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Fuzzy prediction of soil strength based on water content and composition
Journal of Terramechanics 37 (2000) 57±63
www.elsevier.com/locate/jterra
Fuzzy prediction of soil strength based on water content and composition Ji Changying*, Pan Junzheng Agricultural Engineering College, NAU, Puzhen, Nanjing, Jiangsu 210032, People's Rebublic of China Received 18 March 1998; received in revised form 13 July 1998; accepted 19 March 1999
Abstract Sixteen samples representing various paddy ®eld soils of the main rice-planting regions in South China, with their characteristic values, are listed, by which means the soil strength of any other paddy ®eld soil can be fuzzily predicted when its water content, sand content and clay content are given. Illustrative examples show that the result of prediction seems to be acceptable in engineering practice. # 2000 ISTVS. All rights reserved. Keywords: Fuzzy prediction; Soil strength; Paddy ®eld soils
1. Introduction To estimate soil strength, in order to make a decision as to whether a wetland vehicle may operate on a paddy ®eld, the idea of fuzzy prediction is introduced, based on water content and mechanical composition of the paddy ®eld soil, which are readily obtainable parameters. More than 100 paddy ®eld soil samples in South China were tested between 1974 and 1983 by the authors and their colleagues for soil strength, water content and composition. Sixteen of these samples, representing various paddy ®eld soils of the main rice-planting regions are listed below with their characteristic properties. The means by which the soil strength of any other paddy ®eld soil can be predicted when its water content, sand content and clay content are given. Due to its high water content, a paddy soil can be considered to be consisting of incompressible water and incompressible particles, so the eect of bulk density on soil strength is negligible. * Corresponding author. Tel.:+86-25-885-1663; fax:+86-25-885-2785. 0022-4898/00/$20.00 # 2000 ISTVS. All rights reserved. PII: S0022-4898(99)00010-5
58
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
2. Fuzzy prediction of soil strength Sixteen samples with their characteristic properties are listed in Table 1. The cohesion and the coecient of internal friction were measured with a shear ring and the measurement was made singly. According to Dubois and Prade [1], and Pal and Majumder [2] when a universe X is a ®nite set {x1 ; x2 . . . xn }, a fuzzy subset, generally called a fuzzy set, on X is expressed as A
n X A xi =xi il
Where xi is an element of fuzzy set A, and A xi is the membership grade of xi on A. An m-tuple A1 ; A2 . . . Am of fuzzy sets Aj 8j; Aj 6 1 and Aj 6 X such that 8xX;
m X
Aj x 1
jl
is called a fuzzy partition of X. Let Ai, Bi, Ci, Pi, and Qi be the characteristic values of water content, sand content, clay content, cohesion and coecient of internal friction of the ith sample, respectively. Each of them is fuzzily partitioned. It is assumed that the membership functions are all triangular as shown in Fig. 1, the list of Table 1 will be in the Table 1 Paddy ®eld soil samples and their characteristic values No.
Sample sources
Water content (%)
Sand content (%)
Clay content (%)
Cohesion (kPa)
Coecient/angle ( ) of internal friction
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Chengdu, Sichuan Guanghan, Sichuan Jianyang, Sichuan Baxian, Sichuan Yueyang, Hunan Wuhan, Hubei Wuhu, Anhui Chaoxian, Anhui Wujin, Jiangsu Guanyun, Jiangsu Songjiang, Shanghai Chongming, Shanghai Haikou, Guangdong Kaili, Guizhou Guiyang, Guizhou Kuming, Yunnan
57.8 32.2 47.5 58.5 52.3 61.1 58.1 35.2 34.7 58.2 54.0 47.6 35.0 46.2 67.8 61.2
19.9 3.3 10.4 15.9 7.1 4.7 4.9 1.1 3.0 1.0 6.5 0.1 46.0 12.8 9.4 24.9
28.8 34.4 40.6 35.7 32.1 59.3 35.1 60.1 50.3 68.3 39.1 51.2 30.0 47.6 53.8 45.5
1.40 3.07 3.00 4.90 4.71 4.61 4.54 6.76 7.55 8.63 4.47 5.16 3.04 3.60 3.73 10.99
0.598/30.9 0.597/30.8 0.500/26.6 0.277/15.5 0.329/18.2 0.308/17.1 0.355/19.5 0.278/15./6 0.049/2.8 0.268/15.0 0.259/14.5 0.270/15.1 0.447/24.1 0.449/24.2 0.260/14.6 0.003/0.2
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
59
form of Table 2. In Fig. 1, the 1 and 0 parallel to the top and bottom line indicate membership grades. To predict cohesion P and coecient of internal friction Q of any paddy ®eld soil with known water content A, sand content B and clay content C, ®rst ®nd 1 ij sup Aj x ^ Aij x ; x2X
ij sup Bj y ^ Bij y ;
2
ij sup Cj z ^ Cij z ;
3
y2Y
and z2Z
i 1; 2 . . . n j 1; 2 . . . m: Experience shows that cohesion varies mostly with clay content, and the coecient of internal friction varies with sand content, while both vary with water content. Hence
Fig. 1. Trangular membership functions.
60
i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Aj x 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0
0 0 0.50 0 0 0 0 0 0 0 0 0.48 0 0.76 0 0
0 0 0.50 0 0.54 0 0 0 0 0 0.20 0.52 0 0.24 0 0
Bj y 0.44 0 0 0.30 0.46 0 0.19 0 0 0.36 0.80 0 0 0 0 0
0.56 0 0 0.70 0 1 0.81 0 0 0.64 0 0 0 0 1 1
0 0.34 0 0 0 0.06 0.02 0.78 0.40 0.80 0 0.98 0 0 0 0
0 0.66 0 0 0.58 0.94 0.98 0.22 0.60 0.20 0.70 0.02 0 0 0.12 0
0 0 0.92 0 0.42 0 0 0 0 0 0.30 0 0 0.44 0.88 0
Cj z 0.02 0 0.08 0.82 0 0 0 0 0 0 0 0 0 0.56 0 0
0.98 0 0 0.18 0 0 0 0 0 0 0 0 1 0 0 1
1 0.56 0 0.43 0.79 0 0.49 0 0 0 0.09 0 1 0 0 0
0 0.44 0.94 0.57 0.21 0 0.51 0 0 0 0.91 0 0 0.24 0 0.45
0 0 0.06 0 0 0.07 0 0 0.97 0 0 0.88 0 0.76 0.62 0.55
Pj u 0 0 0 0 0 0.93 0 1 0.03 1 0 0.12 0 0 0.38 0
1 0.93 1 0 0 0 0 0 0 0 0 0 0.96 0.40 0.27 0
0 0.07 0 0.10 0.29 0.39 0.46 0 0 0 0.53 0 0.04 0.60 0.73 0
0 0 0 0.90 0.71 0.61 0.54 0 0 0 0.47 0.16 0 0 0 0
Qj v 0 0 0 0 0 0 0 1 1 1 0 0.84 0 0 0 1
0 0 0 0.23 0 0 0 0.22 1 0.32 0.41 0.30 0 0 0.40 1
0 0 0 0.77 0.71 0.92 0.45 0.78 0 0.68 0.59 0.70 0 0 0.60 0
0 0 0 0 0.29 0.08 0.55 0 0 0 0 0 0.53 0.51 0 0
1 1 1 0 0 0 0 0 0 0 0 0 0.47 0.49 0 0
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
Table 2 Membership values of sample characteristics
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
P
n [
61
m ij ^ ij Pi p1 ; p2 . . . pm
4
jl
il
and Q
n [ m ij ^ ij Qi q1 ; q2 . . . qm :
5
jl
il
The predicted values of cohesion and coecient of internal friction can be calculated as follows. P Pj pj ; 6 u P pj P Qj qj ; 7 v P qj j 1; 2 . . . m:
3. Illustrative examples The soil strengths of four samples, which are dierent from the samples in Table 1, shown in Table 3 are predicted based on their respective water contents, sand contents and clay contents. The predictions are later compared with the corresponding measurements. Table 3 Characteristic values of samples for prediction Sample no.
Water content (%)
Sand content (%)
Clay content (%)
Cohesion (kPa)
Coecient of internal friction
I II III IV
62.8 76.4 37.7 57.6
0.1 9.0 27.2 16.4
51.2 29.9 24.8 51.8
4.74 5.48 3.83 4.90
0.212 0.261 0.396 0.242
For Sample I (see Table 4), based on A, B and C, compared with Ai, Bi, and Ci, ij , ij , and ij are found. Then P and Q, and u and v, can be calculated accordingly. P
n [ il
m
ij ^ ij Pi p1 ; p2 . . . p4 0:17; 0:45; 0:07; 0:55; jl
62
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
Table 4 Calculated results for sample 1 i
ij
ij
ij
ij ^ ij
ij ^ ij
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.56 0 0 0.70 0 1 0.81 0 0 0.64 0 0 0 0 1 1
0 0.34 0 0 0.02 0.06 0.02 0.78 0.40 0.80 0.02 0.98 0 0 0.02 0
0 0 0.06 0 0 0.12 0 0.12 0.88 0.12 0 0.88 0 0.76 0.62 0.55
0 0 0 0 0 0.06 0.02 0 0 0.64 0 0 0 0 0.02 0
0 0 0 0 0 0.12 0 0 0 0.12 0 0 0 0 0.62 0.55
and
Qi
0, 0.39, 0.61, 0
0, 0.92, 0.08, 0 0, 0.45, 0.55, 0
0, 0, 0, 1
0.32, 0.68, 0, 0
0.27, 0.73, 0, 0 0, 0, 0, 1
0.40, 0.60, 0, 0
P Pj pj 4:81 u P pj
Q
n [ il
and
Pi
m
ij ^ ij Qi q1 ; q2 . . . q4 0:20; 0:44; 0:01; 0; jl
P Qj qj 0:271: v P qj
In a like manner, the predicted values of cohesion and coecient of internal friction for Samples II, III and IV are obtained. The predicted results are shown in Table 5. Table 5 Predicted and measured results Sample
I II III IV
Cohesion
Coecient of internal friction
Predicted
Measured
Predicted
Measured
4.81 3.86 3.04 4.88
4.74 5.48 3.83 4.90
0.271 0.280 0.447 0.329
0.212 0.261 0.396 0.242
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
63
4. Conclusion The fuzzy relations between soil strength and water content and composition of The fuzzy relations between 16 paddy ®eld soil samples are used to predict the soil strength of any sample with known water content, sand content and clay content. Four illustrating examples give the above results. The predicted results seem to be acceptable in engineering practice, though some predicted values are unexpected, among which the predicted value of cohesion for Sample II is most outstanding. However, it is believed that when more new data are added to the above list, the prediction will be improved gradually for most soil samples except very odd ones. References [1] Dubois D, Prade H. Fuzzy sets and systems. New York: Academic Press, 1980. pp. 9±35. [2] Pal SK, Kajum¯er DKD. Fuzzy mathematical approach to pattern recognition. New Delhi: Wiley Eastern Limited, 1988. pp. 38±69.
www.elsevier.com/locate/jterra
Fuzzy prediction of soil strength based on water content and composition Ji Changying*, Pan Junzheng Agricultural Engineering College, NAU, Puzhen, Nanjing, Jiangsu 210032, People's Rebublic of China Received 18 March 1998; received in revised form 13 July 1998; accepted 19 March 1999
Abstract Sixteen samples representing various paddy ®eld soils of the main rice-planting regions in South China, with their characteristic values, are listed, by which means the soil strength of any other paddy ®eld soil can be fuzzily predicted when its water content, sand content and clay content are given. Illustrative examples show that the result of prediction seems to be acceptable in engineering practice. # 2000 ISTVS. All rights reserved. Keywords: Fuzzy prediction; Soil strength; Paddy ®eld soils
1. Introduction To estimate soil strength, in order to make a decision as to whether a wetland vehicle may operate on a paddy ®eld, the idea of fuzzy prediction is introduced, based on water content and mechanical composition of the paddy ®eld soil, which are readily obtainable parameters. More than 100 paddy ®eld soil samples in South China were tested between 1974 and 1983 by the authors and their colleagues for soil strength, water content and composition. Sixteen of these samples, representing various paddy ®eld soils of the main rice-planting regions are listed below with their characteristic properties. The means by which the soil strength of any other paddy ®eld soil can be predicted when its water content, sand content and clay content are given. Due to its high water content, a paddy soil can be considered to be consisting of incompressible water and incompressible particles, so the eect of bulk density on soil strength is negligible. * Corresponding author. Tel.:+86-25-885-1663; fax:+86-25-885-2785. 0022-4898/00/$20.00 # 2000 ISTVS. All rights reserved. PII: S0022-4898(99)00010-5
58
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
2. Fuzzy prediction of soil strength Sixteen samples with their characteristic properties are listed in Table 1. The cohesion and the coecient of internal friction were measured with a shear ring and the measurement was made singly. According to Dubois and Prade [1], and Pal and Majumder [2] when a universe X is a ®nite set {x1 ; x2 . . . xn }, a fuzzy subset, generally called a fuzzy set, on X is expressed as A
n X A xi =xi il
Where xi is an element of fuzzy set A, and A xi is the membership grade of xi on A. An m-tuple A1 ; A2 . . . Am of fuzzy sets Aj 8j; Aj 6 1 and Aj 6 X such that 8xX;
m X
Aj x 1
jl
is called a fuzzy partition of X. Let Ai, Bi, Ci, Pi, and Qi be the characteristic values of water content, sand content, clay content, cohesion and coecient of internal friction of the ith sample, respectively. Each of them is fuzzily partitioned. It is assumed that the membership functions are all triangular as shown in Fig. 1, the list of Table 1 will be in the Table 1 Paddy ®eld soil samples and their characteristic values No.
Sample sources
Water content (%)
Sand content (%)
Clay content (%)
Cohesion (kPa)
Coecient/angle ( ) of internal friction
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Chengdu, Sichuan Guanghan, Sichuan Jianyang, Sichuan Baxian, Sichuan Yueyang, Hunan Wuhan, Hubei Wuhu, Anhui Chaoxian, Anhui Wujin, Jiangsu Guanyun, Jiangsu Songjiang, Shanghai Chongming, Shanghai Haikou, Guangdong Kaili, Guizhou Guiyang, Guizhou Kuming, Yunnan
57.8 32.2 47.5 58.5 52.3 61.1 58.1 35.2 34.7 58.2 54.0 47.6 35.0 46.2 67.8 61.2
19.9 3.3 10.4 15.9 7.1 4.7 4.9 1.1 3.0 1.0 6.5 0.1 46.0 12.8 9.4 24.9
28.8 34.4 40.6 35.7 32.1 59.3 35.1 60.1 50.3 68.3 39.1 51.2 30.0 47.6 53.8 45.5
1.40 3.07 3.00 4.90 4.71 4.61 4.54 6.76 7.55 8.63 4.47 5.16 3.04 3.60 3.73 10.99
0.598/30.9 0.597/30.8 0.500/26.6 0.277/15.5 0.329/18.2 0.308/17.1 0.355/19.5 0.278/15./6 0.049/2.8 0.268/15.0 0.259/14.5 0.270/15.1 0.447/24.1 0.449/24.2 0.260/14.6 0.003/0.2
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
59
form of Table 2. In Fig. 1, the 1 and 0 parallel to the top and bottom line indicate membership grades. To predict cohesion P and coecient of internal friction Q of any paddy ®eld soil with known water content A, sand content B and clay content C, ®rst ®nd 1 ij sup Aj x ^ Aij x ; x2X
ij sup Bj y ^ Bij y ;
2
ij sup Cj z ^ Cij z ;
3
y2Y
and z2Z
i 1; 2 . . . n j 1; 2 . . . m: Experience shows that cohesion varies mostly with clay content, and the coecient of internal friction varies with sand content, while both vary with water content. Hence
Fig. 1. Trangular membership functions.
60
i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Aj x 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0
0 0 0.50 0 0 0 0 0 0 0 0 0.48 0 0.76 0 0
0 0 0.50 0 0.54 0 0 0 0 0 0.20 0.52 0 0.24 0 0
Bj y 0.44 0 0 0.30 0.46 0 0.19 0 0 0.36 0.80 0 0 0 0 0
0.56 0 0 0.70 0 1 0.81 0 0 0.64 0 0 0 0 1 1
0 0.34 0 0 0 0.06 0.02 0.78 0.40 0.80 0 0.98 0 0 0 0
0 0.66 0 0 0.58 0.94 0.98 0.22 0.60 0.20 0.70 0.02 0 0 0.12 0
0 0 0.92 0 0.42 0 0 0 0 0 0.30 0 0 0.44 0.88 0
Cj z 0.02 0 0.08 0.82 0 0 0 0 0 0 0 0 0 0.56 0 0
0.98 0 0 0.18 0 0 0 0 0 0 0 0 1 0 0 1
1 0.56 0 0.43 0.79 0 0.49 0 0 0 0.09 0 1 0 0 0
0 0.44 0.94 0.57 0.21 0 0.51 0 0 0 0.91 0 0 0.24 0 0.45
0 0 0.06 0 0 0.07 0 0 0.97 0 0 0.88 0 0.76 0.62 0.55
Pj u 0 0 0 0 0 0.93 0 1 0.03 1 0 0.12 0 0 0.38 0
1 0.93 1 0 0 0 0 0 0 0 0 0 0.96 0.40 0.27 0
0 0.07 0 0.10 0.29 0.39 0.46 0 0 0 0.53 0 0.04 0.60 0.73 0
0 0 0 0.90 0.71 0.61 0.54 0 0 0 0.47 0.16 0 0 0 0
Qj v 0 0 0 0 0 0 0 1 1 1 0 0.84 0 0 0 1
0 0 0 0.23 0 0 0 0.22 1 0.32 0.41 0.30 0 0 0.40 1
0 0 0 0.77 0.71 0.92 0.45 0.78 0 0.68 0.59 0.70 0 0 0.60 0
0 0 0 0 0.29 0.08 0.55 0 0 0 0 0 0.53 0.51 0 0
1 1 1 0 0 0 0 0 0 0 0 0 0.47 0.49 0 0
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
Table 2 Membership values of sample characteristics
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
P
n [
61
m ij ^ ij Pi p1 ; p2 . . . pm
4
jl
il
and Q
n [ m ij ^ ij Qi q1 ; q2 . . . qm :
5
jl
il
The predicted values of cohesion and coecient of internal friction can be calculated as follows. P Pj pj ; 6 u P pj P Qj qj ; 7 v P qj j 1; 2 . . . m:
3. Illustrative examples The soil strengths of four samples, which are dierent from the samples in Table 1, shown in Table 3 are predicted based on their respective water contents, sand contents and clay contents. The predictions are later compared with the corresponding measurements. Table 3 Characteristic values of samples for prediction Sample no.
Water content (%)
Sand content (%)
Clay content (%)
Cohesion (kPa)
Coecient of internal friction
I II III IV
62.8 76.4 37.7 57.6
0.1 9.0 27.2 16.4
51.2 29.9 24.8 51.8
4.74 5.48 3.83 4.90
0.212 0.261 0.396 0.242
For Sample I (see Table 4), based on A, B and C, compared with Ai, Bi, and Ci, ij , ij , and ij are found. Then P and Q, and u and v, can be calculated accordingly. P
n [ il
m
ij ^ ij Pi p1 ; p2 . . . p4 0:17; 0:45; 0:07; 0:55; jl
62
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
Table 4 Calculated results for sample 1 i
ij
ij
ij
ij ^ ij
ij ^ ij
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.56 0 0 0.70 0 1 0.81 0 0 0.64 0 0 0 0 1 1
0 0.34 0 0 0.02 0.06 0.02 0.78 0.40 0.80 0.02 0.98 0 0 0.02 0
0 0 0.06 0 0 0.12 0 0.12 0.88 0.12 0 0.88 0 0.76 0.62 0.55
0 0 0 0 0 0.06 0.02 0 0 0.64 0 0 0 0 0.02 0
0 0 0 0 0 0.12 0 0 0 0.12 0 0 0 0 0.62 0.55
and
Qi
0, 0.39, 0.61, 0
0, 0.92, 0.08, 0 0, 0.45, 0.55, 0
0, 0, 0, 1
0.32, 0.68, 0, 0
0.27, 0.73, 0, 0 0, 0, 0, 1
0.40, 0.60, 0, 0
P Pj pj 4:81 u P pj
Q
n [ il
and
Pi
m
ij ^ ij Qi q1 ; q2 . . . q4 0:20; 0:44; 0:01; 0; jl
P Qj qj 0:271: v P qj
In a like manner, the predicted values of cohesion and coecient of internal friction for Samples II, III and IV are obtained. The predicted results are shown in Table 5. Table 5 Predicted and measured results Sample
I II III IV
Cohesion
Coecient of internal friction
Predicted
Measured
Predicted
Measured
4.81 3.86 3.04 4.88
4.74 5.48 3.83 4.90
0.271 0.280 0.447 0.329
0.212 0.261 0.396 0.242
J. Changying, P. Junzheng / Journal of Terramechanics 37 (2000) 57±63
63
4. Conclusion The fuzzy relations between soil strength and water content and composition of The fuzzy relations between 16 paddy ®eld soil samples are used to predict the soil strength of any sample with known water content, sand content and clay content. Four illustrating examples give the above results. The predicted results seem to be acceptable in engineering practice, though some predicted values are unexpected, among which the predicted value of cohesion for Sample II is most outstanding. However, it is believed that when more new data are added to the above list, the prediction will be improved gradually for most soil samples except very odd ones. References [1] Dubois D, Prade H. Fuzzy sets and systems. New York: Academic Press, 1980. pp. 9±35. [2] Pal SK, Kajum¯er DKD. Fuzzy mathematical approach to pattern recognition. New Delhi: Wiley Eastern Limited, 1988. pp. 38±69.