et aI. 1983 [24]
41	Ottawa sand F125 (FI25)	0.1	12	—	—	Vasquez-Herrera and Dobry 1989
42	Sand A (SA)	0.15	13	—	—	Baziar and Dobry 1995 [25]
43	San Fernando SF7 sand (SF7)	0.075	50	0.72 (-)	0.34 (-)	Baziar and Dobry 1995 [25]
44	Toyoura sand (ToS)	0.17	0	0.977 (D)	0.597 (D)	Ishihara 1993 [26]
45	Lagunillas sandy silt (LSS)	0.05	74	1.389 (D)	0.766 (D)	Ishihara 1993 [26]
46	Tia Juana silty sand (TJSS)	0.16	12	1.099 (D)	0.62 (D)	Ishihara 1993 [26]

Table 2. Example of available triaxial compression test database for the sands.^[4]

Pre-test data				initial conditions of void ratio	relative density	major principal effective stresses	minor principal effective stresses	deviator stress at yield
D50	FC				RD	σ’ 1c	σ’ 3c	qu(yield)
(mm)	(%)	emax	emin	ec	(%)	(kPa)	(kPa)	(kPa)
0.21	3	0.91	0.54	0.715	52.7	2800	2800	1000
0.21	3	0.91	0.54	0.67	64.9	2800	2800	1132
0.21	3	0.91	0.54	0.68	62.2	2800	2800	1194
0.21	3	0.91	0.54	0.63	75.7	2800	2800	1224
0.21	3	0.91	0.54	0.75	43.2	2800	2800	1082
0.21	3	0.91	0.54	0.74	45.9	450	450	240
0.175	1	1.06	0.67	0.95	28.2	300	300	158
0.175	1	1.06	0.67	0.98	20.5	500	500	284
0.175	1	1.06	0.67	0.96	25.6	300	300	178

Table 3. Variable used in GRNN building.

Character	Number/Type
training pattern Number	108
test pattern Number	28
production pattern Number	2
optimum neurons in the hidden layer	138
Activation function in the input layer	Linear
Distance metric function	Vanilla (Euclidean)
Training algorithm	Genetic, adaptive
Performance measure	coefficient of multiple determination (R^2)

Figure 3. Results of trained GRNN network for various set.

Table 4. GRNN model results.

	Training set	Testing set	Production set
coefficient of multiple determination (R^2)	0.9937	0.9080	0.7699
minimum absolute error (KPa)	0	0.001	11.103
maximum absolute error (KPa)	96.528	115.000	98.655

Table 5. Variables used in BPNN building.

Character	Number/Type
training pattern Number	93
test pattern Number	41
production pattern Number	7
optimum neurons in the hidden layer	14
Learning rate	0.1
momentum	0.1
Performance measure	coefficient of multiple determination (R^2)

Figure 4. Results of trained BPNN network for various set.

Table 6. BPNN model results.

	Training set	Testing set	Production set
coefficient of multiple determination (R^2)	0.9997	0.8972	0.9829
minimum absolute error (KPa)	0	0.03	10.26
maximum absolute error (KPa)	16.3	491	32.83

Figure 5. Performance of General regression neural network (GRRN) for trained set.

Figure 6. Performance of Backpropagation neural network (BPNN) for trained set.

Figure 7. Interface of yield shear strength prediction application.

Figure 8. Comparison between model predictions and actual results for production set.

Table 7. Input and output for the chosen production pattern presented to the application.

No.	D50	FC	emax	emin	ec	RD	σ’ 1c	σ’ 3c	qu(yield) Actual	qu(yield) predicted network output
1	0.25	9	1	0.6	0.99	2.5	325	325	118	140.39
2	0.33	1	0.796	0.404	0.637	40.6	309	309	121	135.15
3	0.28	12	0.96	0.43	-	-	314	314	130	140.26
4	0.17	10	0.93	0.55	0.757	45.4	830	830	646	675.26
5	0.11	32	0.835	0.3625	0.6	49.7	300	300	119	86.17
6	0.16	0	0.84	0.5	0.714	37.1	392	392	225	255.01
7	0.27	1	0.99	0.66	0.914	23	392	392	253	264.65

Figure 9. Printout file contains the prediction of (Su) and also all the input data.

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