REINFORCED SAND BEHAVIOR OVERLYING COMPRESSIBLE SUBGRADES By Gerald P. Raymond,1 Member, ASCE ABSTRACT: A study of the effect of reinforcement on the (cumulative) plastic settlement, ultimate bearing capacity, and resilient rebound of a repeatedly loaded plane-strain footing on granular soil overlying different compressible bases is pre-sented. Results were obtained using several different granular soils. The repeated load was returned to zero at the end of each cycle. This is characteristic of a rail-guided vehicle loading on a track support. The results demonstrated the importance that both base compressibility and correct location of reinforcement have on the observed plastic and rebound deformations and on ultimate bearing capacity. In-correct location of reinforcement demonstrated no beneficial effect. The plastic settlements were evaluated using a hyperbolic equation. The rebound readings were evaluated using Steinbrenner's analysis. The practical significance to gantry cranes and railway tracks is briefly discussed. INTRODUCTION Tracks for large gantry cranes are commonly subjected to very heavy loads. Recent practice has been to build these tracks on granular support rather than reinforced piled foundation beams resulting in considerable savings. When these granular track supports are built over clay subgrades, even though these subgrades may be firm, seasonal softening of the subgrade layer may be sufficient to permit a bearing capacity failure within the gran-ular material. Loss of granular thickness often results in settlement through the lateral spreading of the granular layer generally (but not always) without damage to the subgrade. A similar problem is that associated with railway tracks. Although train wheel loads are smaller they are more numerous, at least on mainline track. Under repeated loading the ballast undergoes permanent nonrecoverable vertical deformations due, in part, to ballast densification or loosening, particle degradation and, where the maintenance intervals are least, the lateral spread of the ballast. This normally occurs without subgrade damage. Recent experience on British Columbia Rail curved main line is a prime example. Their main line through mountain territory is well drained, free of pumping subgrades, and involves curvatures of up to 12° combined with grades up to 2.2%. Maintenance intervals through these areas are as low as three months. The possibility of ballast reinforcement as a solution to these problems is of major interest to those dealing with track support and is the subject of the work reported herein. PURPOSE AND OBJECTIVE The purpose of the research was to investigate the effect of reinforcement on the settlement and bearing capacity of a plane-strain model footing Prof., Dept. of Civ. Engrg., Queen's Univ., Kingston, Ontario, Canada K7L 3N6. Note. Discussion open until April 1,1993. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on July 19, 1991. This paper is part of the Journal of Geotechnical Engineering, Vol. 118, No. 11, November, 1992. ©ASCE, ISSN 0733-9410/92/0011-1663/$1.00 + $.15 per page. Paper No. 2260. 1663 :(representing a track tie) on a dry granular foundation consisting of sand size particles (representing ballast) overlying single layers of different com-pressibilities, including that of a firm base. The study aimed to do the following. 1. Investigate the effect of foundation reinforcement on the settlement and ultimate bearing capacity of a footing on a granular foundation con-sisting of sand-size particles subjected to repeated loading. 2. Examine the effect of bases of different compressibility, including that of a firm base, on the footing response during cyclic loading. 3. Examine the variation of the elastic rebound deformations resulting from the use of different compressible layers including a firm base. 4. Investigate the effect of the breadth of the footing in relation to foun-dation-soil depth on the observed settlement resulting from the repeated loading. 5. Investigate the effect of different cyclic stresses on the behavior of the footing. 6. Compare some of the results with the response of similar tests on other materials. TESTING EQUIPMENT The test equipment consisted of a material-placement testing tank, load-ing frame, loading pistons, load-measurement device, rigid footing, air-supply system, deformation-dial gauges, soils, layers of different compres-sible material, and grid mesh. A layout is shown in Fig. 1 and is similar to that used by Raymond and El Komos (1978) where major equipment details are given. All loading tests used 19-mm-thick aluminum model footings, whose length extended over the whole width of the tank (200 mm)'. Four sets of thrust bearings, located on drilled seats in a rectangular plate, were used to ensure that the load always acted vertically on the loading plate. In a majority of the tests, neoprene rubber was placed below the foun-LOADING PISTON CIRCULAR BEARING 1£ r Itl THRUST BEARING . .HARDENED STEEL ;*< PLATE FOOTING X DETAIL OF LOADING LAYOUT fi iff rt ^TT 1 = PISTON 2 = FUNNEL 3 = DIAL GAGES = LOAD CELL 5 = TESTING TANK TANK\" ' || ' 6 = FOOTING V FIG. 1. Layout of Test Equipment 1664 dation soil to simulate a softened clay subgrade. This allowed the investi-gation of the effect of different underlying compressible bases. The different compressible materials, when tested alone, gave linear reponses to loads up to those recorded in the model tests. Their properties may be summarized by either the unconfined compression elastic modulus or the modulus of subgrade reaction when the footing was placed without any foundation soil. Results are given in Table 1. The soil reinforcement was provided in the shape of steel mesh. Tests conducted with different aperture sizes gave similar results, so a square 25 mm x 25 mm with opening width of 23.4 mm x 23.4 mm was chosen for the main testing. The mesh was 1.6-mm (16-gauge) welded galvanized wire and was reused from test to test. The reinforcement was cut so that its length and width were 25.4 mm less than the length and the width of the tank. This clearance was provided to ensure that no friction was generated be-tween the reinforcement and the walls of the tank. FOUNDATION SOILS supplied for use to perform ASTM C-190. Check tests were done using The majority of the tests were done using standard 20-30 Ottawa sand crushed limestone and a rounded denstone (ceramic supplied by Norton Chemical Products Inc., Akron, Ohio). The properties of the materials used are given in Table 2. hopper door by 12 mm, and moving the funnel over the whole length of Soil placement was achieved by filling the funnel with soil, opening the the tank at a velocity of 10 cm/s. Each placed layer was 25-mm thick, unless dictated by the placement of a reinforcement layer. For each layer placed, an initial drop of 300 mm established the funnel height. When the required soil depth was reached then a wooden template, equal to the width of the tank, was used at level the soil. Once leveled, the model footing was carefully placed in the middle of the tank and the loading mechanism, dial gauges and load cell carefully positioned. The placement densities given in Table 2 were obtained in the same manner except that several containers of known TABLE 1. Properties of Compressible Base Layers Modulus of Subgrade Base Reaction (MN/m3) Elastic material Thickness B = B = modulus Material type (mm) 75 mm 190 mm (MN/m2) (1) (2) (3) (4) (5) (6) Open-cell neoprene rubber 17-mm compressible layer 1 17.0 9.5 11.7 0.15 Open-cell neoprene rubber 12.5-mm compressible layer I 2 12.5 21 19 0.625 Open-cell neoprene rubber 12.5-mm compressible layer II 3 12.5 85 87 0.725 Closed-cell pure gum amber 12.5-mm compressible layer III durometer 35 4 5 12.5 -420 300 4.4 Rigid — — — — 1665 aximum density 0) 780 kg/m3 610 kg/m3 553 kg/m3 Placement density (10) 1,730 kg/m3 1,560 kg/m3 1,534 kg/m3 Relative density (11) 81% 82% 90% M1,1,1,3 3 3 /m/m/mimumy it) (8kgkgkginns0 0 6 Mde5333361,1,1, ityt en lsci) 1 4 0 oiformfi(71.1.1.Sn Uniefcoioat ndmmm) mou(6 m m81F750 0.4.3. !. 2. LEmmmB A50) m mmTD(571370 0.2.3. tyci ri) he(4ow0 L1.Sp ss nearnd) (36 0.ul0 oung1.AR onz rttisi) uapo(2 qom0%C10 e nd am (Dsanee a toNawesonstttenOimLDvolume were placed within the tank. After filling, these containers were removed and the contained soil weighed to obtain the density. TESTING PROGRAM The procedure used for the repeated load test involving a 75-mm footing is outlined next. Minor modifications were made for other-size footings. At time 0.0 the loading process was started and a 4.0-kPa bearing pressure increment was applied to the footing over 20 s. After 40 s all readings were recorded. These steps were repeated until the peak cyclic load was obtained. Repeated loading was then commenced at a frequency of 1 Hz with stops for readings at 1, 10, 102, 103, and 104 cycles. At the completion of cyclic loading the footing was loaded incrementally to failure. After a failure had occurred, further readings and photographs were taken. Groups of tests were conducted as given in Table 3. Group A tests in-volved five series of tests, the only difference being the compressibility of TABLE 3. Testing Program Cyclic Footing stress width Series (kPa) (mm) (2) (3) (1) I II III IV V 30 30 30 30 30 75 75 75 75 75 Sand Underlying cover base (mm) (see Table 1) (5) (4) Reinforcement depths (mm) (6) 25, 50, 75, 125, none 25, 50, 75, 125, none 25, 50, 75, 125, none 25, 50, 75, 125, none 25, 50, 75, 125, none (a) A Ottawa Sand 150 150 150 150 150 Type 1 Type 2 Type 3 Type 4 Type 5 (b) B Ottawa Sand VI VII 30 30 75 190 75 190 Type 3 Type 3 25, 50, none 38, 76, 114, none (c) C Ottawa Sand VIII 30 75 225 Type 5 25, 50, 75, 100, 125, 150, 175, 225, none (d) D Limestone X XI XII XIII XIV 30 30 30 30 30 75 75 75 75 75 150 150 150 150 150 Type 1 Type 2 Type 3 Type 4 Type 5 50, none 50, none 50, none 50, none 50, none (e) E Limestone XV XVI XVII XVIII XIX 150 150 150 150 150 75 75 75 75 75 150 150 150 150 150 Type 1 Type 2 Type 3 Type 4 50, none 50, none 50, none 50, none 50, none (/) F Denstone XX None 200 200 Type 5 12.5, 25, 38.5, 50, 100, 125, none 1667 the base layer (i.e., the five different base-layer materials in Table 1). Each series involved fivfe different configurations comprising: no reinforcement, reinforcement at 25, 50, 75, and 125 mm depth below the surface. Similarly^ group B, C, D, E, and F tests were divided into different test series that were again divided into a set of tests. Group F involved only static tests to failure. Duplicate tests verified repeatability. GROUP A TESTS—REINFORCEMENT DEPTH AND BASE COMPRESSIBILITY The group A tests were done using a 75-mm-wide footing, 150-mm soil depth, (depth/breadth ratio = 2) loading frequency of 1 Hz, cyclic stress of 30 kPa, and a square wave loading pulse. Plastic Settlements The (culmulative) plastic component of the vertical settlements, observed during repeated loading, for different base compressibilities without any reinforcement are presented in Fig. 2. The settlements are plotted on a natural scale against the number of cycles on a logarithmic scale. These plots show that the plastic vertical settlement increased as both the stiffness of the compressible layer decreased and the number of stress cycles in-creased. At the end of 104 cycles, the vertical settlement was 27 mm for the 17-mm compressible layer (series I with ks = 9.5 MN/m3) and 3 mm for the firm base (series V), a difference of 24 mm. The difference after the first cycle for the same two tests was just 0.45 mm. Clearly the compress-ibility of the base has a dramatic effect on the settlement performance. It may be seen from Fig. 2 that the relationship between the plastic settlement and the number of cycles on a logarithmic scale is not linear. This nonlinearity is in agreement with Raymond and El Komos (1978) and with field data published by the Office for Research and Experiments (ORE) in 1975. The effect on the plastic settlements of placing a reinforcing mesh at varying depths in the foundation sand, using any one given compressibility, is illustrated in Figs. 3, 4, and 5 for base types 1, 3, and 5 (ks = 9.5, 85 MN/m3 and rigid), respectively. For any given compressible base, the per-10° 101 102 103 104 NUMBER OF CYCLES (LOG SCALE) FIG. 2. Unreinforced Soil Plastic Settlements 1668 >/x^ 10 . B = 75 mm 15 D = 2B SERIES 1 \\ \\ Vy Y r/B v D\\ 0.33 \\ VA VAX (OTTAWA SAND) \\\\\\ \\o.66 \" REINF. DEPTH = Dr \\\\\\ 201 ks = 9.5 MN/m3 \\\\ V 1.00 . a, = 30 kPa \\ \\< 1.33 25 f = 1 Hz NO GRID = 25 mm x 25 mm REINF. i i i 30 10° 101 102 103 104 105 NUMBER OF CYCLES (LOG SCALE) FIG. 3. Plastic Settlement Response Using Softest Base (Type 1) when D = 2B | 1.25 g 2.50 S SERIES I ui B = 75 mm 3.75 D = 2B D,/B (OTTAWA SAND) xO.33 O 5.00i REINF. DEPTH = Dr 0.66 ks = 85 MN/m3 1.00 i 1.33 a, = 30 kPa NO 6.25\" f = 1 Hz REINF. GRID = 25 mm x 25 mm 7.50 10° 101 102 103 10\" 105 NUMBER OF CYCLES (LOG SCALE) FIG. 4. Plastic Settlement Response Using 12.5-mm Compressible Layer 2 (Type 3) when D = 2B manent settlement of the footing, when subject to the same load intensity, increased as the depth of reinforcement/footing width ratio increased and as the number of load cycles increased. The curves characterizing the set-tlements all have the same nonlinear pattern that can be curve fitted to an inverted hyperbolic equation as illustrated later. In series I, where the most (17-mm) compressible layer was used (ks = 9.5 MN/m3), the settlement at the end of 104 cycles was 15.5 mm when DJ B = 0.33 and 25.5 mm, when DJB = 1.33, a difference of 10 mm (see Fig. 3). When the same tests were performed using a firm base (series V), settlements of 1.85 mm when DJB = 0.33, and 2.84 mm when DJB = 1.83, were recorded, resulting in a difference of almost 1 mm (see Fig. 5). These reductions represent 35-40% of the maximum settlement. The re-ductions are slightly larger when the DJB = 0.33 results are compared with the unreinforced observations. These results indicated that while foundation reinforcement decreases substantially the observed plastic settlements of the number of load cycles to reach a given settlement, increasing the subgrade 1669 I 0.75 2 1.50 . ^^fc?\\> Dr/B SERIES V \\0.33 UJ B = 75 mm t 2.25\" D = 2B \\o.66 UJ V 1.00 CO (OTTAWA SAND) \\ 1.33 o 3.00 • REINF. DEPTH = Dr NO FIRM BASE REINF. a, = 30 kPa Q! 3.75 f = 1 Hz GRID = 25mmx 25 mm 4.50 10° 101 102 103 —1 10\" 105 NUMBER OF CYCLES (LOG SCALE) FIG. 5. Plastic Settlement Response Using Firm Base (Type 5) When D = 2B qf AFTER SERIES l-V B = 75 mm D = 2B REINF. DEPTH = Dr < ui 101 102 RIGID m SUBGRADE MODULUS (LOG SCALE) FIG. 6. Ultimate Bearing Capacity When I) = 211 rigidity of a soft subgrade has a greater effect. Thus, improving internal drainage so as to decrease subgrade interface softening, where possible, should be a first consideration. Ultimate Bearing Capacity At the end of the repeated load tests the ultimate bearing capacity of the footings were obtained and compared except for the tests on the most compressible material. For the most compressible material large settlements had already occurred. This was 27 mm or 36% of the footing width using no reinforcement, and 15.5 mm or 20% of the footing width with the re-inforcement at 25 mm below the surface (Dr/B = 0.33). Fig. 6 shows the results of the ultimate bearing capacity plotted against the compressibility of the underlying base. There was no systematic trend in the data for the same reinforcement ratio DrIB. For practical purposes the ultimate bearing capacity is little or unaffected by the base compressibility for similar con-figurations {DrlB = constant). The main factor affecting the bearing ca-1670 pacity is the depth of the reinforcement. For any given base compressibility the ultimate bearing capacity increases as the depth of placement or ratio D,JB decreases. This increase was about 35% when the placement depth was 25 mm (DJB = 0.33) and may possibly be higher at smaller placement depths. It was noted that when the mesh was placed at 25 mm it was slightly bent below the edge of the footing and the footing was in contact, or near contact, with the mesh after support failure. Most of the sand deformation at failure occurred above the mesh. Rebound Deformation In practice it is common to use a rebound or loading deformation to evaluate support performance. The measured rebound deformations of the footing on unreinforced sand overlying layers of different compressibilities using an applied pressure of 30 kPa are shown in Fig. 7. The plot shows that rebound readings for tests carried out without reinforcement decreased as the number of cycles increased. This was to be expected since the re-petitive loading not only causes an increase in the soil density with cycling but also improves particle interlock. The interlocking decreases the rebound response far in excess of that caused by the increase in density and is consistent with the railway practice of using slow orders immediately after recompacting ballast to allow particle interlocking time to develop. The change in rebound deformation may be seen to be initially significant. The results shown in Fig. 7 show that in general, at the same number of load cycles, there is a decrease in the rebound deformations as the compressibility of the base decreased. Rebound values were least for the tests using the firm base. While not shown here the effect of reinforcement at varying DJB ratios on the rebound deformation also confirmed that the rebound deformations decreased as the number of cycles increased. The rebound deformations were slightly less than for the comparable unreinforced tests. Another gen-eral trend was that for the same number of applied load cycles, as the depth of reinforcement/footing width (DJB) ratio increased, the rebound readings increased, although there is some scatter in the results. These results are consistent with the total settlement results (Figs. 3,4, and 5) as might be k„ (MN/m3) '10° 101 102 103 10\" 105 NUMBER OF CYCLES (LOG SCALE) FIG. 7. Unloading Rebound for Unreinforced Soil When D = 2B 1671 expected since individual cyclic deformations must be summed to produce total deformations. Summary—Group A In summary the group A tests have shown that the plastic settlements of the footing increased as the compressibilities of the layers increased (Figs. 2-5). Smaller settlements were recorded in the series V tests performed with a firm base while larger settlements were observed in the series I tests performed with the 17 mm compressible layer (ks = 9.5 MN/m3). This trend was also observed from the tests performed with and without reinforcement. The group A tests have also shown (Fig. 6) that the ultimate bearing capacity of the footing after 10,000 cycles was almost unaffected by having layers of different compressibilities underlying the foundation sand regardless of whether the foundation sand was reinforced or not. When reinforcement was introduced into the foundation soil the bearing capacity increased as the reinforcement was placed closer to the contact area. The results of unloading rebound deformation (Fig. 7) show that the smallest readings occurred over a firm base. Reinforcement of the foundation generally re-sulted in smaller elastic rebound deformations although the difference be-tween reinforced and unreinforced test configurations was not significant. Lower reinforcement depth/footing width ratios resulted in lower rebound deformation, although scatter exists in the results. GROUP B TESTS—FOOTING WIDTH AND FOUNDATION SAND DEPTH The group B tests were conducted to examine the effect of footing width and foundation-sand depth. Two series of tests were performed using the 12.5-mm compressible layer II (type 3 base with ks = 85 MN/m3) and a depth/breadth ratio of 1. One series (series VI) used the 75-mm-wide footing on 75 mm of soil for direct comparison of soil depth with series III (D = 25) and the other (series VII) used a 190-mm-wide footing on 190-mm-wide depth of soil. Plastic Settlements The plastic settlements recorded in series VI are shown in Fig. 8 and may be compared with the results shown in Fig. 4 where the only difference was the foundation depth (DIB = 1 for Fig. 8 and 2 for Fig. 4). It is clear from the graphs that the general trend of the results are similar. For the same DIB ratio the greatest amount of settlement occurs when no reinforcement was present. As the sand depth/footing width ratio decreased from 2 to 1, however, the permanent settlement increased. This increased settlement, with lower sand-ratio cover on the compressible subgrade, is believed to be caused by a loosening effect on the sand particles that is intensified by closer proximity to the highly deformable subgrade. Fig. 9 presents plastic settlements obtained from the tests using a 190-mm-wide footing and 12.5 mm compressible layer II {ks = 85 MN/m3). The settlements are less and the curves more linear than the results shown in Fig. 8 for the 75-mm-wide footing and the same base support. This is in agreement with the findings of Raymond and El Komos (1978), who found that wider footings result in smaller plastic settlements for the same bearing pressure. Except for the difference in the shape of the curves in Figs. 8 and 9, the general trends are the same. It may be concluded from the data in Figs. 8 and 9 that as the size of the footing was increased, the plastic 1672 '10° 101 102 103 10\" 106 NUMBER OF CYCLES (LOG SCALE) FIG. 8. Plastic Settlement Response Using 12.5-mm Compressible Layer 2 (Type 3) When D = B ?0.5 I- 1.0-SERIES VII B =190 mm s D = B up.51 (OTTAWA SAND) to 2.0\" REINF. DEPTH = Dr O ks = 85MN/m3 o = 30 kPa | 2.5 rf = 1 Hz UJ z GRID = 25 mm x 25 mm 3.0 10° 101 102 103 104 10s NUMBER OF CYCLES (LOG SCALE) FIG. 9. Plastic Settlement Response with 190-mm-Wide Footing Using 12.5-mm Compressible Layer 2 (Type 3) When D = B settlement decreased after the same number of cyclic loadings of similar average bearing pressure. The number of tests using a 190-mm footing was limited in this investigation but nevertheless they were informative insofar as smaller reinforcement depth continued to give less plastic settlement. Again, the shallower the reinforcement the better (within the range inves-tigated). Rebound Deformation The unloading rebound test results for series VI and VII showed consid-erable scatter and are not shown. After the same number of loading cycles there was a trend that suggests that increasing the Dr/B ratio increased the rebound readings. This would be consistent with a larger rebound being required to produce larger plastic deformations as just observed. At present a comparison of the response of the unloading rebound for constant DIB ratios and base compressiblity is regarded as inconclusive. 1673 GROUP C TESTS—SAND DEPTH ON FIRM BASE Series VIII tests were performed to investigate the effect of reinforcement elevation within a deeper strata of foundation soil. A rigid base was used and the results may be compared with the series V test results. The trends of the total settlements and rebound deformations were similar to the trends already noted for the series V tests. Ultimate Bearing Capacity The major difference was in the results obtained for bearing capacity failure at the end of the cyclic loadings. These results are shown in Fig. 10 and include repeat tests with no reinforcement and with the mesh placed directly on the rigid base. The first point to note from Fig. 10 is that the bearing capacity with the mesh directly on the rigid base results in a higher failure capacity than for the unreinforced foundation soil case. This indicates that complete rough-ness was not achieved on the interface of the foundation soil and the base. It emphasizes the detrimental effect that can occur in practice if only a thin surface layer of the subgrade softens. The second point to note from Fig. 10 is that the reinforcement placed at a depth of 1.3 to 2.0 footing widths results in failure capacities less than that recorded for reinforcement placed at lesser or greater depths and slightly lesser capacities than recorded for the unreinforced soil. It is clearly evident that the location depth of any reinforcement should be of major concern to the designer. Again, the best location of the reinforcement within the range investigated is at a shallow depth nearest the contact face of the footing. GROUP D AND E TESTS—LIMESTONE FOUNDATION SOIL The group D and E tests were performed with an angular freshly crushed limestone to compare trends obtained using the rounded Ottawa sand. The angular limestone sand was chosen because the properties are unlike Ottawa sand. Crushed limestone is more representative of aggregate used for rail-road ballast. Also, the majority of source rocks in railway applications are limestones or dolomites, although these rocks are being replaced by harder n £100 CO HI g 90-REINFi— cc Ul '°\"BASE
(/) LU O 1150 a cc a. < UJ m NO REINF. 100 0 0.2 0.4 0.6 0.8 1.0 REINFORCEMENT DEPTH/FOOTING WIDTH FIG. 13 Ultimate Bearing Capacity for Denstone 1676 N REPEATED LOAD SERIES I a(mm) 0.5 a = 0.2505 + 0.2554 Dr/B 0.24 b 0.23 0.22 0 1 2 DEPTH OF REINFORCEMENT n ,„ WIDTH OF FOOTING ~u''u FIG. 14. Typical Relation between Hyperbolic Equation Constants and Reinforce-ment Depth TABLE 4. a and b for Different Underlying Bases; Ottawa Sand with DIB = 2 Underlying Base 17-mm compressible layer (series I) 12.5-mm compressible layer I (series II) 12.5-mm compressible layer II (series III) 12.5-mm compressible layer III (series IV) Firm base (series V) (D a (mm) (2) b (3) a = 0.2505 + 0.2554Dr/B b = 0.2336 - 0.00416Dr/B a = 0.2404 + 0.1406DJB b = 0.2073 - 0.0062ZVB a = 0.1843 + 0.0863Dr/S b = 0.2120 - 0.0128£>r/B a = 0.2198 + 0.1294DJB b = 0.1753 - 0.0169Dr/B a = 0.1274 + 0.1331ZVB b = 0.1578 - 0.0045Dr/B Dr: depth of reinforcement (from bottom of the footing); B: footing width in same units as Dr. A typical plot for a constant base compressibility is shown in Fig. 14. Com-plete results for the group A tests are given in Table 4. The results shown in Table 4 clearly demonstrate, for these tests, that as the ratio of DrIB increases a increases and b decreases. Increasing a or decreasing b results in higher values of plastic settlement according to (1) for the same number of cycles. Similarly, although not as conclusive, a tends to increase as the base becomes more compressible. There is no significant trend in the value of b given in Table 4, however, when DrIB = 0 the value decreases. Any decrease in b independent of a is counter to the observation that firmer bases result in less plastic settlement. Clearly the effects from the value of a predominate over those from b. REBOUND DEFORMATION ANALYSIS Terzaghi (1943) presents an approximate method of computing the de-formation of an elastic isotropic homogeneous layer of finite depth that he 1677 attributed to Steinbrenner (1984). The method permits calculation of the response of layers of different elastic moduli using the oversimplifying as-sumption that the stress distribution remains unchanged despite the different elastic properties. This is clearly incorrect, but this simplifying assumption is often used in practice, at least for preliminary analysis. It is used herein. given in Table 1. The Poisson's ratio of the open-cell rubber materials is The properties of the underlying compressible tested materials alone are approximately 0.0 and was taken as this value. The Poisson's ratio of the closed-cell rubber material is approximately 0.5 and was taken as this value. The foundation soils were all placed in a relatively dense state (Table 2) and tend to dilate on shearing. Their Poisson's ratio was assumed to be 0.5. No account was taken of the reinforcement. modulus of the foundation soil. Elastic modulus values at each rebound The only unknown, once these assumptions were made, was the elastic reading are easily calculated (for the assumptions made) and are given for the last rebound deformation (at 104apparent, whether reinforcement was used or not, is the effect of the subgrade cycles) in Table 5. What is clearly or base compressibility. The back calculated resilient modulus decreased as the compressibility of the underlying layer increased. For the unreinforced sand an order to magnitude change exists between the extreme values. Similar trends existed when the sand was reinforced, although there is some scatter in the data. There appears to be no obvious trend from Table 5 to indicate the benefit of reinforcement causing an increase in foundation sand stiffness. In view of the data shown in Figs. 7 and 12, where reinforcement resulted in less rebound, the values in Table 5 may result from the known incorrect assumption made. replacing wood ties by stiffer concrete ties British Rail noted a 4% savings The practical significance of stiffer tracks is, however, important. After in fuel consumption. This is in agreement with shorter rolling distances on less deformable track (Reynolds 1876) and less \"wave resistance\" (Reece 1930). The negative factor involved with stiffer track is larger-impact loads. COMPLEMENTARY DATA taken using a railway-width-sized footing on 300 mm of railway-ballast-Following the work reported herein, some large-scale tests were under-reported elsewhere (Bathurst and Raymond 1987; Raymond and Bathurst sized aggregate overlying different compressible bases. The large-scale work, 1987) addressed only a few of the variables used herein. It was, however, able to incorporate aggregate degradation, a factor too small to be measured in this study. Where complimentary, the large-scale study confirmed the TABLE 5. Resilient Modulus after 10,000 Cycles for 30 kPa Tests Ottawa Sand Resilient Modulus (MPa) Limestone MSubgrade material with Reinforcement Depth Ratio Dr rIB (MPa) Dr/B DIB = 2 0.33 0.66 1.00 1.33 None 0.66 None (1) (2) (3) (4) (5) (6) (7) (8) 17-mm compressible layer 29.6 9.7 9.1 9.6 8.1 2.9 8.4 12.5-mm compressible layer I 177.0 44.0 177.0 177.0 177.0 14.0 17.0 12.5-mm compressible layer II 176.0 84.0 107.0 107.0 176.0 46.0 184.0 12.5-mm compressible layer III 369.0 369.0 369.0 185.0 369.0 178.0 56.0 Firm base 146.0 219.0 293.0 439.0 439.0 439.0 146.0 1678 observed behavior of this study. Field data supporting the concepts have been presented by Walls and Galbreath (1987). They reported on a railroad that gave excessive maintenance prior to ballast reinforcement. Excellent success was reported from the use of ballast reinforcement. This is probably due to arching of ballast between ties, causing the track to act as a footing of width equal to the tie length. The reinforcement depth/footing width would then be small. The writer has also used the concept for gantry crane track support repair placing the reinforcement 150 mm below the ties. It is therefore concluded that the model-scale findings are applicable to full-scale field performance of track support. CONCLUSIONS The principal findings obtained from a study of the effect of reinforcement on the plastic settlement, ultimate bearing capacity, and resilient rebound of a repeatedly loaded plane-strain footing on granular soil overlying dif-ferent compressible bases are as follows. 1. The plastic settlements of the granular soil were reduced by increasing the stiffness of the underlying compressible base and by reinforcing the foundation sand. This was apparent for both the measured results and by an overall curve fitting to a hyperbolic function as expressed by (1). 2. Within the range used in the testing program the closer the reinforce-ment to the contact area the smaller the recorded plastic settlements (Figs. 3, 4, 5, 8, 9, and 11). The smallest ratio of reinforcement depth to footing width (Dr/B) used in the cyclic testing was 0.2 (Fig. 9). 3. The ultimate bearing capacity was, in general, observed to increase as the reinforcement depth to footing width (Dr/B) ratio decreased (Figs. 6, 10, and 13). The smallest ratio used was 0.0625 (Fig. 13). Incorrect location of reinforcement can result in a reduction of bearing capacity (Fig. 10). 4. The ultimate bearing capacity was only slightly affected by the com-pressibility of the underlying base when the reinforcement-depth-to-footing-width ratio remained constant (Fig. 6). 5. The footing rebound deformation was generally less when reinforce-ment was present compared with the unreinforced behavior (Figs. 7 and 12). 6. When the footing was repeatedly loaded with the same average pres-sure, broader footings resulted in less plastic settlement. 7. The rebound deformations within the foundation soil were evaluated by assuming Steinbrenner's (1934) equations were valid and full rebound of any underlying layer. Based on this assumption the rebound elastic mod-ulus of the unreinforced foundation soil decreased as the compressibility of base increased (Table 5). IMPLICATIONS TO DESIGN The practical significance of the findings are that the use of reinforcement in a granular foundation subject to repeated loading reduces the rate of plastic deformation. This reduction in plastic deformation would increase maintenance cycle times, thereby reducing maintenance costs. This is true regardless of the compressibility characteristics'of the subsoil. Locating the reinforcing mesh closer to the base of the footing resulted in less plastic 1679 settlements with the least ratio DrIB = 0.2 in this study. Reinforcement also reduced the resilient elastic rebound by increasing the foundation stiff-ness. On soft subgrades, the stiffening could be expected to reduce track maintenance and possible fuel consumption and improve track riding qual-ity. In addition, the presence of reinforcement increased the ultimate bearing capacity of the foundation, allowing for increased axle loads. Finally, and of major significance was the fact that decreasing the compressibility of the subgrade was generally of greater benefit than the addition of foundation reinforcement to reduce plastic deformation. Thus preventing or minimizing subgrade softening should be considered a high design priority since it is difficult to improve internal drainage after construction. ACKNOWLEDGMENTS Research funding was provided by the Tensar Corporation, 130 Adelaide Street, Toronto, Ontario M5H 3R6, through a contract with Queen's Uni-versity at Kingston, Ontario K7L 3N6. The interest and moral support of Messrs. John Templeman, Brendan Saint-George and John Britt who at the time of the contract were members of the Tensar Corporation, is grate-fully acknowledged. Special thanks is accorded to F. Bruce Hayden and Ahmed El Hakim, former graduate students for assistance with the project. APPENDIX. REFERENCES Bathurst, R. J., and Raymond, G. P. (1987). \"Geogrid reinforcement of ballasted track.\" Transp. Res. Rec, 1153, 8-14. \"Optimum adaptation of the conventional track to future traffic. \"(1975). Report No. 7, Office for Research and Experiments of the International Union of Railways, Utrecht. Raymond, G. P., and Bathurst, R. J. (1987). \"Performance of large-scale model single tie-ballast systems.\" Transp. Res. Rec, 1131, 7-14. Raymond, G. P., and El Komos, F. (1978). \"Repeated load testing of a model plane strain footing.\" Can. Geotech. J., 15(2), 190-201. Reece, A. N. (1930). \"Economical selection of rail.\" Proc. 31st Annual Convention, American Railway Engineering Association, 31, 1495-1553. Reynolds, O. (1876). \"On rolling friction.\" Philosophical Trans. Royal Society, Lon-don, England, 166, 155-174. Steinbrenner, W. (1934). \"Tafel zur Setzungsberechung.\" Die Strasse, 1, 121-124. Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley and Sons, New York, N.Y, 510. Walls, J. C, and Galbreath, L. L. (1987). \"Railroad ballast reinforcement using geogrids.\" Proc. Geosynthetics 1987 Conf., 1, 38-45. 1680