NUMERICAL SIMULATION OF THE BEHAVIOR OF AN EXPANSIVE SOIL

Transcription

1 Blucher Mechanical Engineering Proceedings May 214, vol. 1, nu. 1 NUMERICAL SIMULATION OF THE BEHAVIOR OF AN EXPANSIVE SOIL L.M. Costa 1, S. R. M. Ferreira 2, I. D. S. Pontes 2 and L. J. N. Guiarães 2 1 Deartent o Technology, Federal University o Pernabuco (licia@ue.br) 2 Deartent o Civil Engineering, Federal University o Pernabuco Abstract. This aer resents a nuerical analysis o the behavior o an exansive soil o the sei-arid region o the northeast o Brazil. The behavior o exansive soils, due to alied stress or suction, is governed by various henoena occurring at icrostructural level. Gens & Alonso [4] resented a concetual basis or odeling exansive soil, considering two dierent levels: the icrostructural level, at which swelling o active inerals takes lace and the acrostructural level resonsible or ajor structural rearrangeent. Based on this concetual raework and in the iroveents suggested by Alonso et al. [2], Sanchez et al. [] roosed a double structure generalized lasticity odel, which was ileented in the coutational code CODE_BRIGHT. This aer alies the couled hydro-echanical orulation ileented in this code to siulate the behavior o an exansive soil due to changes in water content. Outut results o nuerical siulations o laboratory tests show a good agreeent with exeriental data. Keywords: Exansive soil, double structure odel, hydro-echanical couled analysis. 1. INTRODUCTION Volue change o exansive soils, due to alied stress or suction, is governed by various henoena occurring at icrostructural level, in individual clay articles and their vicinity. Gens & Alonso [4] resented a concetual basis or odeling exansive soil considering two dierent structural levels: the icrostructural level, at which swelling o active inerals takes lace and the acrostructural level resonsible or ajor structural rearrangeent. This aer resents an alication o a double structure odel, roosed by Sanchez et al. [] and ileented in the inite eleent coutational code CODE_BRIGHT to evaluate the behavior o an exansive soil o the sei-arid region o the northeast o Brazil, due to changes in water content. 2. DOUBLE STRUCTURE MODEL The double structure generalized lasticity odel roosed by Sanchez et al. [] was

2 based on the general raework resented by Gens & Alonso [4] and takes into account the iroveents suggested by Alonso et al. [2]. The acrostructure behavior is described by the Barcelona Basic Model (BBM) [1]. Other echaniss, not incororated in the BBM, which occur in the icrostructure, at clay article level, can take lace in exansive soils inducing lastic strains. So the orulation resents the deinition o laws or the acrostructural level, the icrostructure level and the interaction between both structural levels Macrostructure odel BBM considers two indeendent stress variables, the net stress, (σ ij - a δ ij ), and atric suction, s=( a - w ). It is an elastolastic strain-hardening odel, which extends the concet o critical state or saturated soils to unsaturated conditions including a deendence o the yield surace on atric suction. The yield surace is exressed by with * 2 2 (,q,s, ) q M ( + )( ) s = (, ); σ ( σ + σ )/ 3. (1) = σ ax a w σ 3. (2) q = σ 1 σ 3. (3) s = ks. (4) where is the net ean stress, σ 1, σ 2 and σ 3 are the total rincial stress, M is the sloe o the critical state line, is the aarent unsaturated isotroic reconsolidation stress or suction s, * is the saturated reconsolidation stress, k describes the increase o the aarent cohesion with suction. For isotroic conditions yield states associated with suction are described by eans o a yield unction deined in the sace (,s), which is naed the Loading-Collase yield surace (LC). It exlains the collase uon wetting and the increase o aarent reconsolidation stress with suction through the ollowing relationshi c = * c λ( ) κ λ ( ) κ s. () with ( s ) = λ( ) [( r) ex( βs) + r] λ 1. (6) where κ is the elastic stiness araeter against changes in, λ() is the sloe o virgin coression line or saturated isotroic loading, c is a reerence stress and λ(s) is the sloe o virgin coression line or isotroic loading at a constant suction s. β controls the rate o stiness increase with suction and r is a liiting value o soil stiness or very high suction.

3 A non associated lastic otential is deined by g * 2 2 (,q,s, ) q M ( + )( ) = α s. (7) where α is established in such a way that under K loading lateral strains are zero. The hardening araeters, * deends on the rate o voluetric lastic strain. The hardening law is given by d * * ( 1+ e) ( ) = dε. (8) λ κ where e is the void ratio. Elastic strains are induced by changes in net ean stress, deviatoric stress and suction according to d = κ d + 1 dq + e s ε. (9) ds ( 1+ e) 3G ( 1+ e) ( s + ) where G is the shear odulus, κ s is the elastic stiness araeter against changes in suction and at is the atosheric ressure. κ at 2.2. Microstucture odel The icrostructural behaviour is assued elastic and voluetric. The icrostructural voluetric strain deends on a icrostructural eective stress ( ˆ ) deined by ˆ = + χs. (1) where χ is a constant. Another assution adoted in this orulation is the hydraulic equilibriu between icrostructure and acrostructure, thus only one suction variable should be considered. In the (,s) lane, a line corresonding to a constant icrostructural eective stresses is naed neutral line (NL), since no icrostructural strain takes lace along it. The neutral line divides the (,s) lane into two arts, deining a coression icrostructural stress ath and a swelling icrostructural stress ath, as indicated in igure 1. The increent o the icrostructural elastic strain is exressed as a unction o the increent o the icrostructural eective stress as & & s& & ε v = ˆ = + χ K K K. (11) where the subscrit reers to the icrostructural level, the subscrit v reers to the voluetric coonent and K is the icrostructural bulk odulus, that in this aer is couted by the ollowing law

4 K e =. (12) β α ˆ Microstructural eects induce irreversible acrostructural deorations, which are considered roortional to icrostructural strain according to interaction unctions. s NL Microstructural swelling Microstructural coression Figure 1. Deinition o icrostructural swelling and contraction aths. 1 χ 2.3. Interaction unctions Two interaction unctions are deinided: c or icrostructural coression aths and s or icrostructural swelling aths. For isotroic loading the interaction unctions deend on the ratio /. The ratio / indicates the degree o oenness o the acrostructure relative to the alied stress state. When this ratio is low it eans a dense acking o the aterial and it is exected that icrostructural swelling induces large acrostructural lastic strains. According to Alonso et al. [2] any suitable unction or s and c consistent with the hysical ideas resented in Figure 2 can be adoted. exansion accuulates c s Macroorosity develos due to drying coression accuulates equilibriu state Microores invade acrocroores /o Figure 2. Interation echaniss between icro and acroores. In this aer the interaction unctions are exressed by n ( ) s s s + s1 =. (13)

5 n ( ) c c c + c1 =. (14) 3. NUMERICAL SIMULATION The odel described above was ileented in the inite eleent coutational code CODE_BRIGHT and was alied to siulate laboratory tests erored with an exansive soil o the sei-arid region o the northeast o Brazil. In order to evaluate the behavior o an exansive soil due to changes in water content, Ferreira & Ferreira [3] erored a series o oedoetric tests with sales at dierent initial water content. Changing in natural water content was erored taking the sales to desiccators and oistening or drying the. At natural water content the soil resented the ollowing characteristics: w L = 6%, PI = 3%, w c = 19%, w = 17.41% and γ d = 1.kN/ 3. The initial degree o saturation was 9,24% which corresonds to a suction o. MPa. The dierent sale values o water content are resented in table 1, besides other data corresonding to each water content value. Table 1. Inluence o initial water content w (%) s (MPa) S (%) e γ d (KN/ 3 ) In the oedoetric tests carried out the sale was looded under a low vertical stress value (1 kpa) and swelling deoration was easured, then the secien was loaded in stages, with a ratio o loading σ v /σ v =1, u to a vertical ressure o 128 kpa. The stressstrain curves ro the tests are shown in igure 3. Voluetric strain (%) w=22,68% w=2,8% w=17,41% w=7,76% Figure 3. Inluence o initial water content in swelling.

6 The data resented in table 1 show that water content variation changes not only suction (s) and degree o saturation (S) but also void ratio (e) and dry density (γ d ). Thus the sales should resent soe dierent araeters values. The araeters used in the siulation were obtained ro tests results and are listed in Table 2. The interaction unctions are the sae or all the tests. Table 2. Paraeters used in the siulation Paraeter w = 7.76κ s w = w = 2.7 w = 22.6 Macrostructure κ κ s λ() r.... β (MPa -1 ) *(MPa) c (MPa) Microstructure α (MPa -1 ) β (MPa -1 ) χ Initial void ratio e acro e icro Interaction unctions c = -.1 c1 = 1. n c =. s = -1. s1 = 3.7 n s = 3. Laboratory data and the nuerical siulation results are resented in igures 4 and. According to the double structure odel alied a decrease in suction ilies a icrostructural swelling (igure 1). For a constant stress level, the higher the initial suction, the greater the swelling due to looding, which was observed in the tests carried out (igures 4 and ). Voluetric strain (%) Laboratory Siulation Voluetric strain (%) Laboratory Siulation Figure 4. Coarison between laboratory data and siulation results: a) initial water content, w = 7.76%; b) initial water content, w = 17.41%.

7 Voluetric strain (%) 1-1 Laboratory Siulation Voluetric strain (%) -1 Laboratory Siulation Figure. Coarison between laboratory data and siulation results: a) initial water content, w = 2.7%; b) initial water content, w = 22.6%. A good agreeent is observed between exeriental data and siulation results. The swelling deorations easured were well reroduced by the odel, besides the voluetric strains due to loading. Just the last test, at highest initial water content, resents a signiicant dierence or the aount o swelling. 4. CONCLUSIONS According to the results herein resented by the nuerical siulation carried out, it is deonstrated the caability o the double structure odel and the couter code to reroduce the hydro-echanical behavior o exansive soils. It should also be highlighted the inluence o the value o initial water content o the soil or redicting the aount o swelling deoration. Acknowledgeents The authors wish to thank the inancial suort rovided by CNPq/Brazil.. REFERENCES [1] Alonso, E. E.,Gens, A. & Josa, A A constitutive odel or artially saturated soils. Geotechnique, vol. 4, n o 3, [2] Alonso E, Vaunat J, Gens A Modelling the echanical behaviour o exansive clays. Engineering Geology, vol. 4, [3] Ferreira, S. R. M. & Ferreira, M. G. V. X. 29 Mudanças de volue devido à variação do teor de uidade e u vertissolo no sei-árido de Pernabuco. Revista Brasileira de Ciência do Solo, v. 33,

8 [4] Gens A., Alonso E. E A raework or the behaviour o unsaturated exansive clays. Canadian Geotechnical Journal; vol. 29, [] Sanchez, M., Gens A., Guiarães, L. N. & Olivella, S. 2. A double structure generalized lasticity odel or exansive aterials, Int. J. Nuer. Anal. Meth. Geoech.; vol. 29,