A Technical Note Regarding Interpretation of Cohesion and Friction Angle in Direct Shear Tests

A TECHNICAL NOTE REGARDING INTERPRETATION OF COHESION AND FRICTION ANGLE IN DIRECT SHEAR TESTS

There is often confusion expressed in the geosynthetics industry over how laboratory direct shear results should be interpreted, specifically whether one should use both the friction angle and cohesion (or adhesion) parameters. The attached technical note from the April/May 2009 issue of Geosynthetics provides some guidance regarding this question, as well as several other issues related to direct shear results.

Please note that this article is not intended to replace education or experience and should only be used in conjunction with professional judgment. In the end, all data should be evaluated by an experienced practitioner qualified to use the test results properly.

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A technical note regarding interpretation of cohesion (or adhesion) and friction angle in direct shear tests By Richard Thiel

Introduction with geosynthet- MatoriJf: Direct shearics is testing generally performed in accor- ç:::j GSE 40 mH HOPE Tex/Tex (White side towards GCl) Matooo/2: dance with ASTM D5321, Standard Test ,--:) Bentomat ON GCl (black sie up) Roll # 0000041 Subsrow: c--ì GSE 60 mil HOPE Tex-white I Tex-black (Black sie toward GCL) Method for Determining the Coefficient of Soil to Geosynthetic or Geosynthetic to 8000. , i i Peak Shear Geosynthetic Friction by the Direct Shear .v"', 7000 . Test Normal Shear Stess(§ , Method. There is also a related standard, \ , Point i Stss Strss 2.S"Displ i psi D6243, Standard Test Method for Deter- 6000L-----_._-+---~------_._------pst pst pst i " 1. 13.9 2000 940 730 mining the Internal and Interface Shear ì i \, : 2. 27,8 4000 2210 1450 ~sOOO; , Resistance of Geosynthetic Clay Liner by "\" 3. 55.6 8000 3800 2290 i '-. " 4. 111.1 16000 7200 the Direct Shear Method. This technical in : ", 3230 ~ 4000: . - - -. ~ -- ~ - ~ - -.----.------""-;:,...,:.: - - - -. ------. - --- . .---~ note applies to both equally. ~30ooL~:¿--~/~----~~~; ," , . '-'''-, --.."---. .---'-. ¡ Interpreting lab results l ,". /' ~ _._--: There is often confusion expressed in the 2000:- ./ / .- . r- industry regarding how laboratory re- " - sults should be interpreted, specifically: 1000L.; whether one should use both the fric- oi J'~---~-!" . tion angle and cohesion (or adhesion) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 parameters; whether cohesion should be HORIONAL DISA.ce (inches) ignored; whether secant friction angles The "gap" between shear boxes was set at 80 rrl (2.0 rr) The test specirns were flooded during testing. are more appropriate; what to do if the Hgh Norrrl Stresses. "Spsi (35 kP) was applied using air pressure. data are nonlinear; and how the data low Norml Strses, -:psi (35 kP) was applied using dead weights. should be interpolated or extrapolated. The tests were terrrnated after 3.0"(75 om) of displaceirnt unless otherwise noted. Tests were performe in general accordance w ith AS1M procedure D-5321 using a 8rainard-Kinrrn lG-112 direct shear rrchii The goal of this technical note is to with an effectie area of 12" x 12" (300 x300 rr). provide some guidance to take the mys- Each specirrn of 60 rrl georrrrrane w as cutto 14" x 20" and clari to th lower shear box. Avg, Asperit =0.025" tery out of these questions. In the end, Each specirn of 40 rrl geoirrrrane was cullo 14" x 16" and clari to th upper shear box. Avg. Asperit =0.016" all data should be evaluated by an expe- Each GC specirn was Hydrated for 48 hrs at the 250 psf. then placed, unclarred betw een upper & lower Has The grouped speciirns were consolidated 16 hrs, under the specified norrrl stress, then sheared rienced practitioner qualified to use the Shearing occurred at the interface of the GC's and 40 rrl georrrrrane specirns. test results properly. Extrusion of bentontte was noted on the surface of the 40 rrl 8. w Me side of the Go. contact area for points 2,3 & 4 The Fritin Angle and Adhesion (or Cohesion) resutts given here are based on a rrtherrtically deterrred bestftt line. What this note wil not do is go into Furter interpretation should be conducted by a qualified professional experienced in geosynthelc and geotehnical engineering. the subtleties of requesting, setting up, calibrating, and performing a direct shear test. That would be the subject of additional articles. This article wil also not definitively describe how direct the various factors affecting a design and make appropriate shear test data should be interpreted. That is the responsibil- decisions regarding test data interpretations. ity of a professional with specific expertise, and one article The tyical sequence of events related to direct shear testing could never presume to cover all of the considerations that includes the following: might apply to any unique design problem that might arise. 1. An engineer requests a direct shear test series to obtain That is why professionals are trained and mentored in basic data to help solve a problem. The request should be very geotechnical principles: so they can appropriately account for specific with regard to all the necessary details regarding

I Richard Thiel is a senior project manager at Vector Engineering Inc. in Grass Valley, Calif. The Designer's Forum column is refereed by Greg Richardson, Ph.D., P.E., a principal at RSG & Associates, Raleigh, N.C., www.rsgengineers.com

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sampling, specimen preparation and setup vary from as few as one, to perhaps as many as six points, depending on many factors in the testing devìce, and test execution beyond the scope of this article. The figure shows: (a) a table of the normal stresses vs. in accordance with both project-specific peak and large-displacement shear strengths measured at 2.5in. of displacement, (b) conditions and industry standards. graphs of the shear stress vs. displacement measurements, and (c) notes describing 2. A competent and certified labora- test conditions and observations. tory performs the test series in accor- There is adequate information in this figure for a trained practitioner to evaluate dance with the request and the industry and use the data. The laboratory has performed its duty, which is to measure and standard test method (e.g., ASTM D5321 report the shear strength under specified normal stresses (we are simplifyng the dis- or D6243). The laboratory reports results to the engineer. 3. The engineer interprets and applies the results to the project design.

What we are measuring in the direct shear test is shear strength

as a function of normal load. The test does not measure ¡Ifriction" orllcohesion:1 as these are simply mathematical parameters derived from the laboratory test results.

Ideally the engineer who originally specified and required the shear test would be the same one who reviews and interprets the results. Sometimes, such as in a third-party construction quality as- surance (CQA) project, an engineer other than the original designer wil commission and review the testing. Interactions with test laboratories and other engineers over time have shown that there are often misconceptions and misunderstandings related to the interpretation of direct shear test data. Thus, this article is intended to serve the purpose of helping project participants avoid confusion. The key point of this article is that what we are measuring in the direct shear test is shear strength as a function of normal load. The test does not measure "friction" or "cohesion;' as these are simply mathematical parameters derived from the laboratory test results. Figure 1 presents shear test results of a 4-point test for an interface between a textured geomembrane and a reinforced GCL. Three shear points, each at a dif- ferent normal stress, are the most common number of points used to run a test series, but the number of points could

www.geosyntheticsmagazine.infoIGeosynthetics 11 I Designer's Forum I

PEAK STENGTH cussion here by not elaborating on other 160 factors such as hydration, consolidation, Test Noal She ¡sec ¡Pek I POO StÐ st fr 140 I etc.), showing how the shear strength psI ps psf Ang changed with displacement of the two 1. 13.9 20 94 25 120 2- ZlB 40 2210 29 surfaces, and providing descriptive and 55fì c 3. ~~ 3! 25 ! lCX I observational notes. 4- 111.1 160 72 24 ~ I Figure 2 shows additional informa- ~ 80 i ~ t¡ tion that can be provided by a laboratory ~ 60 ~ in the form of a graph of the peak and Adhesion: 260 psI :i en -- large-displacement strengths plotted as a Fr/Ion Angle: 24 degrees 40 /' function of normal stress. Best-fit straight . V CoelJlentof 20 ~ lines, called Mohr-Coulomb strength en- 0.44 Frìclon: ~ velopes, named after the gentlemen who 0 ~ first publicized the relationship between a 20 40 60 80 1CX 1200 140 160 180 NORMAL STRSS (ps~ shear strength and normal stress, have NOTE: GR NO TO SC been drawn through the two sets (peak

and large-displacement) of data points. LD STENGTH ENveOPE Equations can be written for these lat 2.5 in. disolacementl 160 lines, as we learned in first-year algebra Test No She ¡Sec POO --,~Stes st ~ 140 c! 2.5- Dispacent class, in the form of y = mx + b. In this psi psf psf Ang 1. 13.9 73 20 case we define y as the shear strength (S); 20 120 2- ZlB 40 145 20 m as the slope of the line that we call the 3. 55.6 80 22 16 4- 111.1 160 32 11 ~ 1CX "coeffcient of friction" and whose angle en is phi (lj), which we call the "friction wen ~~ a:~ angle" (and thus tan(lj) is the slope of en Adhesion: 650 pst 60 the line); x is the normal stress (N); and :i~ en b is the y-intercept of the line that we FricfonAngle: 10 degrees 40 call either "adhesion" (a, usually used for . -- Coetklentof 20 l-I- 0,17 geosynthetics-only tests) or "cohesion" Frìclon: ,-i- (c, usually used for tests involving soils, 0 r- which wil be used for the remainder of a 20 40 60 80 1~~ 120 140 160 180 NORM STRSS (ps~ this article). NO: GR NOT 10 SCE

Mohr-Coulomb Figure 21 Example of supplemental data interpretation provided by the laboratory. In geotechnical engineering, we write the Mohr-Coulomb equation for these lines as:

S = No tan(lj) + c envelope are non conservative is pre- more apparent. True shear strength enve- This equation is written for peak, sented in Figure 3. Most shear strength lopes are found to be most accurately de- large-displacement, or residual shear envelopes are truly curved (nonlinear). scribed by hyperbolic functions. Giroud strength conditions. The fundamental This tendency for a curved failure en- et aL. (1993) provides a good method to points in this article regarding the pre- velope is exaggerated in Figure 3, but describe hyperbolic strength envelopes. sentation of the data in Figure 2 include can clearly be identified for the real-life 2. The values of phi and c should the following: strength envelopes presented in Figure be considered nothing more than 1. The Mohr-Coulomb envelope 2, in particular for large-displacement mathematical parameters to describe should not be extrapolated beyond conditions. the shear strength vs. normal stress the limits of the normal stresses under The Mohr-Coulomb model is merely over the normal-load range the test which the testing was conducted. To do a linear simplification of a portion of was conducted. It is perhaps better not so would never be conservative and, in the entire envelope over a limited range to think of "friction" and "cohesion" as fact, may be significantly nonconserva- of normal stresses. If testing were per- real material properties, but simply as tive. The reason that simple extension- formed over a large enough range of nor- mathematical parameters to describe extrapolations of the Mohr-Coulomb mal stresses the curvature would become the failure envelope.

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were measured in the test, as ilustrated Linear Approximation of Shear in Figure 3. Strength Over A Limited Ul Normal Stress Range Using the cohesion value at normal ë stresses extrapolated below the range of èñ.. testing, however, could have dire conse- II Shear strength "left on the table" if .iGl cohesion is ignored quences on the safety of a design project. tJ This problem may occur when designers ,//"i/'/"'Linear if cohesion strength is ignored envelope consider only the operational or final build-out of a facility and they ignore the Normal Stress Range Over construction condition. Several failures c Which Linear Approximation t Is Valid have occurred during construction be- L cause of this. For example, an embossed geomembrane against a geotextile may Normal Stress perform well under high normal loads Figure 31 Exaggerated schematic of true curvilinear shear strength envelope, linear by providing a good friction angle and interpretation over a selected normal stress range, and the penalty for ignoring cohesion. a modest y-intercept for operating and final build-out conditions. However,

under the low normal loads experienced Example Safe Shear Strength Results during construction of a thin soil ve- Extrapolations neer on a steep sideslope, testing might reveal that the adhesion extrapolated from the high-normal load results do not :::: I_~~---"-'---"'-"'r"'-"-"""------'j'--'-----'._==l====...r--=______exist at low normal loads. In this case, a 'i 2500 .1.___ ::::-fit straight line through . J more aggressive texturing that exhibits Q. t i ¡ a "Velcro.-effect" type of adhesion, or a i 2000 '1- ra~point~L very high friction angle, at low normal ~ 1500 _ _ typ +---.-.-1.... ~::~:~ forwrds loads may be needed and should be veri- fied at the proper normal loads. tJl '+1000 Extrapolate b- : backrdsi I 4. Figures 1 and 2 also report secant friction angles for each point. These are 500 through origin the angles of the straight lines from each 0- point drawn back to the origin. A key o 2000 4000 6000 8000 10000 concept regarding secant friction angles Normal Stress (pst is that you should never extrapolate a secant angle line beyond the normal load Figure 41 Example of safe shear strength extrapolation. for which it is measured. Secant values are conservative as long as the secant values are derived from a test whose normal stress was greater than the normal stresses In geotechnical practice with soils, a whole in those cases. Other situations of the design. They can quickly become there are situations and examples where may occur, however, where it is appropri- nonconservative if the same friction angle the cohesion parameter is evaluated sepa- ate, but those considerations are beyond is used for higher normal loads. rately from the friction parameter, but the scope of this article. 5. If users wish to extrapolate shear these are sophisticated considerations 3. In many, if not most, cases with strength data, Figure 4 ilustrates the only that involve very project-specific mate- geosynthetics where there is no reason "safe" way to accomplish this. Going from rials and conditions and should only be to ignore the cohesion value, it is impor- the low end of the Mohr-Coulomb enve- done by experienced professionals. tant to re-emphasize that shear strength lope and extrapolating backward, the data For many geosynthetic interfaces and should only be defined within the range can be extrapolated by drawing a straight in the context of many tyes of projects, of normal stresses for which the Mohr- line back to the origin. Going from the there is absolutely no reason to dissociate Coulomb envelope was derived. Ignor- high end of the Mohr-Coulomb envelope the slope of the line from its y-intercept, ing the cohesion may be unjustifiably and extrapolating forward, the data can and the shear strength should be taken as penalizing the shear strength values that be extrapolated by drawing a straight line

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3500 I I Best-fit straight line through c; 3000 data giving reults of c = 520 Š 2500 _ __ psf, and friction angle = 17.4° I ~ 2000 _ _ Data point I e (typ) èñ 1500 i ~ eu (1 1000 ....------r .c i tJ Specification line for friction 500 - angle = 20 degreesI andI c = 0 o i o 2000 4000 6000 8000 10000 Norma I Stress (pst)

Figure 51 Example project results where interpretation of test data results in lower friction angle than specified value, even though shear strength results are higher than the failure envelope implied by the specifications.

horizontally forward. This extrapolation als under zero normal stress (emphasis there is truly zero normal load, and that rule is safe only when considering a single added). Practically, this is determined as cohesion is the mathematical param- interface. When multiple interfaces are the y-intercept to a straight line relating eter of the y- intercept obtained from the involved, it is not safe to extrapolate a the limiting value of shear sLress that Mohr-Coulomb envelope. In the author's multi-layered system on the high side of resists slippage between two materials opinion these definitions are acceptable the Mohr-Coulomb envelope. and the normal stress across the contact as stated, but the audience should know Prom the discussion above, we can surface of the two materials:' that the definition of adhesion may con- now look at the ASTM standard D5321 This is actually two separate defi- flct with other definitions put forward in with more understanding and critical nitions, which are most likely not the the industry. Also, other authors have in- thought. The first thing to note is that the intent of the standard. The first part troduced other terms for the measurable title of that standard is poorly worded. of this definition, which defines the shear strength under zero normal load, The title is "Determining the Coefficient adhesion as the shear strength at zero such as Lambe and Whitman's (1969) of. . Friction. . ." This is somewhat mislead- normal stress, is not applicable relative "true cohesion," Interested readers can ing because it implies that the designer is to the test method. It could be true if we research ASTM D6243 and the literature simply after a coefficient of friction. In proposed to test the interface at zero and judge for themselves. fact, what designers need is a relation- normal load, but that is rarely done and ship between shear strength and normal generally of no use. The industry would Example problem 1 stress. Therefore, a more appropriate title be better served by deleting the first part The following situation ilustrates a com- for this method would be "Determining of the definition. In reality, the second mon example of a problem that occurs the Relationship between Shear Strength part of the definition is the controlling with shear test data interpretation: and Normal Stress for Soil-to-Geosynthetic aspect of the definition, and the "y-in- . A specification is written that or Geosynthetic-to-Geosynthetic Interfaces tercept" concept is the true nature of the requires a certain minimum inter- Using the Direct Shear Method." Note that adhesion value which, as stated above, is face friction angle to be achieved ASTM D6243 has already rectified this simply a mathematical parameter. between a textured geomembrane problem in its title. Note that ASTM D6243 has a differ- and a GCL. For purposes of this ex- Another misleading element in ent set of definitions, and it is not clear ample, the requirement is 20° peak ASTM D5321 is the definition of ad- if those definitions are unique to that shear strength for normal loads hesion (which applies equally to cohe- standard, or are intended to be industry tested between 2,000 and 8,000 sion), which it states as: "The shearing norms. ASTM D6243 suggests that ad- pounds per square foot (psf). resistance between two adjacent materi- hesion is the true shear strength when . The laboratory results, shown as an

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3500 Best-fit straight line through per-normal load shear strength test result data giving results of c = 520 i¡ 3000 plots below the specification line. Based psf, and friction angle = 17.4° .ë 2500 on the failing result of the upper-normal load test, most reviewers would initially ¡ 2000 ~ say that this is a noncompliant test result èñ 1500 and fais to meet the specification. ~ i In the author's experience, curved m 1000 -----+- failure envelopes are common, and the .c tJ 500 Specification line for friction tendency for the highest normal-load angle = 22 degrees and c = 0 result to fall beneath a straight-line fric- o i iI I¡ tion-based specification is not unusuaL. In this case, a more detailed review by o 2000 4000 6000 8000 10000 the design engineer might reveal that the Normal Stress (pst) shear strengt results provide an acceptable factor of safety for the intended purpose. It Figure 61 Example project results where the two lower points are above the specification and the may be that the additional strengt capacity upper point is below the specification. provided in the lower normal load range that is above the specification more than offsets the reduced strength capacity in the example in Figue 5, report a best-fit It is possible that the original specifier upper normal load range that is below the Mohr-Coulomb peak strengt enve- had taken into account the potential for specification. Clearly, the only person who lope with shear strengt parameters of cohesion, and had wished to discount can evaluate this issue, and who carries the 500 psf cohesion and 15° friction. Fig- cohesion, and really wanted a true mini- requisite authority and responsibilty is the ure 5 also shows the line representing mum friction angle of20°. If the specifier design engineer. the minimum project specification. were truly that sophisticated and had The following lessons can be gleaned Inspection of Figure 5 shows that the such complex reasoning, then more than from this example: shear strengths achieved in the direct likely the specification would have also . Design engineers often attempt shear test plot above the shear strength been more sophisticated in explaining to specify a unique set of shear envelope required by the specification. these constraints on the test results. strength parameters as a minimum Even though the plot appears to clearly In the author's experience it is rare requirement for a given design. indicate that the minimum required that other designers and specifiers are Tn reality, there may be an infinite shear strength is achieved by the prod- discounting cohesion with geosynthetic combination of shear strength ucts tested, the author has experienced interfaces, and usualy it is simply a matter variations over the applicable range

several projects where one of the proj- of proper interpretation and communica- of normal loads that may satisfy ect parties (e.g., the design engineer or tion of the design intent compared to the the stabilty and shear resistance perhaps a regulator) have declared the actual test results. Nevertheless, as stated requirements, and many of these test a failure because the reported Mohr- at the beginning of this article, it is not combinations may have a portion Coulomb friction angle was less than the the intent of this article to provide guid- of their failure envelopes that fall specified friction angle. ance and suggestions on interpreting test below the specification. In the author's opinion, in many cases results. Rather, the intent is to shed light . The tendency for natural and geo- involving this particular interface, there is on some common misunderstandings. synthetic interfaces to yield curved no reason to consider this a failing test. failure envelopes can present a This example ilustrates the confusion Example problem 2 challenge to engineers, owners, and that might arise when specification is writ- The following problem has the same lab- manufacturers who wish to optimize ten in terms of a shear -strengt parameter, oratory shear strength results as Problem a design using simple straight-line when the real objective is to achieve a 1, but the specification requirement is shear strength specifications. certain value of absolute shear strength. increased to 22° peak shear strength. . A learned interpretation of direct Even though the materials provided the The relationship between the test re- shear testing data by an experienced shear strength required by the specifica- sults and the specification is shown in practitioner may alow acceptance tion, there is some confusion because one Figure 6. In this example, the two lower- of apparently faiing test results. This of the strength parameters did not meet normal load shear strength test results plot can occur because overly simplistic the specified value for that parameter. above the specification line, while the up- specification parameters may not ac-

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count for other combinations of shear 2. Proper data interpretation may decision of whether to use peak, post- strength results that could provide ac- avoid unnecessary penalization of the peak, or residual shear strength. This ceptable overal shear resistance. results by arbitrarily reducing the mea- discussion is beyond the scope of this sured values. technical note, and anyone commission- Summary 3. This understanding can improve a ing and interpreting shear strength test- The direct shear test measures shear designer's sensitivity to how important it ing should be well versed in the issues strengths as a function of normal stress. is that shear strength is measured within surrounding this topic, as well. Period. the range of normal stresses that repre- The test does not measure "friction sent the design. Thus, the only defend- Acknowledgements angle" or "cohesion;' as these values are able extrapolation of data should be: (a) The author would like to thank Richard Erickson and Chris Athanassopoulos for their review of this article. parameters that are derived from the test back through the origin from the lowest

results. Consideration of "friction angle" normal stress, and (b) horizontally from References and "cohesion" simply as mathemati- the highest normal stress. Giraud, J.P., Darrasse, J., and Bachus, R.C., (1993). cal parameters used to describe shear 4. Laboratory shear strength data "Hyperbolic Expression for Soil-Geosynthetic or strength data is of great benefit to practi- should be interpreted by a qualified Geosynthetic -Geosynthetic Interface Shear Strength'; Geotextiles and Geomembranes, Vol. 12, No.3, pp. 275-286. tioners for the following four reasons: practitioner experienced in the use and 1. Interpretation of laboratory shear application of the results. Lambe, iW. and Whitman, R.V" (1969).Soil Mechanics. John Wiley & Sons, New York, NY. 01 strength data should not be confused Often of much more importance than with the mathematical parameters used deciding whether to include or omit the to describe it. cohesion (or adhesion) parameter is the

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