Cyclic behaviour of a sand steel plate interface

NOTE / NOTE

Cyclic behaviour of a sand – steel plate interface

Tahirou Assane Oumarou and Erman Evgin

Abstract: This paper presents the results of an experimental study on the mechanical behaviour of an interface be-tween sand and a steel plate. A simple shear type interface apparatus is used. Tests are conducted under a two-way,displacement-controlled cyclic loading condition. The effects of the initial soil density, number of displacement cycles,magnitude of normal stress, and amplitude of tangential displacement on the cyclic response of the interface are inves-tigated. The interface behaviour is presented in terms of the shear stress mobilized on the interface, the changes takingplace in sample height, and the components of tangential displacements resulting from soil deformation and from slipbetween the soil and the steel plate during displacement cycles.

Key words: cyclic behaviour, soil–structure interface, simple shear, slip, laboratory testing.

Résumé : Dans cet article, on présente les résultats d’une étude expérimentale sur le comportement mécanique d’uneinterface entre le sable et une plaque d’acier. Un appareil d’interface de type cisaillement simple a été utilisé. Des es-sais ont été conduits sous une condition de chargement cyclique contrôlé avec déplacements aller-retour. On a étudiéles effets de la densité initiale du sol, du nombre de cycles, de la grandeur de la contrainte normale et de l’amplitudedu déplacement tangentiel et de la réponse cyclique de l’interface. Le comportement de l’interface est présenté en ter-mes de la contrainte de cisaillement mobilisée sur l’interface, des changements se produisant dans la hauteur del’échantillon, et les composantes des déplacements tangentiels résultant de la déformation du sol et du glissement entrele sol et la plaque d’acier durant les cycles de déplacements.

Mots clés : comportement cyclique, interface sol-structure, cisaillement simple, glissement, essais en laboratoire.

[Traduit par la Rédaction] Assane Oumarou and Evgin 1704

Introduction

The design of many civil engineering structures such asdeep foundations, earth retaining structures, and buried pipe-lines requires an understanding of the mechanics of theinteraction between soils and structures. During the interac-tion, loads are transferred from one medium to the other.The determination of loads and the calculation of displace-ments are necessary for the design of safe and economicalstructures. The load–displacement behaviour of interfacesdepends on the soil properties, type of loading, surfaceroughness, and stiffness of the structural material.

The behaviour of interfaces has been the subject of manyexperimental studies. The majority of earlier studies, such asthat by Potyondy (1961), dealt with the monotonic behav-iour of interfaces. Monotonic loading, however, is a simpletype of loading. In reality, many civil engineering structuresmust also endure cyclic loading conditions. Cyclic loads can

be quite destructive and may result from several sources in-cluding earthquakes, waves in a marine environment, andmachine operation. Therefore, a sound understanding of thecyclic response of interfaces is of significant importance.

Experimental studies on cyclic behaviour of interfaceswere conducted by various investigators such as Desai et al.(1985), Uesugi et al. (1989, 1990), Al-Douri and Poulos(1992), Airey et al. (1992), Fakharian and Evgin (1996,1997), Shahrour and Rezaie (1997), Mortara et al. (2002),and DeJong et al. (2003). Desai et al. (1985) observed thatthe cyclic interface behaviour is influenced by the amplitudeof tangential displacement, normal stress, density of sand,and number of loading cycles. The study dealt mainly withthe evolution of the mobilized shear stress. The effect of thesame influential factors on vertical (normal) displacementwas reported by Al-Douri and Poulos (1992). The influenceof these factors on sliding displacement (i.e., slip) was notinvestigated, however. Uesugi et al. (1989, 1990) used a sim-ple shear type soil container and measured the componentsof tangential displacement separately, i.e., slip and the soildisplacement at the interface. They observed that slip in-creased with an increase in the number of cycles. DeJong etal. (2003) conducted cyclic interface tests and determinedthe percentage of slip occurring at the interface. The influ-ence of normal stress and density on the amount of slip wasnot fully addressed, however.

Can. Geotech. J. 42: 1695–1704 (2005) doi: 10.1139/T05-083 © 2005 NRC Canada

1695

Received 23 August 2004. Accepted 27 September 2005.Published on the NRC Research Press Web site athttp://cgj.nrc.ca on 6 December 2005.

T. Assane Oumarou and E. Evgin.1 Department of CivilEngineering, University of Ottawa, Ottawa, ON K1N 6N5,Canada.

1Corresponding author (e-mail: [email protected]).

This investigation deals with the influence of sand density,number of displacement cycles, magnitude of normal stress(σn), and amplitude of tangential displacement (A) on theshear stress mobilized at the interface, slip, and change insample height. Earlier studies by Evgin and Assane Oumarou(2004a, 2004b) are extended to dense sand interfaces.

Experimental study

A simple shear type interface apparatus was used(Fakharian and Evgin 1996). The soil container was formedfrom a stack of aluminum plates, which had a horizontalcross-sectional area of 100 mm × 100 mm and a maximumheight of 29 mm. Unlike direct shear type containers, the useof the stack of aluminum plates has the advantage of allow-ing separate measurements of slip and the displacement dueto soil deformation (Uesugi and Kishida 1986).

The interface is between a steel plate and dry quartz sand.The normalized surface roughness (i.e., as defined byKishida and Uesugi 1987) of the steel plate is 0.018. Theroughness is maintained constant by sand blasting the sur-face of the steel plate frequently. The sand grains have asubangular shape, an effective size of 0.86 mm, and a meandiameter of 1.36 mm. The minimum and maximum void ra-tios of this sand are emin = 0.673 and emax = 1.014, respec-tively. The void ratio of the loose and dense sand samplesbefore shearing began in the interface tests is 0.94 and 0.70,respectively.

Eighteen cyclic tests were performed as described in Ta-ble 1. The normal stress was maintained constant duringeach test. Sand samples were loose in tests 1–9 and dense intests 10–18. In addition to the density of soil, the magnitudeof normal stress and the amplitude of tangential displace-ment are used to identify each test. The influence of normalstress was studied by subjecting the samples to a normalstress with three different magnitudes (i.e., 100, 200, and300 kPa). In the same manner, the effect of the amplitude oftangential displacement was investigated by using three dif-ferent displacement amplitudes (i.e., 1, 2, and 3 mm). Eachsample was subjected to 10 two-way displacement cycles.The term initial loading or cycle IL is used to refer to theinitial part of the shear stress versus tangential displacementcurves starting from the rest position (zero displacement) toa displacement of 1, 2, or 3 mm depending on the value of Ain a particular test.

The results of six cyclic tests are presented in graphicalform. In addition, the important parts of all measurementsare tabulated. Figures 1–3 show the results of three testsconducted on loose sand with a normal stress of 200 kPa.The tangential displacement amplitude in these three testswas 1, 2, and 3 mm, respectively. Figures 4–6 show the re-sults of tests conducted on dense sand under similar condi-tions. The label of the horizontal axis in Figs. 1–6, i.e.,“Tangential displacement,” refers to the displacement of thesteel plate. The slip at the interface is obtained by subtract-ing the measured value of soil displacement from the tan-gential displacement of the steel plate. The measurementsrelated to the cycles labeled as IL, 1, 2, 5, and 10 are pro-vided in Tables 2 and 3.

Discussion

The behaviour of the interface using loose sand and densesand is examined separately.

Behaviour of loose sand – steel plate interface

Influence of number of cyclesIn general, the shear stress mobilized at the end of each

displacement cycle increases as the number of cycles in-creases (Figs. 1a, 2a, 3a). The rate of increase in mobilizedshear stress diminishes with an increase in the number of cy-cles (Fig. 7a). The curve corresponding to A = 1 mm showsthat the maximum value of shear stress is reached at thesixth cycle. The other two curves labeled A = 2 and 3 mmindicate that the mobilized shear stress increases to a maxi-mum value at the end of the second to third cycles. Thenumber of cycles has a similar effect on the mobilized shearstress in the experiments with normal stress of 100 and300 kPa (Table 2). With respect to the influence of numberof cycles on the shear stress mobilized in loose sand inter-face tests, comparable results were reported by Desai et al.(1985) and Shahrour and Rezaie (1997).

Sample compression is indicated as negative normal dis-placement. Its absolute value increases at a diminishing ratewith an increase in the number of cycles (Figs. 1b, 2b, 3b,7b). This indicates that the sand sample, which was initiallyloose, becomes denser. Al-Douri and Poulos (1992) andShahrour and Rezaie (1997) have also reported an increasein compression with an increase in the number of cycles.

The experimental results given in Figs. 1c, 1d, 2c, 2d, 3c,and 3d suggest that during the initial monotonic loadingonly a small amount of slip is experienced before the peakstress is reached. After the peak shear stress is mobilized,however, the amount of slip increases substantially. Thistype of behaviour is repeated every time the direction of the

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TestNo.

State ofdensitya

Normal stress,σn (kPa)

Amplitude ofdisplacement, A (mm)

1 L 100 12 L 100 23 L 100 34 L 200 15 L 200 26 L 200 37 L 300 18 L 300 29 L 300 310 D 100 111 D 100 212 D 100 313 D 200 114 D 200 215 D 200 316 D 300 117 D 300 218 D 300 3

aD, dense sand (relative density Dr = 92%); L, loose sand (Dr = 22%).

Table 1. Description of the 18 tests conducted during the investigation.

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Assane Oumarou and Evgin 1697

Fig. 2. Cyclic test on loose sand – steel plate interface (σn = 200 kPa, A = 2 mm).

Fig. 1. Cyclic test on loose sand – steel plate interface (σn = 200 kPa, A = 1 mm). IL, initial loading. The numbers 1 and 10 refer todisplacement cycles (see Tables 2 and 3).

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Fig. 3. Cyclic test on loose sand – steel plate interface (σn = 200 kPa, A = 3 mm).

Fig. 4. Cyclic test on dense sand – steel plate interface (σn = 200 kPa, A = 1 mm).

tangential displacement is reversed. These observations aresimilar to those made by Uesugi and Kishida (1986) andUesugi et al. (1989) but differ from those made by DeJonget al. (2003), who reported a relatively constant percentageof slip during monotonic loading.

The slip increases with an increase in the number of cy-cles (Figs. 1d, 2d, 3d). This trend is illustrated in Fig. 7c byplotting the percentage of slip (i.e., the slip portion of the to-tal tangential displacement) versus the number of cycles. Forexample, in the test with σn = 200 kPa and A = 2 mm, the

percentage of slip increased from 11% at the end of IL to69% at the end of the tenth cycle. DeJong et al. (2003) alsoreported that the percentage of slip increases with an in-crease in the number of cycles.

Influence of normal stressThe tests conducted with the same value of A but with dif-

ferent values of normal stress show that the shear stress mo-bilized at a given tangential displacement is larger for highernormal stress values. The ratio of mobilized shear stress to

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σn = 100 kPa σn = 200 kPa σn = 300 kPa

Cycle No. 1 mm 2 mm 3 mm 1 mm 2 mm 3 mm 1 mm 2 mm 3 mm

Shear stress mobilized (kPa)IL 31.2 39.3 44.7 75.3 84.1 93.6 114.6 135.6 142.4

1 41.7 47.8 49.5 91.6 104.7 107.8 139.7 159.0 164.52 46.4 50.9 50.5 100.7 110.5 111.6 155.0 170.2 167.15 52.5 51.6 48.8 110.2 109.5 107.8 171.9 175.3 166.8

10 55.3 50.5 47.5 117.0 108.1 105.4 179.7 174.6 164.8Normal displacement (mm)IL –0.173 –0.267 –0.279 –0.264 –0.314 –0.325 –0.307 –0.321 –0.329

1 –0.497 –0.798 –0.841 –0.621 –0.778 –0.879 –0.690 –0.872 –0.8992 –0.838 –1.286 –1.343 –0.997 –1.235 –1.461 –1.083 –1.383 –1.4685 –1.394 –1.970 –2.066 –1.567 –1.966 –2.143 –1.682 –2.112 –2.164

10 –1.809 –2.381 –2.465 –2.040 –2.392 –2.560 –2.168 –2.612 –2.614Soil displacement (mm)IL 0.940 1.721 2.534 1.005 1.775 2.784 0.897 1.768 2.538

1 0.891 1.584 2.155 0.917 1.529 2.142 0.808 1.651 2.0772 0.853 1.408 1.806 0.848 1.374 1.746 0.745 1.430 1.5945 0.742 1.067 1.284 0.738 0.901 1.085 0.651 1.004 1.092

10 0.622 0.834 0.967 0.604 0.629 0.805 0.510 0.645 0.751

Table 2. Summary of experimental results at the end of selected cycles for a loose sand – steel plate interface, showing the influenceof normal stress (σn) at displacement amplitudes (A) of 1, 2, and 3 mm.

σn = 100 kPa σn = 200 kPa σn = 300 kPa

Cycle No. 1 mm 2 mm 3 mm 1 mm 2 mm 3 mm 1 mm 2 mm 3 mm

Shear stress mobilized (kPa)IL 56.3 60.3 60.3 118.0 126.8 129.5 183.7 192.5 189.1

1 56.7 56.0 55.0 119.0 125.4 118.7 184.8 187.5 176.62 57.3 53.6 52.6 116.3 120.0 113.3 184.7 175.6 171.65 55.0 50.9 48.8 112.9 114.3 109.8 185.1 170.9 163.7

10 53.2 48.2 46.8 111.5 111.2 106.8 183.4 168.1 162.1Normal displacement (mm)IL 0.083 0.188 0.404 –0.018 0.094 0.170 0.000 0.112 0.177

1 0.074 0.233 0.471 –0.056 0.137 0.260 –0.118 0.076 0.1572 –0.013 0.139 0.388 –0.163 0.013 0.123 –0.268 –0.091 0.0085 –0.163 0.007 0.246 –0.358 –0.202 –0.136 –0.473 –0.358 –0.300

10 –0.273 –0.134 0.112 –0.468 –0.421 –0.313 –0.625 –0.527 –0.509Soil displacement (mm)IL 0.680 1.001 1.262 0.857 1.171 1.341 0.857 1.132 1.345

1 0.564 0.799 1.144 0.606 1.056 1.327 0.680 0.917 1.0422 0.546 0.747 1.003 0.526 0.899 1.003 0.606 0.756 0.8465 0.449 0.622 0.881 0.405 0.714 0.821 0.512 0.559 0.599

10 0.364 0.550 0.709 0.308 0.530 0.663 0.442 0.501 0.499

Table 3. Summary of experimental results at the end of selected cycles for dense sand – steel plate interface, showing the influence ofnormal stress (σn) at displacement amplitudes (A) of 1, 2, and 3 mm.

normal stress (stress ratio) is used in the presentation of re-sults. Figures 8a and 8b (A = 1 and 3 mm, respectively)show that the maximum stress ratio is reached in all tests, al-though it requires more displacement cycles when A =1 mm. These results also indicate that the stress ratio in-creases with increasing normal stress.

The magnitude of normal stress influences the amount ofnormal displacement during shearing as shown in Figs. 8c

and 8d. For larger normal stress values, there is a greaterchange in sample height. This observation is in agreementwith the results published by Al-Douri and Poulos (1992). Itcan also be added that the effect of normal stress on the nor-mal displacement is more pronounced for a smaller ampli-tude of tangential displacement. Moreover, the experimentalresults given in Table 2 show that the soil displacement por-tion of the tangential displacement at the interface tends todecrease with an increase in normal stress values. In otherwords, the amount of slip has a tendency to increase as thenormal stress becomes larger.

Influence of tangential displacement amplitudeThe amplitude of tangential displacement influences the

magnitude of shear stress developed during displacement cy-cles (Figs. 1a, 2a, 3a). The shear stress mobilized at a givennumber of cycles and a normal stress value is larger forlarger values of A for the first few cycles. The nature of thisrelation is reversed, however, during the remaining cycles, asillustrated in Fig. 7a.

In addition, the amplitude of tangential displacement in-fluences the amount of increase in shear stress. For example,considering the test with A = 1 mm and σn = 100 kPa (Ta-ble 2), the shear stress increases from 31.2 kPa at the end ofIL to 41.7 kPa at the end of the first cycle. This representsan increase of 33.7%. For the test conducted under the samenormal stress with A = 3 mm, the shear stress increases from44.7 kPa at the end of IL to 47.5 kPa at the end of the firstcycle. The corresponding increase in shear stress is 6.3%.These results indicate that the increase in shear stress islarger for smaller values of tangential displacement ampli-tude.

The amount of cumulative normal displacement increaseswith an increase in the number of cycles, but the soil samplemay contract and dilate within a displacement cycle. For A =1 mm (Fig. 1b), the sand sample contracts continuously withlittle dilation. For A = 2 mm and 3 mm (Figs. 2b and 3b, re-spectively), however, the sample contracts in cycle IL, but inthe subsequent cycles it displays contraction initially, fol-lowed by dilation. These observations suggest that A affectsthe normal displacement behaviour.

The sample height changes more with larger tangentialdisplacement amplitudes (Fig. 8b). Similar results were re-ported by Al-Douri and Poulos (1992). Although the changein sample height becomes larger with increasing values of A,the overall difference between the results of tests with A =2 mm and those with A = 3 mm is small. This observationsuggests that there is a limiting value of amplitude afterwhich increasing the value of A would not significantly af-fect the change in sample height. This type of behaviour canbe attributed to the fact that the soil sample cannot compressindefinitely.

The percentage of slip taking place at the interface in-creases as the amplitude of tangential displacement increases(Fig. 7c). The amount of slip at the end of the initial loadingfor A = 1, 2, and 3 mm when σn = 100 kPa represents 6%,14%, and 16% of the total tangential displacement of thesteel plate, respectively. These percentages increase to 38%,58%, and 68%, respectively, at the end of the tenth cycle(Table 2).

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Fig. 7. Effect of tangential displacement amplitude and the num-ber of cycles on (a) the mobilized shear stress, (b) the normaldisplacement, and (c) the percentage of slip for the loose sand –steel plate interface subjected to a constant normal stress σn =200 kPa.

Behaviour of dense sand – steel plate interface

Influence of number of cyclesIn general, the mobilized shear stress on interfaces with

dense sand decreases at a diminishing rate with an increasein the number of cycles (Fig. 9a). However, the amount ofdecrease in the mobilized shear stress is a function of theamplitude of tangential displacement and is discussed in thesection related to the influence of tangential displacementamplitude.

During the initial loading part of the tests with densesand, the maximum shear stress is higher than that recordedfor loose sand. For the test conducted with σn = 100 kPa andA = 3 mm, the maximum shear stress is 60.3 kPa for densesand (Table 3) and 44.7 kPa for loose sand (Table 2). Thedifference in the shear stress value decreases with an in-crease in the number of cycles. At the end of the tenth cycle,the shear stress for this particular test is 46.8 kPa for densesand and 47.5 kPa for loose sand. These observations sug-gest that the mobilized shear stress reaches almost a constantvalue, which is independent of the initial density of sandsamples.

In each cycle, the normal displacement curves shown inFigs. 4b, 5b, and 6b indicate contraction first and then dila-tion. During the initial cycles of some tests, the overall nor-mal displacement was positive, meaning that the volume ofsample has increased (Fig. 10b; Table 3). Each displacementreversal is characterized by a contraction of the soil sample,however, and the overall normal displacement becomes neg-ative (contraction in the subsequent cycles). The change innormal displacement occurs at a decreasing rate. The valuesof normal displacement at the end of each cycle (Tables 2, 3)

show that dense sand undergoes much less cumulative con-traction than loose sand. In fact, the normal displacementmeasured at the top of dense sand samples is at least fourtimes less than that of loose sand samples.

The percentage of slip in the experiments with dense sandincreases with an increase in the number of cycles (Fig. 9c).The amount of slip is larger for dense sand when comparedwith that for loose sand (Tables 2, 3). For example, in thetest performed with σn = 100 kPa and A = 1 mm, the slipportion of the total tangential displacement for dense sand is32% and 64% at the end of initial loading and at the end ofthe tenth cycle, respectively. The corresponding portions ofslip for loose sand are 6.0% and 38%.

In most cases the slip at the end of the tenth cycle is themain component of the total tangential displacement (i.e.,percentage of slip >50%). Accordingly, not making a dis-tinction between the slip and the displacement at the inter-face resulting from soil deformation, as is usually donewhen direct shear type interface equipment is used (Desai etal. 1985; Al-Douri and Poulos 1992; Sharour and Rezaie1997), will result in incomplete information on soil–struc-ture interface behaviour.

Influence of normal stressThe magnitude of normal stress influences the stress ratio

in the experiments with dense sand (Figs. 10a, 10b). Thestress ratio corresponding to σn = 100 kPa is less than thatwhen σn is larger than 100 kPa. The normal stress also influ-ences the amount of normal displacement. As shown inFigs. 10c and 10d, the amount of compression increaseswith an increase in the normal stress. In addition, the magni-

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Fig. 8. Influence of normal stress on the stress ratio at (a) A = 1 mm and (b) A = 3 mm and on the normal displacement at (c) A =1 mm and (d) A = 3 mm for the loose sand – steel plate interface.

tude of slip at the interface increases in most tests with anincrease in the normal stress (Table 3).

Influence of tangential displacement amplitudeIn the experiments with dense sand, the evolution of the

mobilized shear stress depends on A. If A is less than theamount of displacement required for the peak shear stress todevelop at the end of IL, such as in the case when A =1 mm, then there is only a small amount of change in the

mobilized shear stress recorded in the subsequent cycles(Figs. 4a, 9a). If the peak shear stress is already mobilized(i.e., A = 2 and 3 mm) during the initial loading, however,the peak shear stress decreases in the subsequent displace-ment cycles at a decreasing rate (Figs. 5a, 6a, 9a).

The relation between the normal displacement and theamplitude of tangential displacement is shown in Fig. 9b.Larger amplitudes of tangential displacement are associatedwith smaller compression of the soil specimen during cyclicloading. This is due to the fact that when the amplitude ofdisplacement is large, the sand sample dilates more. There-fore, the cumulative amount of compression reduces. Al-though Al-Douri and Poulos (1992) reported that the changein sample height increases with an increase in the tangentialdisplacement amplitude, the results of the current investiga-tion indicate that this observation is applicable only to soil–structure interfaces in loose sand. The amplitude of tangen-tial displacement also influences the amount of slip at the in-terface. The percentage of slip increases with an increase inthe tangential displacement amplitude (Fig. 9c).

Conclusions

The conclusions of this experimental study on the cyclicbehaviour of interfaces are summarized as follows:(1) The density of sand significantly affects the interface re-

sponse. (i) The mobilized shear stress on the interfaceincreases for loose sand and decreases for dense sand asthe number of cycles increases. Eventually, the mobi-lized shear stress becomes almost independent of theinitial density. (ii) Loose sand contracts at a diminishingrate as the number of cycles increases. Dense sand di-lates as well as contracts during each cycle with a smallamount of net contractive volume change. (iii) Theamount of slip increases with an increase in the numberof cycles for both densities, but interfaces with densesand experience a larger slip.

(2) Increasing values of normal stress yield increasing val-ues of the shear stress ratio, larger change in sampleheight, and more slip at the interface.

(3) The amplitude of tangential displacement (A) influencesthe interface response. (i) For loose sand, the sampleheight changes more and the slip increases with an in-crease in A. (ii) For dense sand, if A is not large enoughfor the peak shear stress to develop at the end of the ini-tial monotonic loading, the mobilized shear stress doesnot change much in the subsequent cycles. Otherwise,the shear stress decreases in the subsequent cycles. Fur-thermore, the cumulative change in sample height issmaller for larger values of A and the amount of slip islarger for increasing values of A.

(4) The amount of slip increases with an increase in thenumber of cycles and eventually becomes larger thanthe soil displacement. Therefore, not making a distinc-tion between the slip and soil deformation, as is usuallydone when a direct shear type container is used, wouldyield incomplete information about the interface behav-iour.

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Fig. 9. Effect of tangential displacement amplitude and the num-ber of cycles on (a) the mobilized shear stress, (b) the normaldisplacement, and (c) the percentage of slip for the dense sand –steel plate interface subjected to a constant normal stress σn =200 kPa.

Acknowledgment

The financial support for this investigation was providedby the Natural Sciences and Engineering Research Councilof Canada.

References

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Fig. 10. Influence of normal stress on the stress ratio at (a) A = 1 mm and (b) A = 3 mm and on the normal displacement at (c) A =1 mm and (d) A = 3 mm for the dense sand – steel plate interface.

Cyclic behaviour of a sand steel plate interface

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