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Green, R.A. and Marcuson III, W.F. (2014). “The = 0 Concept: Review of its Theoretical Basis and

Pragmatic Issues with its Implementation”, From Soil Behavior Fundamentals to Innovations in

Geotechnical Engineering, Honoring Professor Roy Olson (M. Iskander, J.E. Garlanger, and M.H.

Hussein, eds.) ASCE Geotechnical Special Publication (GSP) 233, 308-321.

The = 0 Concept: Review of its Theoretical Basis and Pragmatic Issues with

Implementation

Russell A. Green1, P.E., M.ASCE, and William F. Marcuson, III2, P.E., Hon.M.ASCE

1Professor, Department of Civil and Environmental Engineering, 120B Patton Hall, Virginia Tech,

Blacksburg, VA 24061; [email protected] Emeritus, Geotechnical Laboratory, U.S. Army Engineer Research and Development Center

(ERDC), 3909 Halls Ferry Road, Vicksburg, MS 39180-6199; [email protected]

ABSTRACT: The “ = 0 Concept” is central to the specification of the undrained shear strengthof saturated clays in engineering practice. While the theoretical basis for the Concept lies in

Mohr’s rupture hypothesis, its pragmatic value to geotechnical engineer s lies in Terzaghi’s

effective stress principle. Specifically, the = 0 Concept circumvents the onerous need forestimating (or measuring) excess pore water pressures in situ during construction, etc., which is

required to perform an effective stress analysis. Despite the significance of the = 0 Concept, asurvey of geotechnical engineering textbooks published over the last 60+ years showed that most

opt to just state the = 0 Concept without putting it into proper theoretical or contextual

perspective. The authors view this as a missed opportunity to put the various rules of thumb andsets of governing principles for the shear strength of soil into a consistent framework.

Accordingly, the objectives of this paper are to review the theoretical basis of the = 0 Conceptin the context of Mohr’s rupture hypothesis and Terzaghi’s effective stress principle and todiscuss some of the pertinent pragmatic issues with implementing the Concept. In relation to thelatter objective, the procedure for multi-staged rapid drawdown analysis for earthen dams

proposed by Duncan et al. and the procedure for determining the strength of liquefied soil proposed by Poulos et al. are reviewed. It is shown that while Duncan et al. fully address all the

pragmatic issues in implementing their procedure, Poulos et al. do not.

INTRODUCTION

A colleague who was preparing to write a new introductory textbook on geotechnicalengineering conducted an informal survey among geotechnical engineering faculty in the USasking about their likes and dislikes of existing texts. The responses to the survey showed analmost ubiquitous dislike for the coverage of shear strength (Fiori, 2008). The reason for this islikely because, in many ways, the texts mimic research papers and reports. And, shear strength

research in the US largely evolved following a semi-empirical approach wherein each soil type-stress state-drainage condition combination was treated as being unique and having its own set ofrules of thumb and governing principles. Few texts put these rules of thumb and sets of principles

into the context of a consistent mechanics-based framework. One example of this is the “ = 0Concept” (e.g., Skempton, 1948a), which is commonly invoked when specifying the undrainedstrength of saturated clays, wherein the soil is assumed to be non-frictional and purely cohesive(i.e., Tresca material). Accordingly, the objectives of this paper are to review the theoretical basis

of the = 0 Concept in the context of Mohr’s rupture hypothesis and Terzaghi’s ef fective stress

principle and to discuss some of the pertinent pragmatic issues with implementing the Concept.

Arguably the most significant theory in all of soil mechanics is Terzaghi’s effective stress

https://weboutlook.vt.edu/owa/redir.aspx?C=fe4ced962b4841a8a1fd6b00e25fc4fe&URL=mailto%3awfm3%40att.nethttps://weboutlook.vt.edu/owa/redir.aspx?C=fe4ced962b4841a8a1fd6b00e25fc4fe&URL=mailto%3awfm3%40att.net


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principle. This principle has two tenets: (1) deformation (i.e., volumetric strain) in soil is afunction of effective stress, and (2) shear strength of soil is a function of effective stress

(Terzaghi, 1936). Although various researchers had identified aspects of the effective stress principle prior to Terzaghi (e.g., Lyell, 1871; Reynolds, 1886; Fillunger, 1915), Terzaghi iscredited with fully developing the effective stress principle and with being the first to use it ingeotechnical engineering practice (e.g., Skempton, 1960; de Boer, 2005). The first tenet was

postulated in the 1920s and underlies consolidation theory (e.g., Terzaghi, 1924 and 1925). Thesecond tenet evolved with time, and to quote Skempton (1960): “Although this principle is of

paramount importance, its development and implications did not occur at once but over a periodof several years and, wholly or in part, in many different publications.” Even at the timeSkempton wrote this statement, the implications of the second tenet were not fully realized in thecontext of plasticity theory that was just being developed and applied to soil mechanics (e.g.,

Drucker and Prager, 1952; Mroz, 1963). And, even today, few geotechnical engineeringtextbooks mention plasticity theory in relation to Terzaghi’s effective stress principle, despite thefact that relevant aspects of this theory have been experimentally verified, as discussed later inthis paper.

The first investigations of the = 0 Concept for geotechnical engineering applicationsactually predate Terzaghi’s effective stress principle and were completely based on empiricallaboratory observations (Bell, 1915; Westerberg, 1926; Fellenius, 1927). However, by the mid-

1930s and throughout the 1940s, the pragmatic issues of implementing the Concept for specifyingthe undrained strength of saturated clays were seemingly a hot topic of research (e.g., Terzaghi,1936; Skempton, 1948a, b; Golder and Skempton, 1948; Skempton and Golder, 1948). Focus was

primarily on the relationship, and seeming inconsistencies, among the = 0 Concept, Terzaghi’seffective stress principle, and the orientation of the slip surface observed both in the laboratory

and in the field. From reviewing numerous papers written at this time, it became obvious that theeffective stress principle was not universally appreciated, as exemplified by the frequent lack of

distinction between and ’ (i.e., total and effective stress angles of internal friction,

respectively). Additionally, during the 1940’s and 50’s, the use of a failure envelope that was

independent of the applied [total] normal stress was referred to as a “ = 0 Analysis”, with the

moniker “ = 0 Concept” not coming until later (e.g., Lambe and Whitman, 1969). Although the

change in the name from “ = 0 Analysis” to “ = 0 Concept” may seem trivial, it clearly

signifies the evolving understanding of the relationship between the = 0 Concept and Terzaghi’s effective stress principle.

To better gage the evolution of the = 0 Concept, the first author performed a survey ofgeotechnical engineering textbooks published over the last 60+ years (i.e., Table 1: Note that noattempt was made to perform an exhaustive review of all geotechnical engineering textbooks

published since the 1930s; rather, the first author only reviewed the texts in his personal library).

The review showed that most of the texts just state the = 0 Concept without putting it into

proper theoretical or contextual perspective. (It is worth noting that in preparation of the finaldraft of this paper Professor Mick Pender, University of Auckland, performed a similar review ofseveral geotechnical engineering textbooks in his personal library that were not reviewed by the

authors, with his conclusion of the coverage of the = 0 Concept being the same as that of theauthors (Pender, 2013)). While this approach to covering the = 0 Concept is not necessarilyincorrect and, by all means, the authors view many of these texts as excellent, in t he authors’

opinion it is a missed opportunity to help put the various rules of thumb and sets of governing principles for the shear strength of soil into a consistent framework. This is just one example of a

potential plethora of reasons for the results of our colleague’s survey which showeddissatisfaction among academicians with the coverage of shear strength by existing geotechnicalengineering textbooks.

https://www.researchgate.net/publication/264739724_The_shear_resistance_of_saturated_soil?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/268915359_Die_Theorie_der_Hydrodynamischen_Spannungserscheinungen_undihr_Erdbautechnisches_Anwendungsgebiet?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/264739724_The_shear_resistance_of_saturated_soil?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/268915359_Die_Theorie_der_Hydrodynamischen_Spannungserscheinungen_undihr_Erdbautechnisches_Anwendungsgebiet?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==


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In the subsequent sections of this paper, the theoretical basis for the = 0 Concept is first presented. This is followed by a discussion of the pragmatic issues on implementing the Concept.

Finally, the procedure for multi-staged rapid drawdown analysis for earthen dams proposed byDuncan et al. (1990) and the procedure for determining the strength of liquefied soil proposed by

Poulos et al. (1985) are reviewed in the context of the = 0 Concept.

Table 1. Geotechnical engineering textbooks reviewed as part of this studyYear

PublishedAuthor(s) Title

1948D.W. Taylor Fundamentals of Soil Mechanics

K. Terzaghi and R.B. Peck Soil Mechanics in Engineering Practice, 1st ed.

1951 G.P. Tschebotarioff Soil Mechanics, Foundations, and Earth Structures

1962 G.A. Leonards, ed. Foundation Engineering

1963 R.F. Scott Principles of Soil Mechanics

1967 K. Terzaghi and R.B. Peck Soil Mechanics in Engineering Practice, 2nd ed.

1969T.W. Lambe and R.V.

WhitmanSoil Mechanics

1991 M.D. Bolton A Guide to Soil Mechanics

2002 V.N.S MurthyGeotechnical Engineering: Principles and Practices of

Soil Mechanics and Foundation Engineering

2005 J.K. Mitchell and K. Soga Fundamentals of Soil Behavior, 3rd ed.

2006 B.M. Das Principles of Geotechnical Engineering, 6t ed.

2007

M. Budhu Soil Mechanics and Foundations, 2nd ed.

R.L. Handy and M.G. SpanglerGeotechnical Engineering: Soil and Foundation

Principles and Practice, 5 th ed.

D.F. McCarthyEssentials of Soil Mechanics and Foundations: Basic

Geotechnics, 7th ed.

2008 R. Salgado The Engineering of Foundations

2011

R.D. Holtz, W.D. Kovacs, and

T.C. SheehanAn Introduction to Geotechnical Engineering, 2nd ed.

I. Ishibashi and H. Hazarika Soil Mechanics Fundamentals

THEORETICAL BASIS FOR THE = 0 CONCEPT

The theoretical basis for the = 0 Concept actually lies in Mohr’s rupture hypothesis, whichis not unique to soil mechanics but rather applies to a range of materials (Mohr, 1882). Mohr

hypothesized that an envelope of plastic states (i.e., failure envelope) exists in which the shearstress mobilized on the slip surface is a function of the normal stress on the slip surface. The

Mohr-Coulomb failure envelope that is commonly used in geotechnical engineering is a specificform of the more general Mohr hypothesis, where the Mohr-Coulomb envelope assumes the shearstress mobilized on the slip surfaces is a linear function of the normal stress acting on the slip

surface. If the Mohr hypothesis is correct, then a stress circle that is tangent to the failure

envelope represents a limit state (i.e., failure). Although the stress vectors corresponding to the point of tangency between the failure circle and failure envelope represent the stress componentsacting on the Coulomb slip surface (Coulomb, 1776), it is important to note that the entire failure

circle represents the stresses in the element at failure. As such, the stress vectors acting on any plane (other than planes parallel to the principal stress planes) cutting through the element are

unique to that plane at failure under the given stress conditions. This notion is central to the = 0

Concept (and to the shear strength of all soils in general, as discussed subsequently), but of thetextbooks listed in Table 1, only Lambe and Whitman (1969) emphasize this point. Their statedrule in this regard is that consistency is required between the assumed failure envelope and


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orientation of the slip surface, where the slope of the assumed failure envelope can be arbitrary.

This rule is illustrated in the retaining wall example shown in Figure 1. In this figure, a 6 m

high retaining wall has a dry sand backfill with ’ = 30°. A wedge analysis is performed todetermine the lateral force imposed on the wall by the backfill for active conditions. In Figure 1b,

the assumed failure envelope is as shown (i.e., ’ = 30° and c’ = 0 kPa, where c’ is the effectivecohesion of the soil) and the corresponding slip surface forms a 60° angle with the horizontal

(i.e., 45° + ’/2 = 60°). The stresses in a soil element at mid-depth in the backfill are taken as being representative of the stress state of the entire backfill and the stress circle for this soilelement is shown in Figure 1b. From a force balance of the wedge, the lateral force per unit widthinto the page imposed on the wall by the backfill is computed to be 113.4 kN/m.

The wedge analysis is repeated for the same retaining wall system in Figure 1c, this time

defining the failure envelope by an arbitrary angle of = 15°. Because the assumed failureenvelope has to be tangent to stress circle representing limit state of our soil element in the

backfill (i.e., the same stress circle used in Figure 1b), for = 15°, c has to be equal to 9.44 kPa,where c is the “apparent” cohesion of the soil. In this case the slip surface corresponding to the

assumed failure envelope has an inclination of 52.5° (i.e., 45° + /2 = 52.5°). Again, from a force balance of the wedge, the lateral force per unit width into the page imposed on the wall by the

backfill is computed to be 113.4 kN/m; the same as computed in Figure 1b! (Note the notationchange from ’ and c’ to and c used to define the Mohr-Coulomb failure envelopes in Figures

1b and 1c, respectively. In this paper, ’ and c’ are used exclusively to represent the Mohr -

Coulomb envelope used in conventional effective stress analyses. In contrast, and c are used todefine a failure envelope having an arbitrary slope.).

Finally, the wedge analysis is repeated one more time for the same retaining wall system in

Figure 1d, this time defining the failure envelope by an arbitrary angle of = 0°. Again, because

the assumed failure envelope has to be tangent to the stress circle representing limit state of our

soil element in the backfill (i.e., the same stress circle used in Figures 1b and 1c), for = 0°, c hasto be equal to 18.9 kPa. In this case the slip surface corresponding to the assumed failure

envelope has an inclination of 45° (i.e., 45° + /2 = 45°). And, once again from a force balance ofthe wedge, the computed lateral force per unit width into the page is 113.4 kN/m; the same as

computed in Figures 1b and 1c! Moreover, using Eqn (1), it can be shown that P a = 113.4 kN/mfor any arbitrarily assumed failure envelope that is tangent to the failure circle shown in Figure 1

and that has -90° < < 90°, with the corresponding inclination of the slip surface between 0° and

90° (i.e., 0° < f < 90°). (Note that in using Eqn (1), either or f is assumed and the remainingunknown parameters are then computed.)

( ) (1a) (1b)

(1c) (1d)

(1e)


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(1f) (1e)

where: Pa = lateral force imposed on the wall by the backfill for active conditions.

R = resultant force acting between the failure wedge and the stable backfill.W = weight of the failure wedge.

C = force acting on the assumed slip surface that is associated with the apparentcohesion of the backfill.

= unit weight of the backfill.L = length of the assumed slip surface.H = height of the wall.

c = intercept of the assumed failure envelope.

= angle of the assumed failure envelope.

f = angle of inclination of the assumed slip surface.

PRAGMATIC ISSUES WITH THE = 0 CONCEPT

As outlined in the preceding section, the assumed -c combination used to define the failureenvelope and corresponding inclination of the slip surface can range widely, yet still yield thesame result (e.g., Figure 1). However, given the semi-empirical path that the evolution of shear

strength concepts has followed, the -c combinations used to define the failure envelopes ingeotechnical engineering practice are often determined from various laboratory tests performed

on soil. While this is surely reasonable and preferred in many cases, the thorough understandingof the relationship between Terzaghi’s effective stress principle and Mohr’s rupture hypothesisthat was required to properly interpret the laboratory data and use it to make design decisions wasstill evolving in the formative days of geotechnical engineering. Of particular issue was the lack

of distinction between effective stress and total stress strength parameters (i.e., ’ and c’ versus

and c). For highly permeable soils (i.e., sandy or coarse grained soils), this was not much of anissue, but it was a significant issue for clays (e.g., Bell, 1915; Westerberg, 1926; Fellenius, 1927).

By the late 1940s, the significance of the change in water content (or lack thereof) of a

saturated clay sample during the application of both confining stress and shearing stress was

generally understood (e.g., Skempton, 1948a,b). Specific to the = 0 Concept, it was understoodthat for a saturated clay specimen under undrained conditions increases in confining stress were

carried by the pore water in the sample, with the effective stress in the sample remainingunchanged. And, consistent with the second tenet of Terzaghi’s effective stress principle, if the

effective stress in a sample does not change, the deviatoric stress required to cause failure in thesample does not change. This results in total stress failure circles having equal diameters, buthaving different total major and minor principal stresses at failure. The failure envelope drawn

tangent to the total stress failure circles is characterized by = 0° and c = Su, where Su is the

undrained shear strength of the soil. This is conceptually illustrated in Figure 2, where the totalstress failure circles from three unconsolidated-undrained (UU) triaxial tests performed onidentical, normally consolidated saturated clay samples are shown. For truly identical samples,the pore pressures developed during the shearing phase of the UU tests would be the same for all

tests, resulting in all the tests having the same effective stress failure circle, also conceptuallyillustrated in Figure 2.


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(a)

(b)

(c)

(d)

Figure 1. Retaining wall example illustrating the concept that the stresses at failure acting onany plane cutting through the element (other than planes parallel to the principal stress planes)

are unique to that plane.

6 m

Dry Sand:

= 18.9 kN/m3

’ = 30o

c’ = 0 kPa

3 m

56.718.9

’ = 30o

s’ (kPa)

t (kPa)

30oPa I

WI

RI

f = 60o

6 m

WI = 196.4 kN/m

RI = 226.8 kN/m

Pa I = 113.4 kN/m

56.718.9

c = 9.44 kPa

s (kPa)

t (kPa)

= 15o

Pa II

WII

RII

CII

15o

f = 52.5o

6 m

WII = 261.0 kN/m

CII = 71.4 kN/m

RII

= 257.7 kN/m

Pa II = 113.4 kN/m

56.718.9

c = 18.9 kPa

s (kPa)

t (kPa)

= 0o

Pa III

WIII

RIII

CIII

f = 45o

6 mWIII = 340.2 kN/mCIII = 160.4 kN/m

RIII = 320.7 kN/m

Pa III = 113.4 kN/m


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Figure 3. Conceptual illustration of the compensating error postulate proposed by two of the textslisted in Table 1.

It needs to be emphasized that the inherent assumption in the = 0 Concept that the slipsurface is oriented 45° from the plane of major principal stress by no means violates Terzaghi’s

effective stress principle. This is because the shear strength of the soil (i.e., S u) that is assumed to be mobilized along this slip surface is indeed a function of effective stress, not total stress. This

can be seen in the following equation, which was derived from the geometry of an effective stressfailure circle.

{

} (2)where s’1f = the major principal effective stress in the element at failure. However, fromexamination of data from isotropically consolidated-undrained compression (CIUC) triaxial tests

performed on normally consolidated saturated clay samples, it was observed that s’1f ≈ s’c ,

where s’c = consolidation stress (Rutledge, 1944). This allows Eqn (2) to be written in a muchmore useful form:

{

} (3)

Skempton and Bishop (1954) further generalized these equations for saturated clay samples thatare initially consolidated to K o conditions (i.e., at rest conditions) and sheared undrained intriaxial compression and extension (i.e., CK oUC and CK oUE, respectively):

[ ̅]( ̅) (CK oUC) (4a)

[ ̅]( ̅) (CK oUE) (4b)

where: K o = coefficient of lateral earth pressure at rest, and ̅ = Skempton’s pore pressurecoefficient at failure (Skempton, 1954), which is an index of the soil’s dilative tendencies amongother things.

Note that Su/s’c is rarely computed using Eqns (3) and (4), but rather, Su/s’c is measureddirectly in the laboratory by subjecting the soil to a stress path representative of that expected in

the field (e.g., Ohta et al., 1985). However, the importance of Eqns (3) and (4) is that they showthat the undrained shear strength of normally consolidated saturated clay can be specified without

the explicit quantification of the effective stress state in the sample at failure, which is required ifshear strength is specified in terms of the Mohr-Coulomb failure criterion. This alleviates the

s

t

qu undist

45o +’

2

tff undist

= 0o

s

t

= 0o

qu dist

Su dist ≈ tff undist

Su distSu undist

https://www.researchgate.net/publication/247947707_The_Pore-Pressure_Coefficients_A_and_B?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/247947707_The_Pore-Pressure_Coefficients_A_and_B?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==


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onerous task of having to estimate (or measure) excess pore pressures in situ during construction,

etc., and lies at the heart of the pragmatic value of the = 0 Concept for engineering practice

(italics used for emphasis). In this vein, the majority of the textbooks listed in Table 1 have

statements to the effect that “… the = 0 Concept is applicable to only saturated clays and silts.”This statement is technically incorrect. A more correct statement would be that the pragmatic

value of the = 0 Concept applies only to saturated clays and silts. As discussed above and as

illustrated in Figure 1d, the = 0 Concept can be used to specify the shear strength of any soil.However, excess pore pressures generated during construction processes rapidly dissipate inhighly permeable, saturated soils. As a result, the pore pressures at failure in these soils arehydrostatic or in steady state seepage conditions, and thus the effective stresses at failure can be

readily computed, allowing shear strength to be determined using the Mohr-Coulomb failurecriterion.

Finally, as stated above, the inclination of the observed slip surfaces in saturated clay

samples that were sheared undrained were closer to 45° + ’/2 from the plane of major principalstress than to 45°, which was used to give credence to Terzaghi’s effective stress principle (Terzaghi, 1936). However, the observed slip surfaces sometimes varied rather significantly from

45° + ’/2. Based on these observations, it was then hypothesized that the slip surfaces were

oriented 45° + ’e/2 from the plane of major principal stress rather than 45° + ’/2 (e.g., Terzaghi,1936; Gibson, 1953), where ’e is the Hvorslev effective friction parameter (Hvorslev, 1960).

Consequently (and among other reasons), ’e was often referred to as the “true angle of internalfriction” (e.g., Leonards, 1962). However, the results of a detailed laboratory study performed by

Rowe (1962, 1963) showed that this was not the case. Although this may have seemed at the timeto be a chink in the armor of Terzaghi’s effective stress principle, it is not. Starting in the 1950’s

– 1960’s, plasticity theor y was being developed and applied to soil mechanics (e.g., Drucker and

Prager, 1952; Mroz, 1963). Per this theory, the predicted orientation of the slip surface is 45° +

/2 from the plane on which the major principal stress acts, where is the dilatancy angle given by Eqn (5) and shown schematically in Figure 4 (e.g., Davis, 1968; Davis and Selvadurai, 2002;Salgado, 2008).

|| (5)

where: v = volumetric strain; z = shear strain in the x1

z-x3

zp plane (Figure 4); x1

z is the direction

of zero normal strain, and x3zp is the direction normal to x1

z (e.g., Salgado, 2008). Accordingly,

the Coulomb slip surface equals that predicted by plasticity theory only if = ’. However, for

most clays is considerably less than ’. Arthur et al. (1977) extended the plasticity theory totake into account strength anisotropy in soil and showed that the inclination of the slip surface

typically varied between 45° + ’/2 and 45° + ¼(+’). Of the textbooks listed in Table 1, only

Mitchell and Soga (2005) and Salgado (2008) discuss that the actual slip surfaces differ from theCoulomb slip surface, which is commonly assumed for effective stress analyses in engineering

practice. Fortunately, however, as discussed above, from an engineering perspective, the correctsolution to an analysis can be achieved as long as there is consistency in the assumed failureenvelope and analyzed slip surface, regardless of whether the analyzed slip surface is the actualslip surface or not.

https://www.researchgate.net/publication/264739724_The_shear_resistance_of_saturated_soil?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/235036847_Physical_Components_of_the_Shear_Strength_of_Saturated_Clays?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/252891807_The_Stress-Dilatancy_Relation_for_Static_Equilibrium_of_an_Assembly_of_Particles_in_Contact?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/245410267_Plastic_deformation_and_failure_of_granular_media_Geotechnique?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/235036847_Physical_Components_of_the_Shear_Strength_of_Saturated_Clays?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/252891807_The_Stress-Dilatancy_Relation_for_Static_Equilibrium_of_an_Assembly_of_Particles_in_Contact?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/245410267_Plastic_deformation_and_failure_of_granular_media_Geotechnique?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==https://www.researchgate.net/publication/264739724_The_shear_resistance_of_saturated_soil?el=1_x_8&enrichId=rgreq-96d42c03-ee33-4e68-98ab-3e2c40e76bd6&enrichSource=Y292ZXJQYWdlOzI2OTA1MjI5MDtBUzoxNzA2NjUzMzIxOTEyMzVAMTQxNzcwMTE5NDEzMA==


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proposed by Duncan et al. is completely consistent in its determination of the critical slip surfaceand its definition of undrained shear strength.

(a) (b)

Figure 5. Undrained strengths as used in the (a) Duncan et al. procedure and (b) Poulos et al. procedure.

Poulos et al. (1985)

The procedure proposed by Poulos et al. (1985) for determining the undrained strength of

liquefied soil for evaluating flow liquefaction potential is based on the steady state conceptinitially proposed by Casagrande (1936, 1938). Per Poulos et al. (1985), “The steady state ofdeformation for any mass of particles is that state in which the mass is continuously deforming at

a constant volume, constant normal effective stress, constant shear stress, and constant rate ofshear strain.” Hence, steady state deformation is an undrained phenomenon. Flow liquefaction is

predicted to occur when the driving shear stresses exceed the steady state strength (Ssu) of the

soil, where Ssu is given by Eqn (7) and shown in Figure 5b.

(7)where s1s and s3s are the total major and minor principal stresses at steady state, respectively, and

’s is the steady state friction angle (in terms of effective stress). As can be seen from Eqn

(7)/Figure 5b, Poulos et al. define the undrained shear strength analogously to Duncan et al.(1990). However, unlike Duncan et al., they do not give explicit directions on how to determinethe critical slip surface but, rather, just state that it should be determined by “… conventional

methods of stability analysis.” Accordingly, it is left up to the user of Poulos et al.’s steady statestrength to know to use an effective stress analysis to determine the critical slip surface, such thatconsistency is maintained between the definition of Ssu and how the critical slip surface is

determined. Fortunately, however, if the critical slip surface is determined using a total stressanalysis (as is likely to be the case), unforeseen failure is not imminent; rather, the factor of safety

against flow failure will be underestimated by {1/cos(’s) - 1}×100% (i.e., ~10% - 15% for loosesands).

CONCLUSIONS

As discussed above, the “ = 0 Concept” is widely used in practice in conjunction with totalstress analyses of saturated soils that have low permeability. The Concept circumvents theonerous need for estimating (or measuring) excess pore pressures in situ during construction, etc.,

which is required for performing effective stress analyses. However, while its pragmatic value iswidely understood and appreciated, its relationship to Mohr’s rupture hypothesis and Terzaghi’seffective stress principle is not. This is illustrated by the results of a review of geotechnicalengineering textbooks published over the last 60+ years, which showed that most texts opt only to

s

t

tff ’

s1f s3f

45o +’

2

s1f – s3f

2

s

t

Ssu ’s

s1ss3s

s1s – s3s

2

45o +’s

2


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state the = 0 Concept and do not put it into proper theoretical or contextual perspective. Theauthors view this as a missed opportunity to tie the various rules of thumb and sets of governing

principles for the shear strength of soil together by presenting them within a consistentframework. Additionally, two procedures that are used in high-end geotechnical engineering

practice that entail using undrained strengths of soil were reviewed in the context of the = 0Concept. It was shown that while the Duncan et al. (1990) procedure for rapid drawdown

analyses fully addresses all the pragmatic issues for implementing their procedure, the Poulos etal. (1985) procedure for determining the strength of liquefied soil does not.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the insightful review comments by Professors Chris

Baxter, University of Rhode Island, Radoslaw Michalowski, University of Michigan, TomBrandon, Virginia Tech, Mick Pender, University of Auckland, and Brady Cox, University ofTexas at Austin, as well as those by Dr. Kord Wissmann, Geopier Foundation Company, and the

two anonymous reviewers. Moreover, the authors acknowledge the many significantcontributions made by Professor Emeritus Roy E. Olson, University of Texas at Austin, to thefield of geotechnical engineering and his impact on our professional practice.

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