Send Orders or Reprints to reprints@benthmscience.e 410 The Open Civil Engineering Journl, 014, 8, 410-415 Open Access The Appliction o Improved Duncn-Chng Model in Unloding Soil Yi He 1, nd Xuejun Chen 1,,* 1 Fculty o Engineering, Chin University o Geosciences (Wuhn), Wuhn 40074, Chin; Civil Engineering Deprtment, Luoyng Institute o Science nd Technology, Luoyng 4710, Chin; Civil Engineering Deprtment, Guilin University o Technology, Guilin 541004, Chin Abstrct: On the bsis o the representtive smples o silty cly ound in Wuhn, Chin, the lterl unloding o soil s stress pth produced by excvting oundtion pit engineering, ws simulted by trixil experiment. A series o consolidted-drined true trixil test nd norml trixil test were conducted. According to the results o tests, the prmeter o the Duncn-Chng Model ws determined. A modulus ormul ws used or the oundtion soil in the lterl unloding stress pth tests to replce the modulus ormul o Duncn-Chng Model bsed on the! = cons t. Moreover, the Duncn-Chng hyperbol nonliner elstic constitutive model ws used to simulte the plne strin test. A method to improve the bility o Duncn-Chng model in order to tke into ccount the eects o the intermedite principl stress on the strength nd deormtion ws presented s well s ll the model prmeters were lso determined. The dptbility o the model or unloding the stress pth ws veriied by compring the theoreticl stress-strin reltionship nd empiricl stress-strin reltionship. Keywords: Foundtion pit excvtion, lterl unlod, improved Duncn-Chng model. 1. INTRODUCTION In excvtion engineering, when soil is in the stte o unloding, it experiences uphevl in the bottom o the excvtion pit. Problems in the lterl displcement o soil induced by unloding nd generl problem in the geotechnicl loding re noticebly dierent. Numericl nlysis ws crried out on the oundtion pit excvtion with the conventionl erth pplied by loding test prmeter nd the design hd vrious I evitble errors. In this pper, excvtion process o ctul pit ws simulted. A series o consolidted-drined true trixil test nd norml trixil test were conducted. According to the experimentl results, under the condition o dringe o oundtion pit in lterl lod shedding, the constitutive model o soil ws pplied ter the excvtion o oundtion pit. Insted o Duncn-Chng model the deormtion modulus or lterl unloding ws used or the clcultion [1] o tngent modulus ormul [, ]. The Duncn-Chng nonliner elstic model ws pplied to the plne strin condition, in view o the ct tht the Duncn-Chng model does not relect the principl stress, thereore, the Duncn Chng model ws improved.. In ddition, the prmeters o the model were determined, nd the income ws observed by the income reltionship curves o stress-strin nd testing curves o stress - strin through the comprtive nlysis with theoreticl clcultion, in order to vlidte the dptbility o the model or unloding engineering o this specil stress pth. *Address correspondence to this uthor t the 1 Jingn Rod Guilin, Guilin University o Technology, Guilin 541004, Chin; Tel: +86190778446; E-mil: chenxj@glut.edu.cn. EXPERIMENTAL STUDY ON CONSTITUTIVE MODEL UNDER THE CONDITION OF DRAINAGE OF UNLOADING SOIL.1. Two Dimensionl Stress-Strin Test This test minly nlysed the soil properties o the surrounding ctive re o the oundtion pit, nd simpliied the orce stte pproximtion or unchnged verticl lod in lterl unloding. Undisturbed soil smples were tken rom Wuhn Shhu Power District high-rise residentil building o oundtion pit construction site ter testing. The city o Wuhn is representtive o the Yngtze River I terrce lluvil silty cly. The physicl nd mechnicl indexes re shown in Tble 1. Tble 1. Physicl nd mechnicl prmeters o soil smples. ω (%) γ ( g/cm ) c ( kp) ( ) φ e I p.4 1.9 1.6.7 0.97 1.0 The smple ws sturted, respectively by 50, 100, 150, 00, 50, 00 KP conining pressure o isotropic consolidtion, mintined ter consolidtion, nd ws immeditely shered with constnt verticl pressure control. In the process o shering, nd clssiiction o unloding, ech stge o unloding grde hd 10 KP with stress s the control vrible. The stress, nd displcement, in ech lod cse were mesured in the whole test process suggesting! 1 >! =!. Results o the stress-strin curve re shown in Fig. (1). 1874-1495/14 014 Benthm Open
The Appliction o Improved Duncn-Chng Model in Unloding Soil The Open Civil Engineering Journl, 014, Volume 8 411.. Trixil Loding Stress-Strin Test Three dimensionl test or testing soil stress stte ws crried out on the ZSY - 1 type by true trixil test pprtus, with smples o sturtion, nd with the consolidtion o norml three xil test conining the pressure o isotropic consolidtion, mintined ter consolidtion, ws immeditely shered. 1 nd remined unchnged due to verticl deormtion o pressure control in the process o shering ε (nmely: 0 )), is grde unloding, ech stge o unloding hd 10KP, with stress s the control vrible. The stress nd displcement were mesured in ech lod cse, in the whole testing process 1. By unloding soil deormtion modulus ormul [1] side o oundtion pit excvtion...1. Anlysis o Duncn-Chng Model Prmeters Li Shoude, Zhng Tuqio, et l. through the lterl unloding stress pth test nlysed the deormtion lws o the soil behind the wll lterl nturl oundtion consolidtion in oundtion pit excvtion unloding process, bsed on the hyperbolic hypothesis, nd cited the clcultion prmeters o Duncn-Chng model or deducing deormtion modulus ormul or nturl soil excvtion in oundtion pit lterl unloding process, which is represented s ollows: " ( 1! sin! )( 1! k E = E i 1! R 0 )! 1 % $ ' ( # ccos" + k 0! 1 sin" & ( )( k 0! 1!! ) ( )( 1! k 0 ) ) 1+ sin" -1! R - 1 ccos! + ) * sin!! 1+ sin! * +. +,!. 1, (1) In the ormul given below, E i is unction o K 0 consolidtion stte o the! 1 : Fig. (1). The stress-strin curves or drined test o norml trixil. According to the dringe o lterl plne, strin conditions were determined by using true trixil instrument under the unloding test to obtin the stress-strin reltion curve s shown in Fig. ().!! E i = kp $ # & " % p n Using the true trixil nd norml trixil, in isotropic consolidtion, i.e.! 1 =! =!, thereore K 0 = 1, then (1) type into: () ( 1+ sinϕ)( ) p E = Ei 1 R 1 1 c cosϕ+ 1 sinϕ () Fig. (). The stress-strin curves or drined test o true trixil... Experimentl Study on Constitutive Model o Unloding Soil At present, mong the nonliner elstic models used in engineering pplictions, the most signiicnt one is the Duncn-Chng [, ] model. The soil hs complicted deormtion etures, such s diltncy, nisotropy, nd the inluence o stress pth. In some soil nonliner elstic or elstic-plstic model, or generl loding conditions, the stisctory results cn be obtined, but or the specil loding condition, the results will not be resonble. In ddition, the model is bsed on the ilure criterion o Mohr-colin in which, =, without considering the middle stress o. In the originl Duncn Zhng model veriiction ppliction, there re certin inevitble errors in the deormtion test o soil under plne strin condition. Thereore, in order to mke the model simulte the ctul soil engineering properties, some improvements must be mde. In ddition, while testing the lterl unloding stress pth, deormtion o the volume curve in the test ws more diicult to scertin the prcticl expression o the Poisson rtio µ. But tests showed! tht the lterl unloding stress pth vried to lesser extent [4]. By ormuls () nd (), it cn be observed tht, there were seven prmeters in the Duncn-Chng model, i.e.: k, R, k b, m, n, c, nd!.... To Determine the Prmeters o the Duncn-Chng Model [5, 6] 1) C, ϕ vlue determintion According to the dt o norml trixil test results, obtined under dierent conining pressure nd dierent principl curves o stress nd xil strin were obtined rendering the molr under dierent conining pressures nd stress circle, s shown below: c kp ϕ 0 = 16.77, =., ) E i, R vlue determintion
41 The Open Civil Engineering Journl, 014, Volume 8 He nd Chen Tble. E i nd R prmeters o ( ) p silty cly. ( kp ) ( - ) ( kp ) E i ( kp) b ( - ) ( kp ) ( kp) 1 1 ult 50 0.08E-05 457.5 0.018044 55.4 0.9019 100 0.4E-05 085.7 0.0185 80.74 0.99080 R Averge 50 160.54E-05 9416.50 0.00617 161.99 0.987647 0.96 00 00.47E-05 40467.75 0.004857 05.88 0.97114 Tble. ( p ) nd ( i ) E p prmeters o silty cly in dierent cell pressure. ( kp) /p ( /p ) i ( kp) E i E / p ( E / p ) i 50 0.5.51115 457.5 4.5-0.01 100 1.488974 085.7 08. 0.000 50.5.595496 9416.50 94.0 0.98 00.60706 40467.75 404.6 0.477 Fig. (). The reltionship between ( p ) nd ( Ei p ). Fig. (4). The reltionship between ( p ) nd ( ) B p. Becuse the ctul stress-strin reltionship ws in line with the bsic ssumptions o the hyperbol, the stress-strin hyperbolic (! 1!! )! " 1 ws converted into liner reltionship between! 1 (" 1!" )!! 1 nd dierent conining pressures re represented s intercepts nd b whose vlues re shown in Tble. E i ) K, n vlue determintion Tke the tmospheric pressure P =101. Kp, ( p ) ws obtined. The vlues o conining pressure, re shown in Tble, nd the ( p ) : ( E p ) i liner reltion mpping, is shown in Fig. (), which cn be used to obtin the prmeters K, nd n vlue which were, K=08.8, nd n= 0.54. 4) K b, m vlue determintion Tke the tmospheric pressure P=101. Kp, ( ) # V, ( B P ) ws obtined ndb vlues o B =! 1 "! ( ) conining pressure, re shown in Tble 4. The! p ( B p ) liner reltion mpping is shown in Fig. (4), which cn be used to obtin the prmeters K b, nd m, nd these were, K b 66.4, nd m=0.764. Thus, the prmeters o Duncn-Chng model were obtined by the experiment o soil, listed in Tble 5. 5) Duncn-Chng hyperbol model or plne problems Duncn Chng hyperbolic E-K model prmeter ws obtined by the norml trixil test to determine the deormtion clcultion with three ordinry specimen with its nturl. Compred with the mesured results, the clcultion o deormtion o plne strin s K b nd specimen prmeters tody with three xis test or determining, or, the simultion o excvtion process will the devitoric stress is divided into severl components, ech increment in men stress on the hyperbolic model or E i nd, the ormtion o lexibility mtrix!c " # $ =! " D # $%1,
The Appliction o Improved Duncn-Chng Model in Unloding Soil The Open Civil Engineering Journl, 014, Volume 8 41 Tble 4. ( p ) nd ( ) B p prmeters. ( kp ) ( /p) ( - ) ( kp) ( - ) ( kp ) ε (%) B ( kp) 1 1 v B/ p ( B/ p ) 50-0.01 50 5 0.0070.. 1.5 100 0.000 80 56 0.0048 7777.77 77.78 1.891 50 0.98 160 11 0.0055 1575.76 15.76.1 00 0.477 00 140 0.0011 84848.48 848.48.99 Tble 5. Prmeters o Duncn-Chng model. C ( kp) φ R K n Kb m 16.77. 0.96 08.8 0.54 66.4 0.764 ( 50 KP) ( 100 KP) ( 150 KP) ( 00 KP ) Fig. (5). The curves or ( 1- ) ε 1. wherein:!d " # $ = K 9K % E! & & & " K + E K % E 0 K % E K + E 0 0 0 E According to the dierent lod o!! 1 ccumultion, the corresponding stress-strin curves were drwn. The curve nd the test curve o Duncn Chng model income theory relly three sht under plne strin conditions s shown in Fig. (5). # ' ' ' $. The min eect o stress considertion The Duncn-Chng model does not consider the intermedite principl stress on strength nd deormtion eect o the! resulting in low deormtion modulus o soil in the speciic clcultion process o lrge deormtion o soil. Thereore, mny domestic nd oreign scholrs hve put orwrd vrious methods or the ppliction o the model nd t the sme time, hve tried to improve the model, by overcoming its weknesses. At present, the modiied elstic modulus, Poisson's rtio nd modiied Mohr-Colin s method re the two kinds o methods [6-8] tht hve been proposed,
414 The Open Civil Engineering Journl, 014, Volume 8 He nd Chen Tble 6. Prmeters o improved Duncn-Chng model. C ( kp) φ R K n Kb m 16.77. 0.96 08.8 0.54 66.4 0.764 but the study used only one correction method o elstic modulus or the simultion o plne strin test results, which relects the complex degree o stress-strin chrcteristics to veriy the improved model. Thus, it provides the reerence or the selection o numericl nlysis in geotechnicl engineering constitutive model. In order to consider the inluence o intermedite principl stress o!, the originl Duncn model o conining pressure!, (! +! ) ws used insted o prtil stress (! 1 "! ),! 1 " (! +! ) to keep the Mohr-colin s stndrds unchnged, nd to consider the degree o inluence o intermedite principl stress! on stress-strin chrcteristics o stress pths. The improved model or considering the inluence o intermedite principl stress! chnged the corresponding prmeter nd the expression o tngent modulus o elsticity model corresponding to: * $ ( 1+ sin" ) # 1! # + # ' -, % & ( ) / E = E, i 1! R /, 1 ccos" + # 1 sin" /, / +,./ 1) The prmeters o the improved model The improved Duncn Chng model prmeters still include seven originl prmeters o Duncn Chng nonliner model, nmely K, K b, m, n, R, c nd!. The improved model prmeters cn still be obtined rom the norml trixil test. The nonliner elstic model with improved prmeter vlues is shown in Tble 6. ) Duncn-Chng modiied hyperbol model or plne problems The Duncn-Chng hyperbol model improved the method which is still used or veriiction beore unloding soil in plne strin side o the oundtion pit excvtion. The obtined experimentl clcultion curves nd the originl Duncn Chng model clcultion curves were drwn together, s shown in Fig. (5). CONCLUSION By compring the grph, it ws observed tht the clculted vlue nd experimentl vlue o Duncn-Zhng model were lrger, even with the modiied Duncn-Chng model. However, the clculted vlue, experimentl vlue nd nstomosis were not pproprite. Following re the resons or this dierence: 1) Duncn Chng nonliner elstic model ws estblished bsed on the conventionl D model o norml trixil test, nd model prmeters were obtined by the ordinry norml trixil test. Although the vlue o this prmeter method is simple nd convenient, its ppliction to D in (4) plne strin test needs to be veriied eective clcultion results. ) Duncn Chng nonliner elstic model ws set up bsed on the norml trixil loding test nd constnt conining pressure conditions. Thereore, it is suitble or generl loding conditions, but or the specil loding condition, resonble results re not obtined. In the excvtion o oundtion pit engineering, unction o soil lod mode is dierent rom the generl loding, thereore, using the model to study the deormtion o soil under the condition o plne strin loding unloding is unresonble. ) In the tests o the plne strin determining dmge devitoric stress rtio o (! 1 "! ) three xil test ws eective, nd the ilure strin with three trixil test ws slightly low. According to the Mohr-Colin ilure criterion, plne strin test o! ngle ws high thn three trixil test, wheres, the three xis mesured! ngle or plne strin problem ws low. This is becuse the min stress on the strength o the Mohr-Colin nd the generted error were not considered. The reson behind ilure in the ppliction o hyperbolic model nd the problem in plne strin is ulty selection, thereby cusing dierence in the clcultion curve nd experimentl curve o income. 4) In view o the inluence o middle principl stress determined by Duncn Chng model, the improvement in Duncn Chng model ws mde to consider the inluence o intermedite principl stress on the strength o soil, the clculted curve ws derived rom it cn be seen tht the Duncn-Chng model curve ter improvement is locted in the ormer Duncn-Chng model, i.e. tngent o the elstic model curve ter correction in the clculted curve ws higher thn the originl Duncn-Chng model results. This lso mkes the clcultion more close to the curve obtined by the plne strin test. Although the improved model improved the tngent modulus curve, on the contrry, it cn be observed rom the grph tht the strin clcultion prediction is still smller thn the experimentl vlue, which suggests tht the Duncn-Chng model hs limited cpcity or determining the stress strin properties o complex stress stte which needs to be urther improved. CONFLICT OF INTEREST The uthors conirm tht this rticle content hs no conlict o interest. ACKNOWLEDGEMENTS Declred none. REFERENCES [1] S. D. Li T. Q. Zhng, B. T. Wng, nd Z. F. Lu, Modulous ormul or oundtion soil under lterl unloding during excvtion, Civil Engineering Journl, vol. 5, no. 5, pp. 70-74, 00.
The Appliction o Improved Duncn-Chng Model in Unloding Soil The Open Civil Engineering Journl, 014, Volume 8 415 [] J. M. Duncn nd C. Y. Chng, Nonliner nlysis o stress nd strin in soils, Journl o the Soil Mechnics nd Foundtion Division, vol. 96, no. 5, pp. 169-165, 1970. [] P. V. Lde, Elsto-plstic Stress-Strin Theory or Cohesionless Soil with Curved Yield Surces, Soilds Structures, vol. 1, pp. 1019-105, 1977. [4] J. H. Qin, The principle nd clcultion o erthwork, Beijing: Chinese wter conservncy nd Hydropower Press, 000. [5] G. X. Li, Advnced soil mechnics, Beijing: Tsinghu University press, 004. [6] T. H. Lu nd Z. D. Liu, Advnced soil mechnics, Beijing: Mchinery Industry Press, 006. [7] Z. L. Liu, Evlution on developing level o unbn gglomertion derived rom resources explortion, Journl o Applied Sciences, vol. 1, no. 1, pp. 470-4707, 01 [8] X. Y. Zhng nd S. W. Yn, Geotechnicl plstic mechnics Foundtion, Tinjin: Tinjin University press, 004. Received: July 09, 014 Revised: October 1, 014 Accepted: November 1, 014 He nd Chen; Licensee Benthm Open. This is n open ccess rticle licensed under the terms o the (https://cretivecommons.org/licenses/by/4.0/leglcode), which permits unrestricted, noncommercil use, distribution nd reproduction in ny medium, provided the work is properly cited.