Behaviour of the model surface strip footing on reinforced sand

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 12, October 2005, pp Behaviour of the model surface strip footing on reinforced sand Berkan Moroglu a, Bayram Ali Uzuner b* & Erol Sadoglu b a Civil Engineering Department, Cumhuriyet University, Sivas, Turkey b Civil Engineering Department, Karadeniz (Black Sea) Technical University, Trabzon, Turkey Received 13 May 2004; accepted 9 May 2005 A series of tests were carried out with an eccentrically loaded model surface strip footing on un-reinforced and reinforced dense sand to investigate the behaviour of the footing (decrease in ultimate load with increasing eccentricity, failure surfaces and load displacement relations). The experimental set-up used to run the tests consists of tank, model footing, sand and loading mechanism. A single woven geotextile strip sheet was placed horizontally below the footing s base at a depth half of the footing s width. The primary failure surfaces occurred at the eccentricity side for this laterally unrestricted footing. The use of this reinforcement increased the ultimate load by about 50% for centrally loaded strip footing in comparison with un-reinforced case and its contribution to ultimate load decreased as eccentricity increased in these conditions. Geotextile not only increased ultimate load, but also increased necessary amount of vertical displacement of footing to reach failure compared with un-reinforced case. The experimental results are in good agreement with Meyerhof s effective width concept than the customary analysis and the customary analysis is unsafe outside the core. IPC Code: E02D1/00 Foundations are frequently subjected to moments in addition to vertical loads in practice. Moments are brought about from lateral or horizontal loads (lateral earth pressures, earthquakes, water and wind) acting on structures. The eccentricity in a strip footing, e, can be defined as the ratio of moment (M) over vertical load (Q) (Fig. 1). There are a number of methods for calculating the ultimate load (Q u ) of the eccentrically loaded foundation. These are Meyerhof s effective width concept 1, the customary analysis (the traditional method, the conventional method), Prakash and Saran Theory 2. Meyerhof 1 put forward that the ultimate load (Q ue ) of an eccentrically loaded strip foundation is equal to the ultimate load (Q uc ) of the centrally loaded strip foundation having a reduced width B obtained by subtracting 2e from B (Fig. 2). Some assumptions are made in customary analysis in order to determine the normal base pressure distributions under an eccentrically loaded foundation. These are stress distribution is linear, vertical equilibrium for forces (ΣV = 0), moment equilibrium (ΣM = 0) and the contact is lost between the footing base and the soil where tensile stresses occur. Uzuner 3 investigated the base stress distribution of the eccentrically loaded model strip *For correspondence ( uzuner@ktu.edu.tr) foundations on sand experimentally and concluded that the assumptions of the customary analysis are satisfactory. The base stress distributions of a strip footing are shown in Fig. 3. The ultimate load of eccentrically loaded strip foundation can be determined from the following condition according to Fig. 1 Eccentricity definition for a strip footing Fig. 2 Meyerhof s effective width concept Fig. 3 The base normal stress distributions in customary analysis

2 420 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 the customary analysis: The value of the maximum base pressure (q max ) should not exceed the ultimate bearing capacity (q u ) of the same centrally loaded strip foundation. An eccentrically loaded strip foundation carries less load as much as the inclined combed areas in Fig. 3 than the same centrally loaded one according to the customary analysis. Both Meyerhof s method and the customary analysis are not independent approaches to calculate ultimate load of eccentric footings and are used in conjunction with a bearing capacity theory for centrally loaded footings. In other words, they give reduction in ultimate load of an eccentrically loaded footing. Prakash and Saran 2 produced a theory and gave their bearing capacity factors as function of both internal friction angle (φ) and the ratio of the eccentricity over width of the foundation (e/b). For the past 30 years geosynthetics are being used to increase the bearing capacity of soil. The application is done by placing geosynthetics horizontally as sheets with interval in vertical under the foundation or by mixing the short pieces of geosynthetics with soil. Apparently, geosynthetics are increasing the bearing capacity of soils 4-7. The eccentrically loaded footings on unreinforced soil attracted the interest of some researchers Experimental works on reinforced soils done by the researchers are mainly for the centrally loaded foundations 4 7. On the other hand, eccentrically loaded foundations on reinforced soil received little attention. In this study, the ultimate load of the eccentrically loaded model strip footing on reinforced sand was investigated experimentally and the results were compared to Meyerhof s method and the customary analysis. Experimental Procedure Details of the experimental procedure is repoted elsewhere 15. The main components of the experimental set-up to run the tests are tank, model strip footing, sand and loading mechanism. Tank The internal dimensions of the tank containing the sand are 0.9 m (length, L) 0.10 m (width, W) 0.65 m (height, H) (Fig. 4). The bottom and the sides of the tank were made of hard wood. The front and back faces were made from 12 mm thick glass plates to observe failure surfaces. The strip footing case corresponds to plane strain condition. There are mainly two conditions for the plane strain case. Firstly, deformation in longitudinal direction should be zero (ε z = 0, where ε z = ΔW/W, ε z is strain in longitudinal direction, ΔW is total lateral deformation of tank s faces, W is tank width). This implies that plane strain models should have rigid front and back faces. It is known that side frictions due to movements of sand mass develop between soil and face walls of the tank during loading of model footing. Side friction forces prevent soil movement and cause error in measuring load applied to footing in model tests. This point is especially important in narrow model tests. So, ideally width of the tank should be as long as possible and side frictions should be reduced to a minimum. To use long models has disadvantages in model tests. Secondly, these frictions between soil and the front and back internal surfaces of the tank should be zero. This implies full frictionless internal surfaces of the tank. Since these conditions cannot be met absolutely in models, some criteria should be fulfilled. Otherwise experimental results may contain serious errors and may not represent a plane strain case 16,17. Kirkpatrick and Yanikian 17 proposed that ε z should be less than 0.1% for plane strain models. Two steel frames made of hollow steel profiles were produced and were connected to each other with steel bolts along the sides of the tank to prevent lateral deformations. Steel elements made of solid profiles were welded in the middle part of the steel frames to prevent deformation of the glass plates. The surfaces of the steel frames on which glass plates touch was produced almost perfect plane so that no glass plate was broken during tests. Two dial gauges were placed perpendicularly on the external faces of the glass plates to measure their deformations. Measured strains of the glass plates during tests were found to be well less than 0.1%, so this experimental work well fulfilled plane strain deformation condition 17. Fig. 4 Three views from the tank

3 MOROGLU et al.: BEHAVIOUR OF THE MODEL SURFACE STRIP FOOTING ON REINFORCED SAND 421 Thin latex plates ideally should be placed on the internal faces of the lightly lubricated glass plates to obtain almost frictionless side faces. This application has the difficulties due to movements of the sand mass in different directions. The sand is in direct contact with glass faces in this experimental work. Kirkpatrick and Uzuner 18 showed that the effect of side friction is less than 10% of the ultimate load in B/W=1 (B is footing width), in glass sides, medium dense sand and surface footing conditions The conditions of this experimental work are close to the conditions of Kirkpatrick and Uzuner 18. On the other side, the effect of side frictions is approximately eliminated in this experimental work due to use of the ratio of the ultimate loads (Q ue /Q uc ) in comparison. Model footing The model strip footing was produced by welding 8 mm thick steel plates for rigid footing condition (Fig. 5). The dimensions of the footing are 100 mm 100 mm 80 mm. The V-shaped grooves were opened along the length of the base plate so different eccentricities (inside, on and outside of the core, e = 0, 8.3, 16.7, 33.3 mm or e/b = 0, 1/12, 1/6, 1/3) can be applied. 2 mm thickness was left under the grooves so that eccentricity cannot change much during tests of a rotating footing. The footing base was covered by coarse sandpaper to obtain a full frictional base. Sand The sand used in tests was local Black Sea coastal sand and it has mm grain size (medium-coarse) and its class is SP (poorly graded). Properties of the sand are given in Table 1. Sand was placed in the tank as dense so general shear failure can be obtained in the tests and its relative density (D r ) was kept constant throughout all the tests as 0.74 (γ dry =15.81 kn/m 3 ). Sand was placed in the tank as 50 mm layers g quantity for a 50 mm thick layer was deposited in the tank loosely as uniform thick (about mm) layer. This loose sand layer was lightly compacted with a wooden hammer in the tank to 50 mm thick layer. To trace 50 mm thickness, lines with 50 mm interval were horizontally drawn on internal face of the glass plates. This process continued until sand mass height reached 0.55 m (Fig. 6). For reinforced tests, first 0.5 m height of sand was formed, then geotextile strip was placed and another 50 mm height sand was deposited m height was thought to be well enough, since significant depth is taken as (3-4)B for strip foundations in practice. Dry unit weight of deposited sand (so relative density) in the tank was calculated by weighing the sand mass removed from tank. Before actual tests, several sand depositions in the tank were made. Good agreement was found in these trials. The error about relative density was less than 1%. Loading system A press of a triaxial apparatus was used for the application of the vertical load. A general scheme of the loading system is seen in Fig. 6. The capacity of the press is 10 kn and its speed was chosen as 0.15 mm/min slow enough to take measurement readings from dial gauges and proving ring. The tank sat on the head of the triaxial piston with a round socket under it. The loading was applied with a sharp edge of a loading knife resting on selected groove according to the eccentricity of the test by taking reaction through a proving ring from the upper beam of the press. The loading mechanism (proving ring + loading knife) altogether was screwed tightly to the upper beam. This was not very rigid connection and due to its flexibility it can rotate a very little causing lateral movement of the model footing. In some tests in Table 1 Properties of the sand used in the tests Property Quantiy Fig. 5 The model strip footing Specific gravity, G s 2.66 Maximum dry unit weight, γ dmax (kn/m 3 ) Minimum dry unit weight, γ dmin (kn/m 3 ) Effective size, D 10 (mm) 0.58 D 30 (mm) 0.80 D 60 (mm) 0.95 Coefficient of uniformity, C u 1.64 Coefficient of curvature, C r 1.16 Angle of internal friction, φ direct shear (degrees) 41

4 422 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 Table 2 Properties of the woven geotextile Property Value Mass per unit area 430 g/m 2 Grab tensile strength 86 kn/m Elongation at break(long.-trans.) 14% Fig. 6 The loading mechanism for tests literature 3, the loading mechanism is guided so model footing cannot move any. The proving ring has 6 kn capacity. The rise of the tank was measured by mounting two dial gauges to the side rods of the press. The vertical displacement of the footing was taken by subtracting the deformation of the proving ring from the average rise of the tank, which was measured by two dial gauges. Typical test The tank was placed on the round piston of the press. The sand was deposited in the tank with a procedure described above as 0.55 m height. A single woven geotextile strip equal to the section of the tank area (0.90 m 0.10 m) was placed horizontally below the sand surface in a depth of half the footing width (B/2= 50 mm) in reinforced tests. This depth was considered as the most effective place. The polypropylene geotextile was supplied by Salteks Ltd., Istanbul, Turkey. Properties of the geotextile are given in Table 2. Small irregularities of surface of the sand mass was horizontally flattened by a special device made of aluminium plate travelling on the upper edges of the glass plates cutting the sand mass from top of the sand mass and accumulating sand at the side of the tank without disturbing it. The accumulated sand was removed with a special shovel. The upper beam was mounted and the loading mechanism was lowered on the selected groove of the model footing sitting on the surface of the sand mass. If there was any deviation for selected groove, the model footing was moved a little by hand so loading knife exactly finds the selected groove. Dial gauges were mounted for glass walls and tank. The loading was started and readings from all dialgauges were recorded with at various time intervals. Failure was reached and after some time the test was stopped. Some measurements were taken about failure surfaces and the system was disassembled. Sand was emptied through a hole under the tank, weighted and its density was determined. In design phase of this experimental work, use of stereo-photogrammetric technique by taking pictures from a constant camera to determine failure surfaces better than naked eye is intended. But while both sand mass and tank moved, the technique could not be applied and unfortunately the sand used in the test was not suitable for good contrast pictures. So, failure surfaces were roughly observed by naked eye and measured by hand in the end of the tests. Results and Discussion A series of laboratory tests was done with a model surface (D f = 0) strip footing (B = 100 mm) with different eccentricities (e/b = 0, 1/12, 1/6, 1/3) on dense reinforced sand (D r = 0.74). The results of total eight diffrent tests are seen in Table 3. Each test was repeated at least twice. The averages of the ultimate loads (Q u ) for each test are seen in Table 3. Tests reproduced well. The error about ultimate loads (Q u ) in these repeated tests was less than 2%. Sand as soil and surface footing (D f = 0) were chosen deliberately. With these conditions experimental results becomes comparable with the main approaches, because some terms are eliminated. Otherwise bearing capacity factors enter in, so internal friction angle, φ. Ιn this case, controversial question arises, which φ value should be used in the bearing capacity factors? The internal friction angle of the sand was only obtained by direct shear tests (in strain controlled shear box apparatus) as 41 in this work and ideally φ plane strain value was necessary for

5 MOROGLU et al.: BEHAVIOUR OF THE MODEL SURFACE STRIP FOOTING ON REINFORCED SAND 423 Table 3 Data of tests Number Depth, D f Eccentricity, e e/b Reinforce- Q ult L 1 L 2 ΔH max ΔH max /B (mm) (mm) ment (kn) B B (mm) No /12 No /6 No /3 No Yes /12 Yes /6 Yes /3 Yes Note: Q ult =Ultimate load this strip footing, but it was not unfortunately available here. In literature it is reported 19 that there is an approximate relation between φ direct shear, φ triaxial and φ plane strain φdir.sh < φtri. < φ pl.... (1) The difference between these could be up to 8 degrees 20. In addition both active and passive conditions prevail in the bearing capacity failure of a strip footing and φ values can be different for both 21. The use of this reinforcement increased ultimate load in comparison with unreinforced cases and the contribution became about 50% in centrally loaded footing in these conditions (Table 3). This contribution decreased as eccentricity increased. The woven geotextile strip was neither broken, nor had excessive elongation during the tests. It was exposed to pull out in advanced phases of the loading. Increase of ultimate load by reinforcement can be explained as footing goes down, it forms a triangular core under it, this core pushes soil laterally and laterally displaced soil pushes side soils upwards. The reinforcement in the soil counteracts this mechanism and it is subject to pulling. Friction between reinforcement and soil develops and counteracts pulling of the reinforcement and this increases ultimate load. There was no contribution of the reinforcement to ultimate load in the test for outside of the core (Test 8 in Table 3). Apparently, the reinforcement was not contained in this test by the failure surfaces due to the experimental observation that the horizontal distances between the intersections of the failure surfaces with the sand surface and footing sides (L 1 and L 2 in Fig. 8a) and depth of failure surfaces decreased as eccentricity increased. The general shear failure was obtained due to dense sand condition. As typical examples, loaddisplacement relations of test 3 (unreinforced case, e/b = 1/6 at core limit) and test 7 (reinforced case, e/b=1/6 at core limit) are seen in Fig. 7 in this strain controlled tests. It is obvious that reinforcement not only increased ultimate load of the footing, also increased vertical displacement (ΔH max ) to reach failure. In other words, reinforcement improved loadsettlement relation, e.g., for a certain settlement (settlement condition), reinforced footing gives bigger load than the same unreinforced footing (Fig. 7). It can be seen from Table 3 that as eccentricity increased ΔH max or ΔH max /B decreased in both unreinforced and reinforced cases. It is well known from literature that failure surfaces occur almost symmetrically at both side of the centrally loaded strip footing, while primary failure surface occur at one side of the eccentrically loaded strip footing either at the eccentricity side or at the opposite side and secondary failure surface at the opposite side of the primary failure surface (Fig. 8). This difference is probably the reason why eccentrically loaded footing carries less load than the same centrally loaded footing. In other words, less failure surfaces results less ultimate load. While the failure surfaces were almost symmetrically occurred at both sides of the centrally loaded footing, the primary failure surfaces occurred at the eccentricity side of the eccentrically loaded footing for both unreinforced and reinforced cases of this work (Table 3). As a typical example, test 6 (reinforced, e/b=1/12) from this work and an example from Uzuner 14 (unreinforced, e/b=1/12) are given in Fig. 9. The primary failure surfaces always occurred on the

6 424 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 Fig. 7 Load-displacement curves for Test 3 and Test 7 Fig. 8 Failure surfaces for eccentrically loaded strip footings eccentricity side even when the footing turned 180 in horizontal plane (left side became right side.) in order to investigate whether there was a coincidental phenomenon in this work. The horizontal distances between the intersections of the failure surfaces with the sand surface and footing sides (L 1 and L 2 in Fig. 8a) were measured at the end of the tests and are seen in Table 3. From Table 3 it can be said that as eccentricity increased, the distances (L 1 and L 2 ) decreased in both unreinforced and reinforced cases. Again from Table 3, in reinforced case the distances are bigger than distances in unreinforced cases. The footing turned a few degrees to the eccentricity side, too. Rotation angle was not measured in this work, but it was observed that rotation angle increased as eccentricity increased. In the literature in some unreinforced cases, it was reported 2,9,10 that the primary failure surfaces occurred on the eccentricity side, while others reported the opposite 3,14. From preliminary evaluation it is believed that this contradiction is due to footing s freedom to move laterally (perpendicular to the length). In literature sometimes there is no clear information about lateral movement of the footing in experimental works. Uzuner 3 and Vafaeian 14 reported lateral movement restrictions, and Meyerhof 1, Prakash and Saran 2 reported unrestricting. In practice, both cases can prevail. For example, there is no lateral movement restriction for a retaining wall foundation in failure, while there is lateral movement restriction for the wall bearing foundations of a masonry structure in failure. The lateral movement of the footing was not measured, although there was no restriction for it in this study. The ratio Q ue /Q uc (where Q ue is the ultimate load of the eccentrically loaded footing and Q uc is the ultimate load of the same centrally loaded strip footing per length) becomes as following in Meyerhof s method 1 in surface footing on sand: Q 0.5 γ( B 2 e) N ( 2 ) ue γ B e 2e = = 1 Q 0.5γBN B B uc γ 2... (2) Fig. 9 Failure surfaces for Test 6 and for a test from Uzuner 3 If 1/12, 1/6, 1/3 are put in place of e/b in Eq. (2), the ratio Q ue /Q uc becomes respectively 0.694, and The controversial N γ term is eliminated here for surface footing. It is known that bearing capacity theories especially gives this term different.

7 MOROGLU et al.: BEHAVIOUR OF THE MODEL SURFACE STRIP FOOTING ON REINFORCED SAND 425 Q Q ue uc 3 2e = 1-4 B (Outside core, e > B/6)... (4) Fig. 10 Comparison of the Q ue /Q uc between unreinforced and reinforced cases Fig. 11 Comparison of the Q ue /Q uc with two main approaches The ratio Q ue /Q uc becomes as following in the customary analysis: Q Q ue uc 1 = 6e 1+ B (Inside core, e B/6)... (3) If 1/12, 1/6, 1/3 are put in place of e/b in Eq. (3) and Eq. (4), the ratio Q ue /Q uc becomes respectively 0.67, 0.5, and The experimental Q ue /Q uc -e/b relation is shown in Fig. 10 for both unreinforced and reinforced cases. As seen from Fig. 10, ultimate load decreases with increasing eccentricity for both unreinforced and reinforced cases as expected from theories and experiments in the literature. From Fig. 11, it can be said that two curves are roughly close each other and reinforced values are lower a little bit than unreinforced values except e/b=1/12 case. The comparison of the unreinforced values with the main approaches takes place elsewhere 22. The experimental Q ue /Q uc ratios of the reinforced case are seen in Fig. 11 with the Meyerhof s method and the customary analysis. From Fig. 11, it is seen that the experimental Q ue /Q uc e/b relation is in good agreement with Meyerhof s method than the customary analysis in reinforced sand. On the other hand, customary analysis becomes unsafe outside of the core. Absolute values of the ultimate loads could not be compared with Prakash and Saran 2 due to uncertainty about internal friction angle φ. Conclusions Tests on an eccentrically loaded model surface strip footing resting on reinforced dense sand were carried out with an experimental set-up fulfilling well the plane strain conditions (especially deformation condition). From experimental findings, the following conclusions can be drawn: (i) The decrease in the ultimate load with increasing eccentricity in reinforced case is in good agreement with Meyerhof s method than with the customary analysis and customary analysis is unsafe outside the core. (ii) The reinforcement used in the tests increased the ultimate load by about 50% in comparison with unreinforced case for the centrally loaded footing. This contribution decreased with increasing eccentricity in eccentrically loaded footings. (iii) The primary failure surfaces occurred at the eccentricity side in this laterally unrestricted footing resting on reinforced sand. This is contrary to the failure mechanism of laterally restricted footing resting on unreinforced sand in literature. The horizontal distances between the intersections of the failure surfaces with sand

8 426 INDIAN J. ENG. MATER. SCI., OCTOBER 2005 surface and footing s sides decreased as eccentricity increased in both unreinforced and reinforced cases. (iv) Reinforcement increased vertical displacement to reach failure compared to unreinforced case and vertical displacement decreased as eccentricity increased. In other words, reinforcement improved load-displacement relation of the footing. Acknowledgement The authors thank for the financial support received from the Research Fund of the Black Sea Technical University, Trabzon, Turkey, under project number References 1 Meyerhof G G, The bearing capacity of foundations under eccentric and inclined loads, paper presented at 3 rd Int Conf Soil Mechanics and Foundation Engineering, Zurich, Switzerland, Prakash S & Saran S, Soil Mech Found Div, ASCE, 97 (1971) Uzuner B A, Centrally and eccentrically loaded strip foundations on sand, Ph.D. Thesis, Strathclyde University, Glasgow, Scotland, Khing K H, Das B M, Puri V K, Cook E E & Yen S C, Geotextiles Geomemb, 12 (1993) Omar M T, Das B M, Puri V K & Yen S C, Can Geotech, 41 (1993) Das B M, Shin E C & Omar M T, Geotech Geolog Eng, 12 (1994) 15 7 Wasti Y & Bütün M D, Geotextiles Geomemb, 14 (1996) Ramelot C & Vandeperre L, Compt Rendus Recherges, 2 (1950) 7 9 Eastwood W, Struct Eng, 29 (1955) Dhillon G S, Nat Build Org, 6 (1961) Zaharescu E, Nat Build Org, 6 (1961) Graudet P & Kerisel J, Ann Ponts Chauses, 13 (1965) Lee I K, Foundations subjected to moments, paper presented at 6th Int Conf On Soil Mechanics and Foundation Engineering, Montreal, Canada, Vafaeian M, Strip foundations on sand under centrally and eccentrically loads, Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, Moroglu B, The bearing capacity of the eccentrically loaded model strip footing on reinforced sand, Ph.D. Thesis, (in Turkish), Black Sea (Karadeniz) Technical University, Trabzon, Turkey, Ko H & Davidson W, Soil Mech Found Div, ASCE, 99 (1973) 1 17 Kirkpatrick W M & Yanikian H A, Side friction in plane strain tests, paper presented at 4 th South East Conf On Soil Engineering, Kuala Lumpur, Malaysia, Kirkpatrick W M & Uzuner B A, paper presented at Istanbul Conf on Soil Mechanics, Istanbul, Turkey, Cornforth D H, Geotechnique, 14 (1964) Lee K L, Soil Mech Found Div, ASCE, 96 (1970) Kirkpatrick W M, The plane strain foundation problem, presented at 1 st Int Conf behaviour of off-shore Structures, Sweden, Uzuner B A & Kirkpatrick W M, The ultimate bearing capacity of the eccentrically loaded strip foundations on sand, paper presented at 6 th Danube-European Conf Soil Mech Found Eng, Varna, Bulgaria, 1980