Artificial neural network for soil cohesion and soil internal friction angle prediction from soil physical properties data

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1 Interntionl Reserch Journl of Agriculturl Science nd Soil Science (ISSN: ) Vol. 4(5) pp , June, 204 DOI: Avilble online Copyright 204 Interntionl Reserch Journls Full Length Reserch Pper Artificil neurl network for soil cohesion nd soil internl friction ngle prediction from soil physicl properties dt Sd Abdulrhmn Al-Hmed, Mohmed Foud Whby * nd Abdulwhed Mohmed Aboukrim 2,3 Deprtment of Agriculturl Engineering, College of Food nd Agriculture Sciences, King Sud University, P.O. Box 2460, Riydh 45, Sudi Arbi 2 Agriculturl Engineering Reserch Institute, Agriculturl Reserch Center, Egypt 3 Community College, Huriml, Shqr University, P.O. Box 300, Huriml 962, Sudi Arbi *Corresponding uthor e-mil: whby@ksu.edu.s ABSTRACT An rtificil neurl network (ANN) model ws employed to predict the soil cohesion nd soil internl friction ngle. The soil smples were collected from different cultivted sites in seven regions in Sudi Arbi. Direct sher box method ws used to determine soil cohesion nd soil internl friction ngle. The input fctors to ANN model were soil dry density, soil moisture content nd soil texture index. The best 3-lyer ANN model produced correltion coefficients of nd between the observed nd predicted soil cohesion nd soil internl friction ngle, respectively during trining phse. Results of using testing dt showed tht the ANN model gve RMSE vlues of kp nd degree for soil cohesion nd soil internl friction ngle, respectively indicting tht ANN-bsed model hd good ccurcy in predicting soil cohesion nd soil internl friction ngle. Keywords: Artificil neurl network, soil cohesion, soil internl friction ngle, prediction INTRODUCTION Soil properties re key fctor in the functioning of soil (Khter et l, 2008). Soil mechnicl properties re ddressed by mny items, mong which the soil cohesion nd dhesion re relevnt for their mor contributors to drft force of tillge implement (Plsse et l, 985). However, the mount of energy consumed during tillge opertion depends on three prmeters including soil prmeters, tool prmeters nd operting prmeters (Zdeh, 2006). Sher strength is the internl resistnce of the soil to externl forces tht cuse two dcent res of soil to move reltive to ech other. It is generlly considered to be function of cohesion between soil prticles nd intergrnulr friction (Grf et l, 2009). The force cting on filure surfce in the soil body cn be determined by Mohr-Coulomb eqution s follows (Tong nd Moyd, 2006). τ = C + σ n tn φ () where τ is the tngentil stress, σ is n the norml stress, C is the cohesion of soil, which is the resistnce of soil prticles to displcement due to intermoleculr ttrction nd surfce tension of the held wter nd it depends upon size of clyey prticles, type of cly minerls, vlence bond between prticles, moisture content, nd proportion of the cly (Jin et l 200), nd φ is the internl frictionl ngle of soil, which depends upon soil dry density, soil prticle size distribution, shpe

2 86 Int. Res. J. Agric. Sci. Soil Sci. of prticles, soil surfce texture, nd soil moisture content (Jin et l, 200). The vlue of soil cohesion vries with soil moisture content, grin size of soil nd its compction (Abd El Mksoud, 2006). Lebert nd Horn (99) found tht in homogeneous, non-structured soils, such s snds nd silts with low cly content (5%, w/w), the sher prmeters were minly texture-dependent. Shinberg et l (994) mentioned tht the most commonly soil physicl properties ffected surfce soil sher strength ws prticle size distribution. Sok et l (200) reported tht soil strength depended on the interction of soil moisture content nd bulk density. Zhng et l (200) mesured the soil strength for the soils from sndy lom to clyey lom t soil surfce t different bulk density nd soil moisture content. The results indicted tht significnt effect of bulk density on soil strength. Bechmnn et l (2006) showed tht soil strength vried frequently due to chnges in soil moisture conditions. Murthy (2008) reported tht the vlues of soil cohesion nd soil internl friction ngle for ny soil depend upon severl fctors such s texturl properties, stress history of soil, initil stte, nd permebility chrcteristics of soil. Ddkhh et l (200) reported tht the soil friction ngle nd cohesion increse with incresing soil density. Mousvi et l (20) found tht s the soil grin size increses, the soil internl friction ngle increses nd its cohesion decreses. The direct sher test is commonly used for mesuring soil cohesion nd soil friction ngle of soils. Furthermore, lbortory or field test, s direct mesurement of soil cohesion nd soil friction ngle is not esy to pply; however, it is time-consuming nd expensive (Arvidsson nd Keller, 20; Zdeh nd Asdi, 202). Besides experimentl determintion of the soil cohesion nd soil friction ngle of soils is extensive, cumbersome nd costly (Mousvi et l, 20). An lterntive pproch to such test is the development empiricl mthemticl models for the prediction of the cohesion nd the ngle of internl friction of soil, in terms of number of ffecting prmeters. Accordingly, it hs been ttrctive for prcticl griculturl engineers to discover indirect nd ccurte techniques to predict the vlue of the cohesion nd the ngle of internl friction of soil. This might be ccomplished by some techniques such s experimentl reltions, sttisticl methods, etc. Recently, rtificil neurl networks (ANNs) hve been used in soil science nd griculture. However, ANNs provide method to chrcterize synthetic neurons to solve complex problems in the sme mnner s the humn brin does (Ayoubi et l, 20). A typicl structure of ANNs consists of number of processing elements, or nodes, tht re usully rrnged in lyers: n input lyer, n output lyer nd one or more hidden lyers. The reltive performnce of ANNs over trditionl sttisticl methods is reported in Zhng et l, (998). One of the most importnt dvntges of ANNs over sttisticl methods is tht they require no ssumptions bout the form of fitting function. Insted, the network is trined with experimentl dt to find the reltionship; so they re becoming very populr estimting tools nd re known to be efficient nd less time consuming in modeling of complex systems compred to other mthemticl models such s regression (Klogirou, 200; Phlvn et l, 202). An rtificil neurl network (ANN) model is usully employed when the reltionship between the input nd output is complicted or ppliction of nother vilble method tkes long computtionl time nd effort (Noorzei et l, 2005). Also, it employed when nother vilble method gives less ccurcy performnce. There re different potentil pplictions of the ANN in soil pplictions such s predicting orgnic mtter content in the soil (Ingleby nd Crowe, 200), soil erosion prediction (Licznr nd Nering, 2003), predicting the hydrulic conductivity of corse grined soils (Akbulut, 2005), determintion of volumetric soil moisture content (Chi et l, 2008) nd modeling soil solution electricl conductivity (Dvood et l, 200). Ds et l (2008) mde vrious ttempts using neurl network model to predict the residul friction ngles bsed on cly frction nd Atterberg s limits. The ANN model with two inputs ws the best model, bsed on sttisticl prmeters, correltion coefficient nd coefficient of efficiency, for trining nd testing dt sets. Goktepe et l (2008) estblished correltion between index properties nd sher strength prmeters of normlly consolidted clys by sttisticl nd neurl pproches. The results indicted tht the ANN-bsed model is superior in determining the reltionships between index properties nd sher strength prmeters. Jin et l (200b) developed ANN models to predict cohesion nd ngle of internl friction of fine-grined high compressible soil. The ANN prediction models were developed from test results obtined by conducting series of unconsolidted undrined trixil compression tests on soil smples. Dry densities, degree of sturtions using different compction energy, liquid limit, plsticity index nd percentge of size of prticles were cted s input prmeters. The prediction ws consistent with the observed dt. Khnlri et l (202) introduced rtificil neurl network models to predict friction ngle nd cohesion of soils. They used the percentges of pssing the No. 200 ( 200), 40 ( 40) nd 4 ( 4) sieves, plsticity index, nd density s inputs fctors. The results indicted tht multilyer perceptron feed forwrd neurl network model shows better performnce rther thn rdil bsis function neurl network model. Rni et l (203) mde n ttempt by the using of multilyer perceptron network with feed forwrd bck propgtion to model soil cohesion nd soil ngle of internl friction in terms of fine frction, liquid limit, plsticity index, mximum dry density nd optimum moisture content by

3 Al-Hmed et l. 87 Figure. Sher stress versus horizontl displcement during direct sher box test under different norml stresses. using ANN. The results indicted tht predicted vlues of soil cohesion nd soil ngle of internl friction for trining nd testing process were close to observed vlues. It is not lwys possible to conduct the tests on every new sitution to get soil cohesion nd soil internl friction ngle. In order to cope with such problems, numericl solutions hve been developed to estimte such prmeters. With such rguments, there is need to find simple model to predict soil cohesion nd soil internl friction ngle in esy wy. So, the obective of this study ws to model the reltionship between soil cohesion nd soil internl friction ngle nd some soil vribles such s soil texture index, soil dry density nd soil moisture content. However, modeling soil mechnicl properties is one of the most importnt tools in the ssessment of tillge drft s well s energy requirements. MATERIALS AND METHODS Study sites The study ws conducted in different cultivted sites, where soil smples from different sites t Al-Khr, Al- Qssim, Wdi El-Dwser, Hil, Alouf, Tbuk nd Riydh regions in Sudi Arbi were collected. Ltitude, longitude nd ltitude of ll the study sites were determined using globl positioning system (Grmin GPS 60) which is stellite bsed positioning nd nvigtion system tht provides position with ccurcy less thn 5 meters. The ltitude men ws rnged from to N; the longitude men ws rnged from to E nd the ltitude men ws rnged from to 87.7 m. Mesuring soil properties 38 Soil smples were collected from surfce to bout 20 cm depth. Soil prticle size distribution ws determined. The cly frction rnged from 3 to 2%; the snd frction rnged from to 88.9% nd the silt frction rnged from 7.2 to 20.%. Direct sher box method ws used in determining soil cohesion nd soil internl friction ngle. Levels of soil moisture content similr to the soil moisture content in the field were tested. During the sher experiments, soil wet density of the soil ws mintined in the rnge relted to soil bulk density. A soil smple is plced in metl sher box nd undergoes horizontl force. The soil fils by shering long plne when the force is pplied. The loding rte during sher tests ws constnt rte of 0.2 mm/min. A norml lod is pplied to the soil plced in the box through the top plte. The pplied sher force nd horizontl displcements were recorded for further nlyses. The norml stresses used for sher testing were 0.5 kg/cm 2,.0 kg/cm 2, nd.5 kg/cm 2. In order to obtin the sher strength chrcteristics of soil (cohesion nd internl friction ngle), two tests on severl identicl smples under different norml lods were performed. By plotting the best liner fit through t three points (pirs of norml stress-pek sher stress), the Mohr-Coulomb filure envelope ws obtined. From this filure envelope, C nd φ were estimted. After crrying out sher box tests on soil with different norml stresses, grph of sher stress versus horizontl displcement ws drwn s illustrted in Figure. After nlyzing of sher stress versus horizontl displcement, nother grph presents sher stress t filure ginst norml stress s shown in Figure 2 ws drwn. From Figure 2, it is usul to

4 88 Int. Res. J. Agric. Sci. Soil Sci. Figure 2. Sher stress t fliur ginst norml stress during direct sher box test. clculte the ngle from the slope of the trend line, since tn φ = slope of trend line. When the trend line intersects with the verticl xis, this vlue of sher stress is clled the cohesion of the soil (C) in kg/cm 2. To combine ll soil frctions, soil texture index ws developed similr to one ppered in Oskoui nd Hrvey (992), but due to the snd content is the mor component in the studied soils, followed by silt then cly so, nother formul to clculte soil texture index (STI) will be developed s follows: Si log (S + CC STI = 00 )... Where S is % of snd content in the soil, S i nd CC re % of silt nd cly frctions in the soil. Oskoui nd Hrvey (992) showed tht the STI reflects the effects of ll three of the soil frctions. The STI produces unique numbers for every combintion of snd, silt nd cly contents. Artificil neurl network rchitecture ANN is one of the computing methods. It uses simple processing elements nmed neuron. ANNs discovers the inherent reltionship between prmeters through lerning process nd cretes mpping between input spce (input lyer) nd trget spce (output lyer) (Chyn et l, 2007). The multilyer perceptron network nd rdil bsis function networks re the most commonly used feed forwrd ANNs. A multilyer perceptron network consists of one input lyer, one or (2) more hidden lyers nd one output lyer (Hssn-Beygi et l, 2007). The network rchitecture used in this reserch consists of three lyers of neurons connected by weights. The weights connecting input neuroni to hidden neuron re denoted by w, while the weights connecting hidden h i neuron to output neuron re denoted by w. The input of ech neuron is the weighted sum of the network inputs, nd the output of the neuron is sigmoid function vlue bsed on its inputs. More specilly, for the th hidden neuron (Zhng et l, 2005). h net y n h = w i xt i= = f h ( net ) + b While for the output neuron o net ~ xt = f m = = w o y o ( net ) + c,,... o (3)... (4)

5 Al-Hmed et l. 89 Figure 3. The developed ANN model for predicting soil cohesion nd soil internl friction ngle. Where b nd c re thresholds (bis), this network hs n neurons in the input lyer nd m neurons in the hidden lyer, f is typiclly tken to be sigmoidl function, such s the logistic function f + e ( x) =... x The inputs to this network re soil dry density ( ρ ), soil moisture content (θ ), soil texture index (STI), the output hs two x~ tht re soil cohesion nd soil internl friction t ngle. Given finite number of pttern pirs consisting of n input pttern X t nd trget output pttern x t, this network is trined by supervised lerning. Generlly, the bckpropgtion lgorithm, which is the most populr lerning lgorithm, is dopted to perform steepest descent on the totl men squred error (MSE): N 2 MSE = 2 t= ( ~ x t x t ) Where N is the totl number of pttern pirs. Building of rtificil neurl network model The dt of inputs nd outputs were 38 rows. 33 of these dt were used to build the rtificil neurl network model nd the rest ws used to test the model. In order to build ANN model, commercil Neurl Network softwre of QNET 2000 for WINDOWS (Vest Services, 2000) ws used. The ANN used in this study ws stndrd bckpropgtion neurl network with three lyers: n input lyer, hidden lyer nd n output lyer. Before trining, certin pre-processing steps on the network inputs nd (5) (6) trgets to mke more efficient neurl network trining ws performed. The rnge of input nd trgets vlues ws from 0.5 to 0.85, i.e., normlizing the inputs nd trget vlues using the following formul: ( V Vmin ) T = ( ) + ( V V ) mx min Where V is the originl vlues of input nd output prmeters, T is the normlized vlue; V mx nd V min re the mximum nd minimum vlues of the input nd the output prmeters, respectively. The rndomized dt were used in trining. Three vrious lyers ANN structures were investigted, including different number of neurons in the hidden lyer, different vlues of the lerning coefficient, different vlues of the momentum, nd different trnsfer functions. Trining given neurl network ws chieved. Its performnce ws evluted using correltion coefficient. The best ANN structure nd optimum vlues of network prmeters were obtined on the bsis of the lowest error on trining dt by tril nd error. Preliminry trils indicted tht one hidden lyer network performed better results thn other hidden lyers ANN to lern nd predict the correltion between input nd output prmeters. To determine the optiml number of neurons in hidden lyer, trining ws used for 3-n-2 rchitectures. The number of neurons in the hidden lyer (n) ws studied from 25. Results show tht mong the vrious structures, the best trining performnce to predict soil cohesion nd soil internl friction ngle belonged to the structure. Figure 3 illustrtes the developed ANN model for predicting soil cohesion nd soil internl friction ngle. The trining prmeters were for trining error, 0.5 for lerning rte, 0.8 for momentum nd for itertions. Tble illustrtes network sttistics fter trining phse. (7)

6 90 Int. Res. J. Agric. Sci. Soil Sci. Tble. Network sttistics from Qnet softwre of trining dt of ANN model. Criteri Stndrd devition Bis Mximum error Correltion coefficient (dimensionless) Output nodes Soil internl friction ngle ( ) Soil cohesion (kp) Tble 2. Person's correltion coefficients between soil cohesion (C) nd soil internl friction ngle (φ ) s the dependent vribles nd soil dry density ( ρ ), soil moisture content (θ ) nd soil texture index (STI) s independent vribles. ρ θ STI C φ φ C STI θ ρ Tble 3. Error criteri during testing process of ANN model. Vribles Soil cohesion (kp) Soil internl friction ngle ( ) R 2 (dimensionless) MAE RMSE Criteri of evlution RESULTS The performnce of the developed model in this study hs been ssessed using vrious stndrd sttisticl performnce evlution criteri. The sttisticl mesures considered hve been three criteri. The first criterion is correltion coefficient. The second one is men bsolute error (MAE). The third criterion is root men squre error (RMSE). The MAE nd RMSE re clculted ccording to the following equtions: MAE = N RMSE = N i= N i= Y ( Y N Y Y p p ) 2... (9) Where Y nd Y p re the observed nd predicted dt, respectively nd N is the number of dt points. (8) A correltion mtrix ws formed to explore the power of the liner reltionships between the vribles included in this study. For tht purpose, the correltion mtrix ws produced by using excel spredsheet under dt nlysis tools to the trining dt set in n ttempt to define the degrees of liner reltionships between ll vribles. In correltion nlysis, Person's correltion coefficients between soil cohesion (C) nd soil internl friction ngle (φ ) being the dependent vribles, nd the other selected soil's properties, being independent vribles, hve been investigted. Person's correltion coefficients (r vlues) re given in Tble 2. The prediction performnce of the ANN model ws tested using dt of 3 % cses, which were not used in the initil trining of the ANN model. The ANN model predicted soil cohesion with RMSE of kp, MAE of 3.63 kp nd coefficient of determintion of 0.93 s depicted in Tble 3. The ANN model predicted soil internl friction ngle with RMSE of degree, MAE of degree nd coefficient of determintion of s depicted in Tble 3.

7 Al-Hmed et l. 9 Figure 4. Reltionship between the observed nd the predicted vlues during testing phse using of ANN model for soil cohesion. Figure 5. Reltionship between the observed nd the predicted vlues during testing phse using of ANN model for soil internl friction ngle. Figure 4 shows the reltionship between the observed nd the predicted vlues of soil cohesion during testing phse using ANN model for the soil cohesion. The figure clerly shows tht the points re uniformly scttered round the : line. Figure 5 shows the reltionships nd coefficients of determintion between the observed nd the predicted soil internl friction ngle vlues during testing phse using ANN model for the soil internl friction ngle. The figure clerly shows tht the points re uniformly scttered round the : line. Qnet2000 neurl network softwre ws lso used to explore the mgnitude of the impct of ech individul vrible in the network outcome. The results of

8 92 Int. Res. J. Agric. Sci. Soil Sci. Figure 6. The contribution percentge of the three input vribles to the outputs. contribution nlysis cn udge wht prmeters re the most significnt (hve the high contribution vlues) in comprison with other inputs. In this work, the reltive influence of ech of the input vribles upon predicted soil cohesion nd soil internl friction ngle ws presented s percentge contribution of ech vrible to the network predictions. The contribution percentge of the three input vribles to the outputs ws illustrted in Figure 6. DISSCUSSION According to correltion nlysis (Tble 2), soil dry density hs influences on soil cohesion nd soil internl friction ngle with positive r-vlues of nd for C ndφ, respectively. This finding ws greed with Abd El Mksoud (2006). However, soil moisture content hs negtive effect on soil cohesion nd soil internl friction ngle with negtive r-vlues of nd for C ndφ, respectively. Agin this result is greed with the findings of Abd El Mksoud (2006). Soil texture index hs low effect on soil cohesion nd soil internl friction ngle with positive r-vlues of nd for C ndφ, respectively As indicted by the vlues of RMSE nd MAE, it ws concluded tht the developed ANN model could be used for prediction of soil cohesion nd soil internl friction ngle. However, the potentil benefit of estimting soil cohesion nd soil internl friction ngle from soil physicl properties is tht the mesurements of soil physicl properties cn be chieved using simple instrumenttions in lbortory or in the field. The results reported in this work re vlid only over the rnge investigted. As it cn be seen in Figure 6 the highest contribution vlue (38.27%) belonged to soil moisture content which showed the highest impct of this input between three evluted fctors on soil cohesion. The result ws greement with the findings of Bechmnn et l (2006) who indicted tht soil strength vried frequently due to chnges in soil moisture conditions. Besides, the highest contribution vlue (38.40%) belonged to soil dry density which showed the highest impct of this input between three evluted fctors on soil internl friction ngle s illustrted in Figure 6. The result ws greement with Zhng et l (200) reserch results which indicted tht soil strength for the soils from sndy lom to clyey lom t soil surfce ws significnt ffected by soil density. CONCLUSION This study evluted the bility of n rtificil neurl network (ANN) model to predict nd model the reltionship between the soil dry density, soil moisture

9 Al-Hmed et l. 93 content nd soil texture index nd its corresponding the soil cohesion nd soil internl friction ngle. Three fctors were selected s the most importnt fctors which cn ffect (or hve effect on) soil cohesion nd soil internl friction ngle. The min conclusions re s follows: () The ANN model with structure ws recognized s the best model for predicting the soil cohesion nd soil internl friction ngle. The vlidity of developed model ws confirmed due to the high vlue of the coefficient of determintion (R 2 = 0.93) nd the low vlues of men bsolute error (MAE = 3.63 kp) nd the root men squre error (RMSE = kp) for soil cohesion. Menwhile, these vlues for soil internl friction ngle were R 2 = 0.983, MAE = degree nd RMSE = degree. (2) The contribution nlysis of input prmeters on outputs reveled tht soil moisture content hs the higher contribution on soil cohesion in comprison with soil dry density nd soil texture index. Agin, contribution nlysis of input prmeters on outputs reveled tht soil dry density hs the higher contribution on soil internl friction ngle in comprison with soil moisture content nd soil texture index.from the results of this study, it is concluded tht the ANNs re useful tools to predict the soil cohesion nd soil internl friction ngle with respect to the soil physicl properties fctors which impct on soil strength prmeters. ACKNOWLEDGEMENTS The uthors express their grtitude to the Ntionl Pln for Science, Technology nd Innovtion Progrm, King Sud University, Sudi Arbi for finncilly supporting this reserch effort s prt of the proect entitled "Modeling of energy consumption during seed bed preprtion opertion bsed on soil mechnicl properties", No. 09-SPA REFERENCES Abd El Mksoud MAF (2006). Lbortory determining of soil strength prmeters in clcreous soils nd their effect on chiseling drft prediction. 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