96 TRANSPORTATON RESEARCH RECORD 1336 Vertical Uplift Load-Displacement Relationship of Horizontal Anchors in Sand BRAJA M. DAS AND VJAY K. PUR Small-scale laboratory model test results for the uplift capacity of horizonta l rectangular anchors embedded at shallow depths in medium and dense sand are presented. The ultimate uplift capacities obtained from the laboratory model tests are compared with the theory proposed by Meyerhof and Adams. On the basis of model test results, an approximate nondimen ional uplift loaddisplacement relationship is developed. This relationship is useful in the determination of the allowable anchor holding capacity at a given level of vertical displacement of the anchor. n many instances, horizontal plate anchors are used in the construction of foundations to resist uplifting loads. n most cases they are either square or circular in shape. Generally, the design limitation for plate anchors must address concerns for (a) the allowable uplift capacity, which is estimated by applying a suitable factor of safety to the theoretical ultimate uplift capacity, and (b) the allowable uplift displacement when subjected to allowable load. Several theoretical and experimental studies are available (J-4) for prediction of the ultimate uplift capacity of horizontal plate anchors. Practically all theories, with the exception of that given by Meyerhof and Adams (3), are valid only for circular anchors. Meyerhof and Adams's theory provides relationships for the ultimate uplift capacity of circular and rectangular plate anchors. A review of the existing literature indicates that no serious effort has thus far been made to develop the relationships between uplift load and corresponding displacement of horizontal plate anchors. Reported herein are some small-scale laboratory model test results on shallow horizontal rectangular plate anchors embedded in sand. The ultimate uplift capacity of those rectangular anchors determined experimentally has been compared with the existing theory of Meyerhof and Adams (3). n addition, a nondimensional relationship for the load and displacement of rectangular plate anchors has been developed. GEOMETRC PARAMETERS FOR AN ANCHOR Figure 1 shows a horizontal plate anchor with length L and width B. The depth of embedment of this plate anchor is D. When the embedment ratio DB is relatively small and the anchor is subjected to ultimate uplift load (Qu), the failure Department of Civil Engineering and Mechanics, Southern llinois University at Carbondale, Carbondale,. 6291-663. surface in soil located above the anchor extends to the ground surface, and these anchors are referred to as shallow anchors. However, at larger values of DB, local shear failure in soil located around the anchor takes place; thus, these anchors are referred to as deep anchors. On the basis of several laboratory and field test results, Meyerhof and Adams (3) determined the critical values of the embedment ratio below which shallow anchor conditions for circular and square anchor plates exist. Those values of the critical embedment ratio that are functions of the soil friction angle <!> are given in the following table. Soil Friction Angle, <!> (deg) 3 35 4 45 Critical Embedment Ratio, DB = D/Bm for Circular and Square Plate Anchor 4 5 7 9 The critical embedment ratio for rectangular anchors can be 4 to 5 percent higher than the square or circular anchors (5). ULTMATE UPLFT CAPACTY As mentioned earlier, the theory of Meyerhof and Adams (3) is the only analytical expression presently available to estimate D 1, w,,._a~ Sand Uoh weight = y rnction angle s f> FGURE 1 Geometrical parameters of shallow horizontal anchor.
Das and Puri the ultimate uplift capacity ofrectangular anchors. According to this theory, for shallow rectangular anchors Q" = -yd 2 (2SB + L - B)K tan <!> + W + W. (1) where = gross ultimate uplift capacity, -y = unit weight of soil, D = depth of embedment, B = anchor width, L = anchor length, Ku = uplift coefficient, <!> = soil friction angle, S = shape factor, W = effective weight of the soil located immediately above the anchor, and w. = effective weight of the anchor and the rod. The theoretical variation of th uplift coefficient K,. for various soil friction angle. fall within a narrow range and may be taken as.95. For shallow anchors, the shape factor increases linearly with the embedment ratio DB, or S = 1 + m(~) (2) where m is the shape factor coefficient. The variation of the shape factor coefficient m with the soil friction angle <> as suggested by Meyerhof and Adams (3) is as follows: Soil Friction Angle, <!> (deg) 3 35 4 45 Shape Factor Coefficie111, m.15.25.35.5 The net ultimate uplift capacity of an anchor can be expressed in a non dimensional form as ( 6) 3 U.S. sieve, 53 percent passing No. 4 U.S. sieve, 7 percent passing No. 6 U.S. sieve, and 3 percent passing No. 2 U.S. sieve. Three model aluminum plates measuring 5.8 mm x 5.8 mm, 5.8 mm x 11.6 mm, and 5.8 mm x 152.4 mm were used for the tests giving length-to-width ratios (LB) of 1, 2, and 3. All of the aluminum plates were 3.18 mm thick. n conducting the model tests, sand was compacted in 25.4- mm-thick layers in the box to a desired height. Uplift force to the plates was applied through a 6.35-mm-diameter steel rod rigidly attached at the center of each plate. The rod was connected to a lever arm attached to the side of the test box. Step loads were applied at the other end of the lever arm. The lever-arm ratio was 1:1. The upward movement /:J,. of the anchor was measured by a dial gauge. Two series of tests were conducted by changing the unit weight of compaction of the sand. The average unit weight of compaction for each serie and the corresponding angle of friction determined from the standard triaxial tests are given in Table. For a given series the ultimate pullout load for each plate was obtained from embedment ratios varying from 1 to 5. This range of embedment ratio applies to shallow anchor condition. LABORATORY MODEL TEST RESULTS Typical variations of the net load Q versus the vertical displacement /:J,./B (/:J,. = vertical displacement) obtained from the present laboratory model tests are shown in Figure 2. Each test was conducted twice, and the Q versus /:J,./B plots shown in Figure 2 are the average plots. The net ultimate uplift load is defined as the load at which sudden pullout occurred, or where the Q versus /:J,./B plot showed a practically linear relationship. The net ultimate capacities thus determined for tests in medium (Series 1) and dense (Series 2) sands are shown in Figure 3. 97 where Nq is the breakout factor and = net ultimate uplift capacity = - W. (4) Combining Equations 1 through 4, for shallow rectangular anchor, The preceding expres ion is valid for shallow anchors, that is, up to a limit of DB = (DB),. LABORATORY MODEL TESTS Laboratory model pullout tests were conducted in a box measuring.6 m x.6 m x.6 m. A poorly graded silica sand was used for the tests. The sand had 84 percent passing No. (3) VARATON OF BREAKOUT FACTOR, Nq Using the experimental ultimate uplift capacities shown in Figure 3 and Equation 3, the experimental variations of the breakout factors with embedment ratio for all tests have been calculated and are shown in Figures 4 and 5. For comparison purposes, the theoretical variation of N, 1 calculated using Equarion 5, which is based on the theory of Meyerhof and Adams (3), are also hown in these figure. A compari on between the theoretical and experimental curves indicates that the experimental values are slightly higher than those predicted by theory. TABLE 1 AVERAGE UNT WEGHT OF COMPACTON AND CORRESPONDNG TRAXAL FRCTON ANGLE Average Unit Series Nature of Rclalive Weight of Friction Compaction Density, D, Compaction. y Angle,</> (%) (kn/m') (deg) Medium 47.6 15.79 34 Dense n.9 16.88 4.5
98 TRANSPORTATON RESEARCH RECORD 1336 24 2 ' /...- o/b 4,/,- ' LB= 3 18. 4 ljb. 3 _ Experiment ----- Theory Meyerhof and Adams (1968) LB E 1 g 16 1 ~ 12 Series 1 8 4 --Series! ----- Series 2 O/B 3 LB Ultimate load (.j ; Q.) OL-----'----"'----~--~.2.4.6.8 Vcnlcal dlsplaccmeo~ A Anchor width, B FGURE 2 Typical variation of Q versus 4/B. Embed.meat ratio, D B FGURE 4 Variation of Nq versus DB, Series 1. 2. For a given anchor plate and type of sand compaction, the magnitude of 11" increases with the embedment ratio within the limits of the test (that is, DB :s 5). 3. For a given embedment ratio and type of sand compaction, the magnitude of 11" decreases with increase in the engthto-width ratio (LB). VARATON OF ~u WTH DB Figure 6 shows the variation of the nondimensional ultimate displacement 11jB (11" = anchor displacement at ultimate load) with the embedment ratio of anchors. From this figure, the following general conclusions can be drawn. 1. For similar embedment ratios and anchor plates, the magnitude of the displacement at ultimate load is about 1.5 to 2 times higher in medium sand than in dense sand. NET LOAD VERSUS DSPLACEMENT RELATONSHP On the basis of the experimental net load Q and corresponding displacement /1 relationships obtained from the present tests, it appears that they can be approximated in a nondimensional rectangular hyperbolic form as (6) 4 ~-----,-----.-------, -- Experiment ------Theory- Meyerllof and Adams (1968) LB K 2 DB 6 LB= 3 4 Q,(N) 2 Series 2 O'--_.::;,.. ~ DB FGURE 3 Variation of versus DB: a, Series 1; b, Series 2. 2 '---~--L----L---~ 2 Embedment ratio, D B FGURE 5 Variation of Nq versus DB, Serles 2.
Das and Puri 99.12.-----.-- -.---...----.----.,---....1.8 11,/B.6.4.2 O o 3 D/B s 6 '---~----'---.. -~-~. -~ FGURE 6 Plot of L!..JB versus DB. (b) Series 2... J!/,-o,',.o, 'H 'a~ '" O..' '", 9 f ' ' &",.,, ofx l o,; r / N,;' / / }1 6. Symbol D/B LB 1 1 2 3 4 4 9 s 1 + 2. '! 2 3 2 4 7 s 2 1 l 2 l 3 3 4 3 s ~....... ~.25.5.75 1..25.5.75 1. FGURE 7 Plot of!q versus : a, Series l; b, Serles 2. where - Q Q = Qo' - A A= Ā' u Q = net load at an anchor displacement of A, = net load at an anchor displacement of Au, and C 1, C 2 = constants. Equation 6 can be arranged in the form Q (net load) versus A (uplift displacement) obtained from the laboratory test (similar to those shown in Figure 2), the variation of KfQ versus K has been plotted in Figure 7. From the plots it can be seen that all points fall in a rather narrow band. The average values of C 1 and C 2 can be given as.175 and.825, respectively. f these values are substituted into Equation 6, the net load at given displacement A can be expressed as Q Qo[.175 + :" ].825 (:..) (8) The preceding relationship implies that the plot of KQ versus K will be a straight line. On the basis of the average plots of (7) CONCLUSONS The results of a number of laboratory model uplift tests on shallow rectangular anchor plates embedded in sand have
1 been presented. On the basis of the model test results, the following conclusions can be drawn. 1. The experimental ultimate uplift capacity of rectangular anchor plates is generally in good agreement with those predicted by the theory of Meyerhof and Adams (3). 2. The approximate range of the anchor displacement fl" at ultimate load can be estimated from Figure 6. 3. On the basis of present model tests, an approximate nondimensional load-displacement relationship has been developed (Equation 8). REFERENCES 1. A. Balla. The Resistance to Breaking-Out of Mushroom Foundations for Pylons. Proc., 5th nternational Conference on Soil TRANSPORTATON RESEARCH RECORD 1336 Mechanics and Foundation Engineering, Vol. 1, 1961, pp. 569-576. 2. L. G. Mariupolskii. TheBcari.ngCapaci1yofAnchorFoundations. Soil Mechanics and Foundation Engineering, Vol. 3, No. 1, 1965, pp. 14-18. 3. G. G. Meyerhof and J.. Adams. The Ultimate Uplift Capacity of Foundations. Canadian Geoteclmic:al 111mal, Vol. 5, No. 4, 1968, pp. 225-244. 4. C. J. Veesaert and S. P. Clemence. Dynamic Pullout Resistance of Anchors in Sand. Proc., nternational Symposium on Soi/ Structure nteraction, Rourkee, ndia, 1977, pp. 389-397. 5. G. G. Meyerhof. Uplift Resistance of nclined Anchors and Piles. Proc., 8th /11ternatio11al Conference on Soil Mechanic and Foundation 11gineeri11g, Moscow, Vol. 2.1, 1973, pp. 167-172. 6. A. S. Vesic. Breakout Resistance of Object Embedded in Ocean Bottom. Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM9, 1971, pp. 1183-125. Publication of this paper sponsored by Committee on Foundations of Bridges and Other Structures.