Bbm Shear Strength

7/27/2019 Bbm Shear Strength

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By : Ala Thajil



K=parameter describing the increase in cohesion with

suction.

N(s)=specific volume at p = ῥ

p at= atmospheric pressure

p◦= preconsolidation stress

p◦*= preconsolidation stress for saturated conditions

ῥ =reference stress

r= parameter defining the maximum soil stiffness

ß = parameter controlling the rate of increase of soilstiffness with suction

S = matric suction



Introduction

Unsaturated soils occur widely in the form of compacted fills and natural soils above thewater table. As a result there are manyproblems of geotechnical analysis or design

where an understanding of the mechanicalbehaviour of unsaturated soil is important.

Jennings & Burland (1962) and manysubsequent authors have shown that the

volume change and shear strength of unsaturated soil cannot be related to a singleeffective stress.



Introduction

(continued …) Instead, the total stress σ , pore-air pressure Ua, and

pore-water pressure Uw, must be combined in twoindependent stress tensors, typically chosen as the netstress σ - Ua and the matrix suction Ua - Uw, (Bishop &Blight, 1963; Fredlund & Morgenstern, 1977). There arenumerous examples in the literature in which either thevolumetric behaviour or the shear strength of unsaturatedsoil has been related to these two stress parameters (see,for example, Matyas & Radhakrishna, 1968; Fredlund,Morgenstern & Widger, 1978).

In saturated soil mechanics the important links betweenvolume change and shear strength have beenappreciated for many years, and generalized constitutivemodels based on critical state theory are now wellestablished.



Introduction

(continued …) More recently, results concerning the change of cohesion

and friction angle as a function of the suction have been

presented by Escario & Saez1986.

As far as constitutive laws are concerned, the first

integrated model able to predict the various aspects of unsaturated soil behaviour, called the loading_collapse

(LC) model, was presented by Alonso, Gens & Hight (1987)

The Barcelona Basic Model (BBM) proposed by Alonso etal. (1990) is perhaps the most widely used nonlinear

continuum constitutive model for unsaturated soils.



Introduction

(continued …) For a limited range of confining stress and applied

suction, shear strength tests reported by Fredlund et al.(1978),may be interpreted in the sense that anincrease in suction results in an increase in effectivecohesion while maintaining constant the (saturated)friction angle Ø.

Departures from this pattern have been reported byEscario and Saez (1986). The increase in strengthcannot continue indefinitely with applied suction. Somerecent results reported by Escario and Saez , whichextend the suction ranges used in previously publishedresults, indicate a non-linear increase of strength withsuction and a tendency towards a maximum at somegiven (high) suction.



FORMULATION OF MODEL

FOR ISOTROPIC STRESS

STATES Stress states inducing yield

A suitable stress space to describe isotropic states

is (p, s) where:(s=suction ,p=σ-Ua).

Consider an isotropic test in which a soil sample ata given suction (subsequently maintained) is

subjected to p-load increments along virgin states.

ν = N(s) - λ (s) In p/ῥ…………(1) where ῥ is a

reference stress state for which v = N(s).

On unloading and reloading (at constants) the soil

is supposed to behave elastically:

dv= -K*dp/p……………...…….(2)















The suction unloading (wetting) from 2 to 3 occurs in the elastic

domain.

dv= -Ks*ds/(s + Pat )………………( 4)

(l), (2) and (4), in equ. (3) we get:

N(s)-λ(s) (In p◦/ῥ)+K In(p◦/ p◦*)+Ks In((s+ Pat )/Pat ) =N(0)-λ(0) (In p◦*/ῥ)………………………(5)

which provides a relationship between p◦ and s as a function of

some reference stress values (p◦*, ῥ) and some soil parameters

(N(s), λ(s), K, Ks). A convenient choice of ῥ and N(s) to

simplify Equation(5) is to assume (Fig. 2(a))

Δv(ῥ)|°=N(0)-N(s)= Ks In((s+ Pat )/Pat )……( 6)

̾

(5) In (6) we get: (p◦/ῥ)=(p◦*/ῥ)ˆ[λ(0)-K][λ(s)-K] ……….(7)





An asymptotic maximum stiffness, which is probably

closer to real behaviour, is predicted by the alternativeequation

λ(s) = λ(0)[(l - r) expˆ(-ßs) + r]............(8)



It is proposed that whenever the soil reaches a maximumpreviously attained value of the suction s˳ , irreversiblestrains will begin to develop. As a preliminary and simplechoice, before more experimental evidence becomesavailable, the following yield condition

s = s˳ = constant……………….. (9) is adopted. s˳ has the meaning of the maximum past suction ever experienced by the soil and bounds the transition from theelastic state to the virgin range when suction is increased(Fig. 5). This yield locus is named SI (after suctionincrease). Both, LC and SI yield loci enclose an elasticregion in the (p, s) plane (Fig. 6). Adopting˳ a linear dependence between v and In (s + Pat), both in theelasto-plastic and elastic range, one may write, for virginstates

dv= -λs*ds/(s + Pat)………………(10)









0

0.05

0.1

0.15

0.2

0.25

0.20 0.30 0.40 0.50 0.60 0.70

Series1



Bbm Shear Strength

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