Formulation of structured bounding surface model with a destructuration law for natural soft clay

A destructuration law considering both isotropic destructuration and frictional destructuration was suggested to simulate the loss of structure of natural soft clay during plastic straining. The term isotropic destructuration was used to address the reduction of the bounding surface, and frictional...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Functional Materials
Datum:	2017
Hauptverfasser:	Yunliang Cui, Xinquan Wang, Shiming Zhang
Format:	Artikel
Sprache:	English
Veröffentlicht:	НТК «Інститут монокристалів» НАН України 2017
Schlagworte:	Modeling and simulation
Online Zugang:	https://nasplib.isofts.kiev.ua/handle/123456789/136878
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:	Formulation of structured bounding surface model with a destructuration law for natural soft clay / Yunliang Cui, Xinquan Wang, Shiming Zhang // Functional Materials. — 2017. — Т. 24, № 4. — С. 628-634. — Бібліогр.: 18 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	nasplib_isofts_kiev_ua-123456789-136878
record_format	dspace
spelling	Yunliang Cui Xinquan Wang Shiming Zhang 2018-06-16T17:15:34Z 2018-06-16T17:15:34Z 2017 Formulation of structured bounding surface model with a destructuration law for natural soft clay / Yunliang Cui, Xinquan Wang, Shiming Zhang // Functional Materials. — 2017. — Т. 24, № 4. — С. 628-634. — Бібліогр.: 18 назв. — англ. 1027-5495 DOI: https://doi.org/10.15407/fm24.04.628 https://nasplib.isofts.kiev.ua/handle/123456789/136878 A destructuration law considering both isotropic destructuration and frictional destructuration was suggested to simulate the loss of structure of natural soft clay during plastic straining. The term isotropic destructuration was used to address the reduction of the bounding surface, and frictional destructuration addresses the decrease of the critical state stress ratio as a reflection of reduction of internal friction angle. A structured bounding surface model was formulated by incorporating the proposed destructuration law into the framework of bounding surface constitutive model theory. The proposed model was validated on Osaka clay through undrained triaxial compression test and one-dimensional compression test. The influences of model parameters and bounding surface on the performance of the proposed model were also investigated. It is proved by the good agreement between predictions and experiments that the proposed model can well capture the structured behaviors of natural soft clay. en НТК «Інститут монокристалів» НАН України Functional Materials Modeling and simulation Formulation of structured bounding surface model with a destructuration law for natural soft clay Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Formulation of structured bounding surface model with a destructuration law for natural soft clay
spellingShingle	Formulation of structured bounding surface model with a destructuration law for natural soft clay Yunliang Cui Xinquan Wang Shiming Zhang Modeling and simulation
title_short	Formulation of structured bounding surface model with a destructuration law for natural soft clay
title_full	Formulation of structured bounding surface model with a destructuration law for natural soft clay
title_fullStr	Formulation of structured bounding surface model with a destructuration law for natural soft clay
title_full_unstemmed	Formulation of structured bounding surface model with a destructuration law for natural soft clay
title_sort	formulation of structured bounding surface model with a destructuration law for natural soft clay
author	Yunliang Cui Xinquan Wang Shiming Zhang
author_facet	Yunliang Cui Xinquan Wang Shiming Zhang
topic	Modeling and simulation
topic_facet	Modeling and simulation
publishDate	2017
language	English
container_title	Functional Materials
publisher	НТК «Інститут монокристалів» НАН України
format	Article
description	A destructuration law considering both isotropic destructuration and frictional destructuration was suggested to simulate the loss of structure of natural soft clay during plastic straining. The term isotropic destructuration was used to address the reduction of the bounding surface, and frictional destructuration addresses the decrease of the critical state stress ratio as a reflection of reduction of internal friction angle. A structured bounding surface model was formulated by incorporating the proposed destructuration law into the framework of bounding surface constitutive model theory. The proposed model was validated on Osaka clay through undrained triaxial compression test and one-dimensional compression test. The influences of model parameters and bounding surface on the performance of the proposed model were also investigated. It is proved by the good agreement between predictions and experiments that the proposed model can well capture the structured behaviors of natural soft clay.
issn	1027-5495
url	https://nasplib.isofts.kiev.ua/handle/123456789/136878
citation_txt	Formulation of structured bounding surface model with a destructuration law for natural soft clay / Yunliang Cui, Xinquan Wang, Shiming Zhang // Functional Materials. — 2017. — Т. 24, № 4. — С. 628-634. — Бібліогр.: 18 назв. — англ.
work_keys_str_mv	AT yunliangcui formulationofstructuredboundingsurfacemodelwithadestructurationlawfornaturalsoftclay AT xinquanwang formulationofstructuredboundingsurfacemodelwithadestructurationlawfornaturalsoftclay AT shimingzhang formulationofstructuredboundingsurfacemodelwithadestructurationlawfornaturalsoftclay
first_indexed	2025-11-26T01:42:54Z
last_indexed	2025-11-26T01:42:54Z
_version_	1850605490109677568
fulltext	628 Functional materials, 24, 4, 2017 ISSN 1027-5495. Functional Materials, 24, No.4 (2017), p. 628-634 doi:https://doi.org/10.15407/fm24.04.628 © 2017 — STC “Institute for Single Crystals” Formulation of structured bounding surface model with a destructuration law for natural soft clay Yunliang Cui, Xinquan Wang, Shiming Zhang Department of Civil Engineering, Zhejiang University City College, Hangzhou, China Received September 23, 2017 A destructuration law considering both isotropic destructuration and frictional destructura- tion was suggested to simulate the loss of structure of natural soft clay during plastic straining. The term isotropic destructuration was used to address the reduction of the bounding surface, and frictional destructuration addresses the decrease of the critical state stress ratio as a reflec- tion of reduction of internal friction angle. A structured bounding surface model was formulated by incorporating the proposed destructuration law into the framework of bounding surface con- stitutive model theory. The proposed model was validated on Osaka clay through undrained triaxial compression test and one-dimensional compression test. The influences of model param- eters and bounding surface on the performance of the proposed model were also investigated. It is proved by the good agreement between predictions and experiments that the proposed model can well capture the structured behaviors of natural soft clay. Keywords: natural soft clay; destructuration law; bounding surface; structured behavior Для моделирования изменения структуры естественной мягкой глины при пластической деформации предложен метод деструктурирования с учетом изотропной деструктуры и фрикционной деструктуры. Структурная модель ограничивающей поверхности была сформулирована, применяя закон реструктурирования в рамках теории ограничивающих поверхностных конститутивных моделей. Предложенная модель была проверена на глине Осаки с помощью недренированного теста на трехосный компрессионный тест и одномерного теста на сжатие. Исследованы влияние параметров модели и ограничивающей поверхности на характеристики предложенной модели. Подтверждением хорошего согласования между прогнозами и экспериментами является то, что предлагаемая модель может хорошо фиксировать структурированное поведение естественной мягкой глины. Утворення моделі структурованої граничної поверхні відповідно до руйну- вання природної глини. Yunliang Cui, Changguang Qi, Xinquan Wang, Shiming Zhang. Для моделювання зміни структури природної м’якої глини при пластичній деформації запропоновано метод деструктурування з урахуванням ізотропної деструктури і фрикційної деструктури. Структурна модель обмеженої поверхні була сформульована, застосовуючи закон реструктурування в рамках теорії поверхневих конститутивних моделей. Запропонована модель була перевірена на глині Осаки за допомогою недренірованого тесту на тривісний компресійний тест і одновимірного тесту на стиск. Досліджено вплив параметрів моделі і обмеженої поверхні на характеристики запропонованої моделі. Підтвердженням згоди між прогнозами і експериментами є те, що пропонована модель може добре фіксувати структуровану поведінку природною м’якої глини. I. Introduction Structure is common in natural soft clay, which is often defined as the fabric and bond- ing of soil particles. The progressive loss of soil structure during plastic straining is always called “disturbance”[1], “degradation”[2] or “destructuration”[3]. The term destructuration is used in this paper to describe this kind of loss of structure. The destructuration leads to additional compression and strain softening of natural structured (or intact) clay which is Functional materials, 24, 34 2017 629 Yunliang Cui et al. / Formulation of structured bounding surface model ... much different from the remoulded soil in stress- strain relationship. Experimental results[4, 5] indicate that the stress-strain relationship curve of natural clay has a softening after peak stress in triaxial compression with low confin- ing pressure, and the compression rate of one- dimensional compression becomes faster when the compression pressure exceeds the structure yielding stress. It is well known that the well- established Modified Cam-Clay Model, which is based on remoulded soils, cannot capture the structured behaviors of natural soft clay. Some more advanced constitutive models[1, 2, 6] had been proposed to overcome this limitation. The pioneer introduction of bounding surface concept was initiated by Dafalias and Popov[7, 8] for met- als’ constitutive model. Dafalias[9] then extended and applied the bounding surface model to soils. AI-tabbaa and Wood[10] set a kinematic harden- ing yield surface, called ‘bubble surface’, inside the bounding surface to formulate a bubble mod- el for soil. Based on the bubble model, Rouainia and Wood[11] presented a structured bounding surface model, using the structure surface as the bounding surface and incorporating a structure measure of the bounding surface. The structure measure allows the size of the bounding surface to decay with plastic straining, so that the proposed model can describe the loss of structure. With the similar method, Kavvadas and Amorosi[12] also proposed a model for structured soils which al- lows the external bond strength envelope (BSE) to shrink with the kinematic hardening of the in- ternal plastic yield envelope (PYE). Some other researchers have done further research on such kind of structured bounding surface model and verified it with laboratory tests[13, 14]. Maranha and Vieira[15] implemented a “bubble” bounding surface model for structured soils, formulated by Kavvadas and Belokas[16] in finite element software FLAC to evaluate the influence of the initial plastic anisotropy in the excavation of a tunnel. Belokas and Kavvadas[17] also developed an incremental plasticity constitutive Model for Structured Soils to describe the effects of struc- tured soils, such as high initial stiffness, dilatan- cy, peak strength and the evolution anisotropy. Overall, the various structured bounding surface models are based on the similar bounding surface framework, and mainly differ in the precise form of destructuration laws adopted. Therefore, it is of great importance to do research on destruc- turation law. It is seen in the above models that the destructuration laws only take the reduction of bounding surface into considered which can be defined as isotropic destructuration. However, some studies and experiments[3-5] show that natural structured clay has a higher internal friction angle than the corresponding remoulded clay. The friction angle of natural clay decreases due to loss of structure. This is also demonstrated by the fact that the intact failure line lying above the post-rupture failure envelope. Because the critical state stress ratio is only related with the internal friction angle, the critical state stress ra- tio also decreases due to the reduction of friction angle. The frictional destructuration is defined to address the decrease of the critical state stress ra- tio as a reflection of reduction of internal friction angle. Taiebat et al.[3] suggested a destructura- tion law to address both isotropic and frictional destructuration and applied it on SANICLAY model. The frictional destructuration is proved to have significant effect on the loss of structure[3]. This study proposed a simple bounding surface model incorporating the destructuration law with some modifications. The proposed model can be seen as a simplified model of the existing struc- tured bounding surface models[11-14], because it neglected some complex properties of soil, such as the kinematic hardening and anisotropy but considered the frictional destructuration. The performance of the proposed model is verified by typical experimental results on intact samples of natural soft clays. 2. Bounding surface model framework 2.1.General Elastic Stress-strain Relationship It is the same as the Modified Cam-Clay model to calculate elastic stain with the follow- ing hypo-elastic stress-strain relationship:  µ Гij e e ij e= ×C (1) where µij e is the incremental elastic strain, Гij e is the incremental elastic stress, and Ce is the elastic flexibility matrix. A dot (‘·’) operator de- notes the matrix-vector and the matrix-matrix multiplications for clarity. Ce can be written as Ce E = - - - - - - é ë ê ê ê êê ù û ú ú ú úú 1 1 1 1 ν ν ν ν ν ν (2) where ν is the Poisson’s ratio and E is the elastic modulus which can be presented as E p e= - +3 1 2 1 0( )( ) /ν κ . In this e�uation, In this e�uation, e0 is the initial void ratio and κ is the slope of the swelling line in a volumetric strain-logarithmic mean stress plane. p is the mean effective stress, recalling that p = + +( ) /σ σ σ1 2 3 3 in principal stress space. 2.2. Bounding Surface Function and Map- ping Rule It is considered for simplicity that the bound- ing surface has the same elliptical shape with the Modified Cam-Clay model. 630 Functional materials, 24, 4, 2017 Yunliang Cui et al. / Formulation of structured bounding surface model ... F p p p q Mc= - +* 2 2 2/ (3) In E�. (3), p and q are the mean effective stress and the generalized shear effective stress of the mapping point on the bounding surface of the current stress point, respectively. pc is the intersection point of the bounding surface and the axial of p , which denotes the size of the bounding surface. M* is the critical state stress ratio that is the slope of the critical state line. In this paper, pc * and M* are the struc- ture parameters related with plastic strain, which will be presented in detail later. A radial mapping rule is adopted. The zero point in the stress space is taken as the map- ping center. So the stress of the mapping point on the bounding surface is given by Г Гij ijb= (4) where b is the measure of the distance between the loading surface and the bounding surface, assuming that b = -( )δ δ δ0 0/ and b ³ 1 . A schematic view of bounding surface model can be seen in Fig. 1.. 1. 1. According to the associated flow rule, the bounding surface is taken as the plastic poten- tial surface, so the incremental plastic strain can be written as   µ Г Г Г Г Гij p p kl kl ij p kl klK F F K F = ¶ ¶ æ è çççç ö ø ÷÷÷÷÷ ¶ ¶ = ¶ ¶ æ è çççç 1 1 öö ø ÷÷÷÷÷ ¶ ¶ F ijГ (�� where Kp is the plastic modulus at the map- ping point on the bounding surface and Kp is the plastic modulus at the current stress point. As is known, M is a constant and pc is a hardening parameter in the Modified Cam-Clay model. This study changes M to M* and pc to pc * by means of adding destructuration factors which will be presented in detail in next sec- tion. The destructuration factors added to M and pc involve plastic strains to form an evolu- tion law. pc * and M* will be both considered as internal variables in this model. Therefore, the consistency condition on the bounding surface should be written as ¶ ¶ + ¶ ¶ ¶ ¶ + ¶ ¶ ¶ ¶ = F F P P F M M kl kl c c ij p ij p ij p ij p Г Г µ µ µ µ   * * * * 0 (6) Substituting E�. (5) into E�. (6), the plastic modulus on the bounding surface is obtained by K F P P F F M M F p c c ij p ij ij p ij = - ¶ ¶ ¶ ¶ ¶ ¶ + ¶ ¶ ¶ ¶ ¶ ¶ ( ) * * * * µ Г µ Г (7) The plastic modulus Kp can be obtained by interpolating according to the distance between the current stress point and the mapping point. On one hand, it is assumed that the interpo- lation modulus is zero when b = 1 , that is to say Kp = Kp when the current stress reaches the bounding surface. On the other hand, when the current stress point is very close to the zero stress point ( b = ¥ ), the plastic modulus Kp = ¥ .Then it is possible to take a reasonable interpolation formula to obtain Kp at any cur- rent stress point. According to the proposal of Dafalias and Herrmann[9], the following inter- polation formula is adopted: Kp = Kp + ζ ψP F p F q ba (( ) ( ) )( ) ¶ ¶ + ¶ ¶ -2 2 1 (8) where ζ and ψ are interpolation parameters, reflecting the impact of the stress level on the modulus. Their values can be determined based on experimental curve fitting. According to the associated flow rule, the plastic flexibility matrix can be presented as C p ij kl p F F K = ¶ ¶ ¶ ¶Г Г (9) 3. Formulation of structured bounding surface model The basic framework of bounding surface model has been given above. In order to make the presented bounding surface model to con- sider the structure of soil, a reasonable struc- tured hardening law will be introduced into the model. The hardening law used herein should combine hardening and softening. It is a com- mon way to introduce a structure softening fac- tor into the hardening parameter pc to consid- er the destructuraion of the soil structure. This method allows the structured bounding surface to expand or shrink with plastic straining with- out changing of shape. This kind of destructur- ation is isotropic. However, there is a reduction of internal friction angle during the progressive loss of structure, reflected by the reduction of the critical state stress ratio, which is demon- strated by the bigger internal friction angle of the natural clay than that of the remoulded. It is named the frictinal destructuraion. In order Fig. 1. Schematic view of bounding surface model. Functional materials, 24, 34 2017 631 Yunliang Cui et al. / Formulation of structured bounding surface model ... to consider the two kind of destructuration, two structured factors, that are isotropic destructur- aion factor Si and frictional destructuraion fac- tor Sf , are incorporated in the proposed bound- ing surface model. A convenient approach is to revise pc and M by Si and Sf . Hence, pc * and M* can be written as following: p S pc i c * = (10) M S Mf * = (11) where pc contains a volumetric hardening rule controlled by the incremental plastic volumet- ric strain εv p as the Modified Cam-Clay Model, which can be shown as   p p e c c v p = + - ( )1 0 ε λ κ (12) M is the critical state stress ratio which can be derived by M c c= -6 3sin / ( sin )ϕ ϕ . ϕc is the critical state internal friction angle of re- moulded soil. Assuming that Si and Sf are controlled by plastic strain, pc * and M* can be rewritten in incremental form as following:   p S p S pc i c i c * = + (13)  M S Mf * = (14) In E�. (13), Si is assumed to be negative for softening while pc is positive for hardening, so S pi c  is the hardening part while S pi c is the softening part. During the initial stage of the plastic straining, the size of bounding sur- face expands due to more hardening produced than softening. With more plastic stain occur- ring, the softening rate will become faster than hardening rate, leading to the shrinkage of the bounding surface. In E�. (14), Sf is also as- sumed to be negative due to the frictional de- structuration, causing to the reduction of M* . In this way, the critical state stress ratio of natural clay decreases progressively to be that of the remoulded soil with the loss of the struc- ture. Thus an evolution e�uation for the Si and Sf must be established. Taiebat et al.[3] has proposed an specific form of the evolution equa- tion which reads  S k e Si i i d p= - + - æ è ççç ö ø ÷÷÷÷ - 1 1 λ κ ε( ) (15)  S k e Sf f f d p= - + - æ è ççç ö ø ÷÷÷÷ - 1 1 λ κ ε( ) (16) As noted by Taiebat et al.[3], the above form is not the uni�ue form for the evolution for the Si and Sf , other forms can also be used. This study modified the above form and proposed an exponential form which reads  S S i i m d p i = - - - ( )1 λ κ ε (17)  S S f f m d p f = - - - ( )1 λ κ ε (18) In E�. (17) and E�. (18), λ and κ are the slopes of the compression line and the swelling line in a volumetric strain-logarithmic mean stress plane, respectively. Both of mi and mf are material constants, which control the speed of the destructuration. The greater mi and mf are, the faster the destructuration are, there- fore the faster the structured clay comes to the remoulded state. Since the main effect to be taken into account is the damage caused to the structure by both volumetric plastic strain εv p and deviatoric plastic strain εq p , the destruc- turation strain rate εd p , which is a coupling internal variable, will be assumed to have the following form, as seen in literatures[11, 14].   ε β ε βεd p v p q p= - +( )1 2 2 (19) where β is a material constant distributing the effect of volumetric and deviatoric plastic strain rates to the value of εd p . β could be set to 0.5 as a default value. The form of Eq. (19) suggests that for β =0 the destructuration is totally volumetric, while the destructuration is only controlled by deviatoric plastic strain when β =1. Substituting Eqs. (17), (18) and (19) into E�s. (13) and (14), one can obtain the incre- mental expression of pc * and M* . Substitut- ing the destructuration laws E�s. (12), (13) and (14) into E�. (7), one can obtain Kp , the plastic modulus at the bounding surface. K S p e p F p p p S F p p i c c i mi = +( ) - ¶ ¶ - - -( ) - ( ) ¶ ¶ æ è çççç ö ø ÷÷÷÷ 1 1 0 λ κ λ κ β1- 22 2 + ¶ ¶ æ è çççç ö ø ÷÷÷÷ -β F q Table 1: Parameters of the model for Osaka clay λ κ ν M Si0 Sf0 mi mf β ζ ψ 0.154 0.02 0.25 1.279 6.9 1.102 1.2 1.2 0.5 18.0 0.5 632 Functional materials, 24, 4, 2017 Yunliang Cui et al. / Formulation of structured bounding surface model ... - -( ) - ( ) ¶ ¶ æ è çççç ö ø ÷÷÷÷ + ¶ ¶ æ è çççç ö ø ÷÷2 12 2 3 2 q M S S F p F qf f mf λ κ β β1- ÷÷÷ 2 (20) The plastic modulus at the current stress point, that is Kp , can be derived by substituting Eq. (20) into Eq. (8). Therefore, the plastic flex- ibility matrix Cp can be obtained by Eq. (9). 4. Parameters determination and model verification Parameters of the proposed model can be determined in following ways: To begin with, λ , κ and the initial isotropic structure param- eter Si0 are determined by one-dimensional compression test. Critical state stress ratio M , Poisson’s ratio v and initial frictional structure parameter Sf0 are determined by triaxial com- pression test. Then, the adaptive parameter µ is determined by true trixial test. Finally, the material constants mi , mf , ς and ψ are determined by fitting the stress-strain curve of trixial compression. For Osaka Clay[4], the values of parameters λ , κ were obtained from an isotropic consolida- tion test[4], which gives λ =0.355/2.303=0.154, κ =0.0477/2.303=0.02. Si0 and Sf0 are used to denote the initial value of Si and Sf , re- spectively, which reflect the initial degree of the structure of natural soil. Si0 can be de- termined by one-dimensional compression tests on natural soil and the corresponding remoulded soil. Its value is e�ual to the ratio of py to p0 where py is the structure yield- ing pressure on the compression line of natu- ral soil and p0 is the pressure on the compres- sion line of the remoulded soil corresponding to the same void ratio with py . The concept of structure yielding pressure py is based on the assumption that structure begins to loose when compression pressure exceeds py and no structure loss occurs if compression pressure is less than py . As seen in Figure 5, the value of Si0 for Osaka clay is determined by Si0 = p py / 0 =94.1/13.7=6.9. Sf0 can be determined by trixial compression tests on natural soil and the corresponding remoulded soil. Its value is e�ual to the ratio of M* to M . M* and M are the critical state stress ratios of natural soil and the remoulded soil, respectively. As shown in reference[4], M* .= 1 41 , effective internal frictional angle of remoulded soil ϕ ' .= 31 8 . Then M = - = 6 3 1 279 sin sin . ' ' ϕ ϕ , and the value of Sf0 for Osaka clay is determined by Sf0 = M M* / =1.102. The adaptive parameter µ can be derived by comparing the predictions of the adaptive criterion with the experimental results from true triaxial test. mi and mf are used to control the isotropic destructuration rate and the frictional destructuration rate, respec- tively. Given that the isotropic destructuration and the frictional destructuration proceed at the same rate, their values can be assumed to be the same. The values of mi and mf for Osaka clay is determined to be mi = mf =1.2 by fitting the stress-strain curve of trixial compression test. β controls the relative contributions of εv p and εq p to the incremental destructuraion plastic strain εd p , so its value can be determined as β =0.5 in default before further study. ς and ψ are used for modulus interpolation between the bounding surface and the current stress point. Their values can be determined by fitting the stress-strain curve of trixial compression. In this way, the values of ς and ψ for Osaka clay are determined as ς = 18.0 and ψ =0.5. The triaxial compression test performed on sample TS5-2 of Osaka clay[4] is used herein to verify the model’s capabilities. In this test, the sample was compressed under undrained con- dition after isotropic consolidation. The initial stress state is σ σ σ1 2 3 78 4= = = . kPa, The initial void ratio of the specimen is e0 1 9= . . The optimized parameters used in these simu- lations are listed in Table 1. These optimized parameters are described as the reference pa- rameters. Figure 2 gives the simulation stress- strain curve and the test stress-strain curve of the consolidated undrained triaxial compression test. Figure 3 shows the comparison of the simu- lation stress path and the test stress path. A good agreement of simulation curves with experimen- tal curves can be seen in Figure 2 and Figure 3. This demonstrates that the proposed model is ca- pable of modeling the peak strength and strain softening of natural soft clay under the condition of consolidated undrained triaxial compression. The best way to validate the capabilities of the model is to validate it with a parameters- independent test. Parameters-independent test refers to a set of tests which have not been used to determine parameters. As a parameters-in- dependent test, test TS5-3[4] is simulated by taking the same parameters with test TS5-2. Test TS5-3 was also performed with consoli- dated undrained triaxial compression. The con- solidation stress is σ σ σ1 2 3 39 2= = = . kPa, which is much lower than that of test TS5-2. The comparisons of predictions and experi- ments of TS5-3 can be seen in Figure 3 and Figure 4. As shown in Figure 3 and Figure 4, the predictions and experiments of test TS5- 3 show worse agreement compared with test TS5-2. However, the agreement is good enough for engineering calculations. Modified Cam- clay model was also used to simulate test TS5- 3 to be compared with the structured bounding surface model in this work. The parameters Functional materials, 24, 34 2017 633 Yunliang Cui et al. / Formulation of structured bounding surface model ... of Modified Cam-clay model λ , κ , v and M have the same values with the proposed model, which are shown in Table 1. As seen in Figure 4, the comparisons indicate that Modified Cam- clay model is not able to predict the experimen- tal stress-strain curve and the proposed model can give a better agreement. Modified Cam- clay model predicts a much lower strength due to neglecting the structure of soil. A general indication of the influences of the fitting parameters on the response in the test is also shown in Figure 2. Such a study pro- vides assistance in the search for the optimized parameters to match experimental observa- tions. The conse�uences can be summarized as follows: Reducing mi and mf reduces the rate of destructuration, and hence raises the peak strength because destructuration occurs more slowly. Reducing ς reduces the plastic modu- lus and hence smoothes the peak. ψ has the similar influence with ς . Increasing ψ leads to a higher and sharper peak of the stress-strain relationship. The oedometer test was performed to get the one-dimensional compression results. The initial void ratio of the specimen is e0 1 9= . . It was first consolidated by vertical pressure σv kPa' .= 4 9 to be at the state of e = 1 8. , and then loaded stage by stage. The model param- eters are the same with those of the triaxial compression test, which are shown in Table 1. Figure 5 shows the comparison between the simulation curve and the experimental curve. It can be seen that the proposed model can well capture the structured characteristics that the compression of natural clay become faster when the pressure exceed the structure yield stress. This work introduces the destructuration law into a bounding surface model instead of a simple yield surface model, although the bounding surface theory makes the model com- plex. Inorder to show the importance of using the bounding surface, this study repeats some simulations of undrained triaxial compression tests of Osaka clay without the use of bound- ing surface and compares the new simulations with the one with the bounding surface. The change of bounding surface model to a regular yield surface model is done by modifying the formula of plastic modulus which uses bound- ing surface as yield surface, namely, b =1 in E�. (8). As seen in Figure 6, the comparisons show that the simulations with bounding sur- face are much better than the ones without bounding surface. Thus, from a practical per- spective, using the bounding surface in the pro- posed model is important. Besides, the use of bounding surface brings the advantage of sim- ulating cyclic loading which cannot be properly done by the model with regular yield surface. This is also one of the reasons to use bounding surface in this work, which will be discussed more in further study. 4. Conclusions Both isotropic destructuration and frictional destructuration of natural clay can be consid- ered by adopting the suggested destructuration law in bounding surface constitutive model. Fig. 2. Comparisons of prediction and experi- mental stress-strain curves of test TS5-2. Fig. 3. Comparisons of prediction and experi- mental stress paths of Osaka clay. Fig. 4. Comparisons of prediction and experi- mental stress-strain curves of test TS5-3. 634 Functional materials, 24, 4, 2017 Yunliang Cui et al. / Formulation of structured bounding surface model ... Isotropic destructuration was used to ad- dress the reduction of the bounding surface, and frictional destructuration addresses the decrease of the critical state stress ratio as a reflection of reduction of internal friction angle. The Isotropic destructuration and frictional destructuration laws were proposed by incor- porating isotropic destructuraion factor Si and frictional destructuraion factor Sf to revise isotropic hardening parameter pc and critical state stress ratio M . The evolution law for the Si and Sf has an exponential form. By simulating undrained triaxial test and one dimensional compression test on Osaka clay, it is proved that the formulated bounding surface model in this study can well capture the structured behaviors of natural soft clay. This model is capable of modeling the peak strength and strain softening of natural soft clay under the condition of consolidated undrained triaxial compression, and it can well reflect the struc- tured characteristics that the compression of natural clay become faster when the pressure exceed the structure yield stress. This bounding surface model can be changed to be a regular yield surface model by modify- ing the formula of plastic modulus. However, the simulations of experiments of the model with bounding surface are much better than the ones without bounding surface. Acknowledgment The support of Zheji- ang Provincial Natural Science Foundation of China (Grant no. LQ16E080007), National Natural Science Foundation of China(Grant no. 51508507) and Zhejiang Provincial Edu- cational Scientific Research project(Grant no. Y201533738) are gratefully acknowledged. References 1. C. S. Desai, J. GeoMech., 7, 83, 2007. doi: 10.1061/(ASCE)1532-3641(2007)7:2(83). 2. C. Hu, H. Liu. W. Huang, . Comp.Geotechn.,. 44,34, 2012. doi: 10.1016/j.compgeo.2012.03.009. 3. M. Taiebat, Y. F. Dafalias and R. Peek, Int. J.Num.Anal Meth.Geomech., 34, 1009, 2010, doi: 10.1002/nag.841. 4. T. Adachi, F. Oka, T. Hirata, T. Hashimoto, J. Nagaya, M. Mimura and TBS. Pradahan, Soils Found,. 35, 1. 1995. 5. L. Callisto and G. Calabresi, Geotechn, 48, 495, 1998. 6. H. S. Yu, Int. J. Num. Anal Meth. Geo- mech, 22,621,1998. doi: 10.1002/(SICI)1096- 853(199808)22:8<621::AIDNAG937>3.0.CO;2-8. 7. Y. F. Dafalias, E. P. Popov, Acta Mech., 21, 173,1975. 8. Y. F. Dafalias, E. P. Popov, “Plastic Internal Variables Formalism of Cyclic Plasticity,” Amer- ican Society of Mechanical Engineers, 1976. 9. Y. F.Dafalias, L. R. Herrmann, J.Eng. Mech., 112, 1263, 1986. 10. A. AI-Tabbaa, D. M. Wood, Proceeding of the 3rd International Conference on Numerical Models in Geomechanics, 1989, pp.91-99. 11. M. Rouainia, D. M.Wood, Geotechn., 50, 153, 2000. 12. M. Kavvadas, A. Amorosi, Geotechn., 50, 263, 2000. 13. L. Callisto, A. Gajo, D. M. Wood, Geo- techn..52,649,.2002.dol:10.1680/geot.52.9.649. 38840. 14. A . Gajo, D. M. Wood Int. J. Num. Anal Meth. Geomech, 25, 207, 2001. doi: 10.1002/nag.126. 15. J. R.Maranha, A. Vieira, Acta Geotech., 3, 259, 2008. 16. M. Kavvadas and G. Belokas, “An Anisotropic Elastoplastic Constitutive Model for Natural Soils,” Desai et al. (eds) Computer methods and advances in geomechanics, Balkema Rotterdam, 2001, pp.335–340. 17. G. Belokas, M. Kavvadas, Comp.Geotechn, 37, 737, 2010, doi: 10.1016/j.compgeo.2010.05.001. Fig. 5. Comparisons of prediction and experi- mental stress-strain curves of test TS5-3. Fig. 6. Comparison of predictions with and with- out bounding surface.

Formulation of structured bounding surface model with a destructuration law for natural soft clay

Institution

Ähnliche Einträge