NRC Publications Archive Archives des publications du CNRC

Transcription

1 NRC Publications Archive Archives des publications du CNRC On measuring the shear strength of ice Frederking, Robert M (Bob); Svec, O. J.; Timco, G. W. For the publisher s version, please access the DOI link below./ Pour consulter la version de l éditeur, utilisez le lien DOI ci-dessous. Publisher s version / Version de l'éditeur: Paper (National Research Council Canada. Institute for Research in Construction), 1988 NRC Publications Record / Notice d'archives des publications de CNRC: Access and use of this website and the material on it are subject to the Terms and Conditions set forth at READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. L accès à ce site Web et l utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D UTILISER CE SITE WEB. Questions? Contact the NRC Publications Archive team at PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to the authors directly, please see the first page of the publication for their contact information. Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

2 Ser TH1 ~ 2 1 d National Research Conseil natsonai de mhetches Canada c, 2 Institute for lnstitut de BLDG Research in recherche en Construction construction no * 1 Council Canada --.- On Measuring the Shear Strength of Ice by R.M.W. Frederking, O.J. Svec and G.W. T imco Appeared in Proceedings of the 9th International Symposium on Ice Sapporo, Japan, August 23-27,1988 IAHR Committee on Ice Problems, Vol. 3 p (IRC Paper No. 1612) Reprinted with permission LIBRARY NRCC L BIBLIOTH~QUE IRC CNRC - tclst

3 L'analyse par la mcthode des ClCments finis de poutres soumises Zi des charges en quaue points asyxnktriques a 6tC utilistk pour calculer les champs de contraintes internes pour d8fchents Cchantillons et diffkrentes gbmcmes d'application des charges. Les contraintes de cisdement dctamh&s d'aprks ces champs de contrahe diffdraient nettement de celles cdcdies &ap& la thcorie de la poutre unique. Des exp5riences effectu6es en labratoire avec des Cchantdlons de glace d'eau douee h gains columnaires ont montr6 que des valeurs cshhntes Ctaient obtenues pourvu que les Cchantillons ~t les g&&tries &application des charges ne varient pas au-del8 d'une plage pdcub2re. A -10 OC une dsistance au cisaillement moyenne de 600 kpa a it6 dct-k. Des mesures sp&iales adoptks afin de r6duire la concentration des contraintes aux points d'application des charges ont entrahi un accroissement de la dsistance au cisaillement moyenne qui est passee B 1100 kpa. Une m6thode d'essai de cisaillement dans la glace bade sur cette e&rience est proposce.

4 IAHR Ice Symposium 1988 Sapporo ON MEASURING THE SHEAR STRENGTH OF ICE Re Frederking and O.J. Svec Geotechnical Section Institute for Research in Construction G.W. Timco Division of Mechanical Engineering National Research Council of Canada Ottawa, Ontario, CANADA KIA OR6 ABSTRACT Finite element analysis of beams subjected to fourcpoint asymmetric loading has been used to calculate the internal stress ffelds for different specimen and 1 oading geometries. The shear stresses determi ned from these stress fields were significantly different from those calculated from simple beam theory. Laboratory experiments done on samples of columnar-grained fresh water ice showed that consistent values of shear strength were obtained provided specimen and 1 oading geometries di d not vary beyond a particular range. At -1rC an average shear strength of 600 kpa was determined. Special measures taken to reduce stress concentrations at the load application points resulted in an increase of the average shear strength to 1100 kpa. Based on this experience, a shear testing method for ice is proposed.

5 IAHR Ice Symposium 1988 Sapporo Introduction Analytical models of ice forces on structures have generally considered the ice in the interaction zone to be under a uniaxial or multiaxial compressive stress condition. It is quite possible, however, that significant parts of the interaction zone may be subjected to biaxial stress conditions involving tensile in addition to compressive stresses. Measurements of shear stress are relevant to defining this stress condition. Therefore information on shear strength is necessary in analytical predictions of ice loads where this type of failure behaviour is occurring. Shear-strength data are also useful in determining the failure envelope of ice under multiaxial stress conditions. The shear strength of ice is a difficult property to measure in an unambiguous fashion. The techniques commonly used, di rect shear, punching, or torsion, create stress fields that cannot be quantified simply. Normally it is assuned that a uniform shear stress is generated on a plane of failure, but in many instances indeterminate normal stresses are also generated on the plane of failure. For example, Butkovich (1956) obtained values in the ranges 500 to 1200 kpa using the double shear technique, while Paige and Lee (1967) and Dykins (1971) obtained values in the ranges 500 to 1200 kpa and 100 to 250 kpa respectively for single shear. In all three cases, results were for first-year sea ice of similar salinity and temperature. This large disparity in results brings into question the validity of the test methods used in the past. The off-axis strength test (Pipes, 1973), in which the specimen axis is oriented at some angle to the material coordinate systems, has been used to obtain strength data under a loading condition with tensile and compressive principal stresses (shear). It produces both normal and shear stresses on the failure plane. The asymmetric four-point loading method has been proposed as a means of performing improved shear tests (Iosipescu, 1967). This method was applied to an investigation of granula~structured first-year ice from the Beaufort Sea (Frederking and Timco, 1984) and to columnarcgrained and frazil sea ice from Labrador (Frederking and Timco, 1986). Consistent results were obtained. This paper will present the results of finite element (FE) calculations of beam subjected to fourcpoint asymmetric loading. Strengths calculated from the FE analysis and simple beamtheory -n-

6 IAHR Ice Symposium 1988 supporo w~ll be conpared with results of laboratory tests and a recommended calculation and test method for shear proposed. Asymnetrical Four-point Bending Method for Shear The asymmetrical four-point bending method was used in performing the shear tests. Load is appl ied at four points on a beam so that a region of high shear stress and low bending stress is generated at the mid-section of the beam. The geometry of load application and resulting idealized shear forces and bending moments are illustrated in Figure 1. The shearcstress distribution at the centre plane, x = 0, is assuned to be parabolic which gives a maximm shear stress, +, at the mid height of the beam where P is total applied load, b is specimen thickness, h is specimen 1111, /')Ir, BAR UPPER PLATE c l x SPEC I MEN I I I / P LOWER PLATE J -a - P -&P SHEAR FORCE DIAGRAM I+= BENDING MOMENT DIAGRAM Figure 1. Asymmetric four-point loading apparatus and shear force and bending moment diagrams (from Frederk ing and Timco, 1984)

7 IAHR Ice Symposium 1988 Sappon, h, and a relates to the loading geometry. The specimen geometry proposed by Iosipescu, (1967) included notches in the top and bottom surfaces of the beam at the mid-plane, x = 0. This procedure has the effect of reducing the cross-sectional area subjected to the shear stress and of producing a nearly uniform shearcstress distribution, provided that each notch depth is between 20-25% of the specimen heigtit, h. For the notched beam, maxirmm shear stress is given by where P,- a, and b are as defined for equation (1) and ho is the net height of the beam across the notches. Finite Element Analysis A finite element analysis, using quadrilateral 1 inear elements, was employed to examine the stress field in the central region of the test specimens. Linear elastic behaviour was assuned for the ice (elastic modulus 10 GPa and Poisson's ratio 0.3) and the plane stress (az = o) condition appl ied. The factors of specimen depth, h, loading position, a and notch or saw cut at the central plane of the beam were treated. A standard mesh of 66 elements along the length of the beam and 20 elements over the depth was used for all the cases investigated. Only element size and shape (trapezoidal for the notch and saw-cut) were varied. The stresses in all cases are for an applied load of P = 1080 N. The results of the finite element calculations are summarized in Table 1. Maximum values of shear stress,.cmax, and tensile stress, ul, at the centre plane (x = 0) and loading plane (x = ax) are presented for a variety of cases. For comparison shear stress,.c calculated from simple beam XY ' theory is also included. It can be seen that the results for maxinum shear stress, s and are in reasonable agreement for the two calculation x Y methods, in the case of plain beams. Figure 2 presents the stress distributions at the central plane (x = 0) of the beam for the case of beam depth h 100 mm and load position a = 0.1. The left hand part of the figure shows the stresses in terms of the Cartesian coordinate system (x, y) and in the right hand part the same

8 IAHR Ice Symposium 1988 ble 1 Calculated maxlmrrn shear and tensile stress usinq finite element analysis (FE) and simple beam theory (SB) for variois beam geometries and loading positions. Stresses, in kpa, are for 50 mm thick beams with a nominal load P = 1080 N. + h=70 mm h=100 mm h=140 mm plain plain V-notch saw-cut plain eo.1 SB %y ' FEhx,x=O %ins x'qr ul, x h0.2 SB FE hx, FO %i n* X" ul, x=o ' stresses have been converted to principal stresses, qand %, and maxinum shear stress, rma, = (4 - u22)12. Note, tensile stresses are taken as positive. The FE analysis produces values of -40 kpa for s at the beam XY surface, whereas the value here should be zero. This anomaly indicates that the results of the analysis at or near a free surface have to be STRESS, kpa (COMPRESSION) (TENSION) STRESS Figure 2. Stress distribution plots at central plans (x = 0) of a 100 mm deep beam in tern of (a) specimen coordinates (%, and (b) principal stress coordinates (=, and ), position a = 0.1. q and %3. ~ o a n g

9 IAHR Ice SymPosium 1988 Snpporo rntesprcted with some caution, Figure 2 shows the shear stress, r XY ' distribution detennined from the FE analysis differs substantially from the parabolic distribution assuned in the simple beam theory (Equation I), even though the maxirmm values of shear stress are similar for the two calculation methods. The results also shw that a condition of pure shear (ax = u = 0 or q = -?) does not exist at the central plane, there Y is in fact a mean compressive stress of 140 kpa on the plane of largest s ma x (260kPa). In Figure 3 the principal stresses, 9 and 4, and zmx are plotted for two loading positions, a = 0.1 and 0.2, for a 100 mm deep beam. Figure 3a, for the stresses at the centre plane, shws that the stress distributions change slightly and that the maxirmm shear stress on the centre plane (x = 0) is 250 kpa in the case of load position a = 0.1 versus 200 kpa for load position 0.2. Figure 3b, for stresses at the plane of load application (x = d), indicates that both distributions are generally similar but that, again, -rmax is larger for load position a = 0.1. Note that Figure 3b also indicates the presence of a high shear stress just belm the surface of the beam and a high tensile stress on the opposite side of the beam at the load application plane (x = aa). The stress distributions at the centre plane for a 20 mm deep 90' V-notch in a beam of depth 100 mm are presented in Figure 4. Note that the net section depth at the notch, ho, is 6 0 m In this case, rmx in the notch is uniform with a maxirmm value of 230 kpa. This stress is slightly larger than the value of 210 kpa obtained for an unnotched beam with load position a = 0.2 (see Table 1). The stress distributions at the loading plane (x = UA) were similar to those of the un-notched beam. The stress distrikrtions calculated for the saw cut case are not plotted, but it can be seen in Table 1 that they gave a very high value for r There is some question as to the accuracy of the stresses calculated max' at the tip of the cut. It is planned for future research to use higher order elements and a more refined FE mesh, particularly in locations of stress concentration. Developnent of a FE model capable of approximating nonl inear behaviour of ice might also become necessary.

10 IAHR Ice SympOsium 1988 Sapporo q, kpa %OX 9 IcF'a a) STRESSES AT CENTRAL PLANE ( x = 0 ) q, kpa %, kpa T,,,~, kpa b) STRESSES AT LOAD PLANE ( x = a I) Figure 3. Distributions of principal stresses, q and 42, and maximm shear stress, for a plain 100 mm deep beam with load F = 1080N. Test Method and Specimen Preparation A test apparatus has been built to rep1 icate the conditions indicated in Figure 1. The distance of the outer loading points (a ball in each

11 IAHR Ice Sym~osium 1988 Sapporo STRESS, kpa 'igure 4. Distributions of principal stresses, q, and 9, and maximm shear stress, ha, at the central plane (x = 0) of a 100 mm deep beam with 2 20 mm deep 90' notches. case), A, is 150 mm from the centre 1 ine, x = 0, Two sets of notches are provided in each plate at 15 and 30 mm distance (a = 0.1 and 0.2 respectively) from the centre. At these inner loading positions a bar is used to distribute the load across the width of the specimen. plate, through which the load P is applied, The upper is free to rotate about the 1 oad-appl ication point. Loading was carried out using a 50-kN capacity field portable conpression tester designed and built at the National Research Council of Canada. The machine has a screw drive actuator. A1 1 testing was done at a nominal actuator rate of 0.5 mm sml. Continuous records of load versus time were made for each test. In a few cases, high speed 16 mm movie film were also taken, at a rate of 400 frames/s. The purpose of the filming was to detect the location of failure initiation and to follow its progress. A 60 mm thick columnar-grained freshwater ice sheet (C2, according to IAHR, 1986 classification or S2 according to Michel and Ramseier, 1971) was grwn in the Ice Test Basin of NRC's Hydraulics Laboratory in Ottawa. top 10 mm of the ice sheet was discarded, leaving uniform columnar ice with an average grain diameter of 3 mm. The Specimens were cut to rough dimensions on a band saw and then planed on a power planer to final nominal dimensions

12 IAHR Ics Symposium 1988 s*m 350 nun length, 50 mm thickness and 70, 100 or 140 mm depth. Additionally, some of the 100 mm deep specimens were prepared with a pair of 90' notches or 2 mm wide saw cuts at the central plane of the beam (x = 0). These notches or cuts each extended to a depth of about 20 mm, leaving a net section depth of about 60 mm. grains were always normal to the largest faces. testing was carried out at a temperature of -10'C The long axis of the columnar Specimen preparation and + 1'C. Test Results and Discussion Tests were performed on a total of 57 beams. Table 2 summarizes all the cases examined. The main parameters varied were beam depth, h, load position, a, notching and saw cuts of beams, and the absence or presence of stress relief material under the loading bars. Force time curves for repeat tests done on a 100 mm deep beam with load position a = 0.1 are presented f n Figure S(a). The general consistency of the test results can be seen. These curves also shcw the effects of local cracking and spa11 ing of the specimen at the loading points when no stress relief is used at the loading bars. The small decreases in load occur due to relaxation in the test system which is loading at a nominally constant rate of displacement. This behaviour was not noted in a previous application of this test method to saline ice (Fredeking and Timco, 1984, 1986). Figure 5(b), by contrast, presents results with a local stress relief material under the loading points. The first obvious factor in this case is the smooth monotonic increase in load up to failure. Also, significantly higher failure loads were obtained. This difference in loading behaviour was also observed in the high speed 16 mm filming, in which small pieces of ice Table 2 Summary of cases examined in test program Beam h=70 mm h=100 mm - h=140 mm a = 0.1 plain X, S plain X, s V-notch -- saw-cut X,S plain X < a = 0.2 X X X,S x,s X X, tested; S, tested with stress relief material

13 -- -- IAHR Ice Symposium 1988 Sapporo 6000 a) I TIME, s Figure 5. Plots of force versus time for 100 mm deep beams with load position a = 0.1; (a) no stress relief material under loading bars, (b) stress relief material under ban, (sol id lines - bake1 ite), (dashed 1 ines - cardboard). could be seen spalling off the beam when no stress relief material was used. Plain specimens failed with a single crack which extended from load bar to load bar. The V-notched and saw-cut specimens failed with two cracks, each extending from the load bar to the opposite notch or saw-cut tip. The high speed film was examined to see whether the point of cradt initiation and di rection of propagation could be detected, the plane beam, In the case of crack initiation and propagation occurred in less time than the s (2.5 ms) between frames. In the case of the V-notch, it appeared that the crack initiated at the bar and then ran to the notch tip. Propagation time in this instance was less than 5 ms. The test results were analysed for shear strength and tensile strength using simple beam theory (Equations(1) and (2)) and finite element analysis (Table 1). In terms of deriving a shear strength from the data, the most consistent results were obtained using the maxim. shear strength, bax, determined from the finite element analysis. This can be seen in Table 3 which summarizes all the test results

14 IAHR Ice Symposium 1988 S*IO There were no instances of the failure plane propagating towards or away from the zone of high tensile stress opposite the loading points. Therefore calculated tensile strengths are not presented here even though the finite element calculations would indicate that they were high, particularly for the 70 mm deep beams (see Table 1). Figure 3 and Table 1 also shw high shear stresses under the loading points (x = +a~) but these have been disregarded i n subsequent cal cul ations of shear strength. were exami ned, but produced 1 ess consistent results. They The results of Table 3 shcw that there is better consistency in the shear strength values when they are evaluated using a finite element analysis rather than simple beam theory, particularly in the case of plane beams and V-notched beams. The plain beams of depth 70, 100 and 140 mm and load position a = 0.1 as well as the 100 mm deep beam with load position a = 0.2 all had remarkably similar results when evaluated using the finite element analysis. These results are underlined in Table 3. It can also be seen that introducing a stress relief materfal results in about a doubling of the shear strength. This result implies that for no stress relief material under the loading points different stresses are produced than those fndicated by the finite element analysis. Some indentation of the bars into the ice was noted. This indentation could induce high tensile stresses in the beam and initiate premature failure under the loading bars. Sum ry a nil Rectnmiendat i ons, Shear strengths calculated from finite element analysis or simple beam theory give similar results for plane and 90' V-notch beams. The shear stress distributions calculated with finite element analysis, however, are more accurate than those calculated using simple beam theory. Experiments performed on columnar-grained fresh water ice were used to evaluate the calculation methods. Test results indicated that keeping beam dimensions and loading positions within limits determined by the tests allowed consistent shear strength values to be determined. The follwing recomnendations are made for testing and interpretion of shear strength:

15 IAHR Ice Symposium 1988 sapporn Table 3 ~um'ma ry of average shear strengths in kpa at the central plane (x = 0) calculated using simple beam theory (SB) and finite element analysis (FE). Columna~grained fresh water ice at -10.C 1) Test Conditions - beam dimensions 100 mm deep, 50 mm thick and 350 mm long - plain beam cross section. - loading position a = use stress relief material under loading bars (bakelite or cardboard fo r exampl e) 2) Interpretation of shear strength - for index shear strength use r calculated using simple beam theory, XY Equation (I), provided the test conditions above are follwed. - for failure envelope determinations use actual biaxial stresses u1 and u2 as determined from FE cal culations. Ack now1 edgements The authors would like to acknwledge the assistance of Frarqois Carrier, Summer Assistant, in performing the finite element calculations, and J. Neil and R. Bowen, Technical Officers, National Research Council of Canada in assisting with the testing.

16 IAHR Ice Symposium 1988 Sapporo Butkovich, T.C Strength of sea ice. Snow, Ice and Permafrost Research Establishnent, Research Report RR-20. W i 1 lamette, I1 1 i nois, 15 p. Dykins, J.E Ice engineering - material properties of saline ice for a limited range of conditions. Naval Civil Engineering Laboratory, Technical Report R720, Port Hueneme, California, 96 p. Frederking, R.M.W. and Timco, G.W Measurement of shear strength of granul ar/discontinuous-columnar sea ice. Cold Regions Science and Technology, Vol. 9, pp Fredehing, R., and Timco, G.W Field measurements of the shear strength of columnar-grai ned sea ice. Proceedings of IAHR Ice Symposium 1986, Iowa City, Iowa, August 1986, Vol. 1, pp IAHR, IAHR - Recommendations on testingmethods of ice, 5th report of Working Group on Testing Methods in Ice. IAHR Ice Symposium, Iowa City, Iowa, August 1986, Vo1. I I, pp Iosipescu, N New accurate method for single shear testing of metals. Journal of Materials, Vol. 2 (3), pp Michel, B., and Ramseier, R Classification of river and lake ice. Canadian Geotechnical Journal, Vol. 8, No. 1, pp Paige, R.A. and Lee, C.W Preliminary studies on sea ice in Mdtlurdo Sound, Antarctica, during "Deep Freeze 65". Journal of Glaciology, Vol. 4 (46), p Pipes, R The off-axis strength test for anisotropic materials. J. Comp. Mat., Vol. 7, p

17 This paper is being distributed in reprint form by the Institute for Research in Construction. A list of building practice and research publications available from the Institute may be obtained by writing to the Publications Section, Institute for Research in Construction, National Research Council of Canada, Ottawa, Ontario, KIA 0R6. Ce document est distribuk sous forme de tirb-h-part par 1'Institut de recherche en construction. On peut obtenir une liste des publications de 1'Institut portant sur les tcchniqucs ou les recherches en matikre de bstiment en Ccrivant A la Section des publications, Institut de recherche en construction, Conseil national de rechcrches du Canada, Ottawa (Ontario), KIA 0R6.