Experimental and numerical investigation of footing behaviour on multi-layered rubber-reinforced soil

This paper describes the beneficial effects of multiple layers of rubber–sand mixture (RSM). The plate load tests, using circular plate of 300 mm diameter, were performed at an outdoor test pit, dug in natural ground with dimensions of 2000 × 2000 mm in plan and 720 mm in depth to facilitate realistic test conditions. The rubber used in the RSM layers was granulated rubber, produced from waste tires. The optimum thickness of the RSM layer was determined to be approximately 0.4 times the footing diameter. By increasing the number of RSM layers, the bearing capacity of the foundation can be increased and the footing settlement reduced. The influence of the number of RSM layers on bearing capacity and settlement become almost insignificant beyond three layers of RSM, particularly at low settlement ratios. At a ratio of settlement to plate diameter of 4%, the values of bearing pressure for the installation with one, two, three and four layers of RSM were about 1.26, 1.47, 1.52 and 1.54 times greater, respectively, than that for the unreinforced installation. Layers of the RSM reduced the vertical stress transferred through the foundation depth by distributing the load over a wider area. For example, at an applied footing pressure of 560 kPa, the transferred pressure at a depth of 570 mm was about 58, 45 and 35% for one, two and three layers of RSM, respectively, compared to the transferred stress in the unreinforced bed. By numerical analysis, it was found that the presence of soil-rubber layers resulted in expansion of passive zones in the foundation due to the effectiveness of the confinement provided by the rubber inclusions, and this tends to make the bed deflect less. On the basis of this study, the concept of using multiple RSM layers has not only been shown to improve the performance of foundations under heavy loading, but also, the environmental impacts of waste tires are attenuated by re-using their rubber as part of a composite soil material in civil engineering works.


Introduction
In recent decades, the volume of scrap tire rubber in the world has increased significantly because of the globally developing vehicle industry and due to growing population (Recycling Research Institute [RRI], 2009;Rubber Manufacturers Association [RMA], 2013). Consequently, their disposal has become a major environmental problem The results demonstrated that combined use of the geocell layer and rubber-soil mixture reduces soil surface settlement and pipe deflection and eventually provides a secure condition for buried pipes even under strong repeated loads.
Since one-layer rubber-soil mixtures with optimum thickness could be effective in improving the behaviour of a foundation (Moghaddas Tafreshi & Norouzi, 2012), it seems likely that multi-layered rubber-soil mixture, used in the active zone beneath the footingperhaps over a depth of 1-2 times the footing diametercan improve the foundation response by reducing deformations. Consequently, this paper seeks to investigate the concept of the beneficial effect of multiple rubber-soil mixture layers constructed in the foundation, as might be used in roads, highways, embankments, footings, etc. The vertical spacing between successive layers is particularly considered.
In this paper the abbreviation 'RSM' is used by the authors to describe 'Rubber-Soil Mixture'. Additionally, a numerical study, representative of the full-scale model test, is reported. This was undertaken to understand the behaviour of multi-layered rubberreinforced foundations so as to propose empirical relationships of stress propagation through the unreinforced and reinforced foundation which was not easily achievable using results from the experimental model alone.

Objectives
The overall goal is to demonstrate the beneficial effects of multi-layered RSM with optimum of rubber content, optimum thickness of RSM layers and optimum vertical space between successive layers on the bearing capacity and settlement of foundation beds. Also, the effect of RSM layers on the stress distribution and deformation profile with depth is investigated. The results consist of two parts including results of the plate load tests (Section 6.1) and of the three-dimensional numerical modelling of the foundation bed (Section 6.2).

Test materials 3.1. Backfill soil
A sandy soil passing through the 38 mm sieve with a specific gravity, G s , of 2.62 was used as backfill for the unreinforced layers and also to mix with rubber for construction of the RSM layers. This type of soil was sourced from a local quarry and satisfies the criteria and limitations recommended in ASTM D 2940-09. The soil grading is presented graphically in Figure 1. This soil is classified as well-graded sand (SW) in the Unified Soil Classification System (ASTM D 2487-11). Modified proctor compaction tests were performed on the soil, according to ASTM D 1557-12. A summary of soil properties is presented as Table 1.

Rubber
Granulated tire rubbers, clean and free of any steel and cord, were used in all the tests. The particles have a specific gravity, G s , of 1.17, major dimensions between 2 and 25 mm and a mean particle size of 14 mm. Figures 1 and 2 show, respectively, the grading and a photograph of the rubber particles used in the tests. The rubbers particles were carefully blended with the soil, by a mixer and with manual intervention if necessary, so as to produce a reasonably uniform, non-segregated rubber-soil mixture.

Test set-up
Full-scale plate load tests, simulating small foundations, were performed to investigate the response of untreated soil and the soil-rubber mixture with respect to bearing capacity and settlement. The schematic cross-section of the test set-up, including the model test pit, layers of the backfill soil, RSM layers, the loading system, data acquisition systems (including dial gauges and soil pressure cells) and the geometry of the test configurations (including the parameter definitions) are shown in Figure 3. The following sections present the essential details of the test set-up.

Test pit and instrumentation
All plate load tests were conducted in an outdoor test pit (see Acknowledgements). The test pit, measuring 2000 × 2000 mm in plan and 720 mm in depth, was excavated in   Figure 3. Schematic cross-section of the test set-up of the foundation bed (not to scale) containing a model test pit trench, soil and RSM layers, the loading plate model, loading system, dial gauges and soil pressure cells ('SPC 1', 'SPC 2', and 'SPC 3') inside the foundation bed. middle soil pressure cell ('SPC 2') and bottom soil pressure cell ('SPC 3') are located, respectively, at depths of 210, 390 and 570 mm beneath the centre of loading plate ( Figure 3). The instruments' outputs were recorded in mV and then converted to real stress units using calibration factors supplied by the manufacturer.

Backfill compaction
In order to compact the layers of the foundation including soil and RSM layers, a walkbehind vibrating plate compactor, 450 mm in width, was used. To achieve the required density of backfill layers, the soil and RSM mixture layers were compacted at a thickness of 60 mm and at the optimum moisture content of 5.7% with one and three passes of the compactor, respectively. In all, 20 layers required compaction. In order to try to keep the compaction effort, and consequently the compaction energy, constant, the forward velocity of the compactor was kept constant. To better assess the layers' compaction, cone tests in accordance with ASTM D 1557-12 were performed in some installations, to check the densities and moisture contents of the compacted soil layers and RSM layers. The density values measured in the three cone tests revealed density differences ≤1.8%. The average measured (recovered) moisture content of the layers was between 5.4 and 5.8%. To prevent loss of moisture from the backfill during the load test, the exposed backfill was covered by a waterproof paper. The average measured dry densities (average of three sand cone tests) of soil and RSM layers after compaction were about 16.52 kN/m 3 (approximately 80% of maximum soil dry density) and 13.6 kN/m 3 , respectively.

Loading system
The plate loading system was a hand-operated hydraulic jack, supported against a strong reaction beam spanning the width of the test pit, with the capability of applying a stepwise controlled load up to 50 kN. The diameter, D, and thickness of the loading plate were 300 and 25.4 mm, respectively, according to ASTM D 1196-04. The standard declares that the circular steel plate should be not less than 25.4 mm in thickness, having a diameter between 150 and 750 mm. The steel rigid circular plate was placed at the centre of the ground surface. In all tests, the load was applied monotonically to the model footing at a rate of 1.5 kPa per second until reaching 1000 kPa or until backfill failure. In the absence of a clear-cut failure, the footing was loaded to reach a footing settlement of 75 mm (s/D = 25%). Figure 4 depicts a photograph of the test set-up and operator.

Test programme
To investigate the beneficial effect of RSM layers on the behaviour of foundation, three test series including one, two, three and four layers of RSM (Test Series 2, 3 and 4), as well as an unreinforced condition (Test Series 1) with monotonically increasing load, were conducted. Details of the tests configurations are given in Table 2. 'Test Series 1' provided a control case to which the response of all other foundation arrangements could be referenced. The optimum value of rubber content in a rubber-soil mixture is obtained from the results of 'Test Series 2' which used one layer of RSM with no soil cover (u/D = 0). In this Test Series, the rubber content (R c ) in the rubber-soil mixture was varied between 4 and 16%, by mass of the mixture, in 2% steps. 'Test Series 3' was performed to obtain the optimum value of the thickness of RSM layers (h rs /D) using one layer of RSM. The beneficial effect of number of multiple RSM layers (N = 1, 2, 3, 4) was examined in Test Series 4.
Depth of the first layer of RSM beneath the loading plate (u) in Test Series 3 and 4 and thickness of the soil layer between the mixture layers (h) in Test Series 4 were selected to be 0.2D (based on Yoon, Heo, and Kim (2008)). The width of the RSM layers (b) is expressed in non-dimensional form (b/D) with respect to loading plate diameter (D = 300 mm). In line with the findings of Dash, Sireesh, and Sitharam (2003), Yoon et al. (2008) and Thakur, Han, Pokharel, and Parsons (2012) for 3D reinforcement (i.e. geocell and tire-cell), the parameter b/D was kept constant in all the tests at b/D = 5 on the basis that reinforcement and RSM layers beneath the footing might have, approximately, the same basic mechanisms of foundation reinforcement.

Dial Gauges
Hydraulic Jack

Reaction Beam
Supporting beam to fix dial gauges Figure 4. Photograph of test installation prior to loading include reaction beam, load plate, hydraulic jack and three dial gauges. In order to assess the utility of the apparatus, the accuracy of the measurements, the repeatability of the system, the reliability of the results and finally to verify the consistency of the test data, many of the tests described in Table 2 were repeated at least twice. The results obtained revealed a close match between results of the two or three trial tests with maximum differences in results of around 4-7%. This difference was considered to be small and is subsequently neglected. The consistency of the results demonstrates that the mixture of soil and rubber, the test procedure and the technique adopted can produce repeatable tests within the bounds that may be expected from geotechnical and pavement testing apparatuses.
In order to prevent damage of the soil pressure cells (SPC), they are installed only for Test Series 1 and 4 (i.e. for the foundation beds with one layer of RSM in Test Series 2 and 3, no pressure cells are installed).

Experimental results
In this section, the results of plate load tests are presented along with a discussion, highlighting effects of the different parameters such as rubber content, number of RSM layer and its thickness. Here, the performance improvement of the foundation is represented by considering the bearing pressure, settlement and the pressure distribution down through the foundation.

The effect of the rubber content (R c )
To investigate the effect of the rubber content on foundation performance, Test Series 2 was implemented, placing one layer of rubber-soil mixture, beneath the footing base (with no soil cover, u/D = 0). The thickness of the RSM layer, h rs , was selected as 60 mm (h rs /D = 0.2). The variation in bearing pressure with rubber content at different values of settlement is depicted in Figure 5. This figure reveals that rubber content is more effective in improving the footing bearing capacity at higher footing settlements. Also, the reinforcement effect achieved by adding the rubber is highly dependent on the rate of shear strain. From this figure, it can be concluded that there is an optimum rubber content, about 8%, irrespective of the loading plate's settlement which delivers the maximum increase in the bearing capacity. This rubber content is in the middle of the range of 6-10% as reported by Prasad and Prasada Raju (2009) and Munnoli et al. (2013). Increasing the rubber content more than 8% makes the system response much softer (as also reported by Prasada Raju (2009) andEdincliler et al. (2012)), tending to increase the deformability of the foundation beyond the value for the unreinforced soil. This replacement of the soil grains by a compressible material, like rubber, changes the composite's behaviour from a soil-like behaviour towards a rubber-like behaviour (i.e. an increase in settlement and a reduction in bearing capacity).

The effect of the thickness of RSM layer (h rs /D)
Figure 6(a) shows the applied pressure-settlement response (Tests Series 1 and 3) of the foundation with as a function of the thickness of a RSM layer, h rs /D, when the content of granulated rubber is 8% and the layer is placed at a depth of 0.2 (u/D = 0.2) beneath the footing. As can be seen, in all tests, no clear failure point is evident from the pressure-settlement behaviour. It is clear that, regardless of the level of settlement, when increasing the thickness of the RSM layer, both stiffness and bearing pressure were considerably improved compared to the values measured on untreated soils.
To gain a better assessment of the RSM layer performance, the variation in bearing capacity with thickness of RSM layer (h rs /D) is plotted for different footing settlement ratios (s/D = 2, 4, 6, 8, 10 and 12%) in Figure 6(b). The maximum footing settlement equals 12% of footing diameter, a rather large value. However, the discussion in this paper concentrates on the behaviour at more tolerable settlement ratio values (e.g. s/D = 4%). From Figure 6(b) it can be seen that, with an increase in h rs /D ratio, the bearing capacity increases until, approximately, h rs /D = 0.4, after which its value decreases, irrespective of footing settlement ratio. For example, at a settlement ratio of s/D = 4%, the bearing pressure increases by about 25, 27, 13 and 5% compared to that of the unreinforced bed, for RSM layer thickness ratios, h rs /D, equal to 0.2, 0.4, 0.6 and 0.8, respectively. This example suggests that a foundation system with a RSM layer thickness of more than 0.8 times the footing diameter (h rs /D > 0.8) probably experiences punching failure resulting in a significant reduction in bearing pressure value, even less than that of the unreinforced bed. An alternative explanation is that the large thicknesses of RSM will make the system response much softer (Moghaddas Tafreshi & Norouzi, 2012, causing more deflection to occur, such that no reinforcement effect can be seen.

The effect of the number of RSM layers (N)
To investigate the effect of the number of RSM layers on the foundation response, three additional tests, including two, three and four layers of RSM, were conducted at the optimum thickness of h rs /D = 0.4. They were placed at u/D = h/D = 0.2 (see Table 2, Test Series 4). Figure 7(a) presents the response of the loading plate in unreinforced and reinforced conditions. It is clearly observed that, as the number of RSM layers increases (i.e. as the depth of the reinforced zone increases), both stiffness and bearing capacity at a specified settlement increased, substantially. Similarly, at any given bearing pressure, the value of the settlement decreases with increase in the number of RSM layers. These changes could be attributed to the internal confinement provided by RSM layers in the active zone beneath the footing base, which restricts lateral displacement of different layers and, hence, tends to increase the bearing capacity. The concept of confinement due to fibre reinforcement, which has been termed 'internal confinement', was explained by Yang (1974). In the present situation, the confinement effect may be attributed to the mobilised tensile strength of the rubber particles exploited by interaction between aggregate and rubber particles. In order to make a direct comparison between the results for the unreinforced and multi-layered RSM beds, the bearing pressure values for different numbers of RSM layers, corresponding to the different settlement ratios, are plotted in Figure 7(b). It can be seen that as the number of RSM layers increases, the bearing pressure increases steadily, regardless of the settlement ratio. For instance, at a settlement ratio of s/D = 4%, the bearing capacity values are ≈293, 340, 353 and 358 kPa for one, two, three and four layers of RSMincreases, respectively, in bearing capacity of about 26, 47, 52 and 54% over the unreinforced bed's bearing capacity of 232 kPa. This example shows that the rate of enhancement in load-carrying capacity of the footing reduces with increase in number of RSM layers (N) such that one can anticipate the improvement rates will become insignificant with any further increase in the number of RSM layers. The reason is that the significantly stressed zone beneath the footing is estimated to be about 1-2 times the footing diameter/width into which only two/three layers of RSM can be placed. Any RSM placed below this zone will then only deliver marginal improvement in the foundation's response.

The pressure transferred in depth of foundation bed
The variation in measured pressure inside the unreinforced and multi-layered RSM beds at the three levels of 210 mm ('SPC 1'), 390 mm ('SPC 2'), and 570 mm ('SPC 3') beneath the centre of footing (see Figure 3) is illustrated in Figure 8. In this figure, the pressure values at applied surface pressures of 280 and 560 kPa are plotted with dotted and solid lines, respectively. The significant reduction in pressure inside the foundation bed is easily observed. This reduction is irrespective of the number of RSM layers and of the magnitude of applied load. For example, for a foundation bed containing three layers of RSM (N = 3) at an applied pressure of 280 kPa, the pressure measured at depths of 210, 390 and 570 mm are 176.6, 42.7 and 15.8 kPa, respectively. The pressure measured by the top soil pressure cell ('SPC 1'), at a depth of 210 mm, is only affected by the first layer of RSM (N = 1). The presence or absence of the second-or third-layer RSM has no significant effect on its reading. Similarly, the pressures measured by the middle and bottom soil pressure cells ('SPC 2' and 'SPC 3') are affected, respectively, only by the first two layers (N = 1, 2) and only by the first three layers (N = 1, 2, 3). Thus, the stress at any depth is only affected by the construction above it and never by that below. Figure 8 also shows that the proportion of the applied surface pressure transferred down to a depth of 570 mm beneath the centre of footing base, as measured by the bottom soil pressure cell ('SPC 3'), considerably decreases relative to the unreinforced bed. It appears that an increase in the number of RSM layers improves the foundation's ability to spread load, regardless of the level of applied load (Tavakoli Mehrjardi et al., 2015). For example, at an applied pressure of 560 kPa, the vertical stress at a depth of 570 mm was 149.3, 87.5, 67.1 and 52.2 kPa for the unreinforced bed, and RSM beds with one, two and three layers of RSM, respectively. It also appears that the in-soil stress increases non-linearly with increase in the applied surface stress.
Taken together, the results presented in Figures 5-8 reveal that use of RSM layers in a foundation reduces in-soil stresses and restricts vertical displacements. Insufficient data are available to categorically determine the mechanism by which this is achieved, but the response is consistent with the mechanism, known as the 'confinement effect' in literature of soil reinforcement (Yang, 1974). This mechanism occurs when a reinforced layer acts like a large mat, spreading an applied load over an extended area, instead of directly at the point of contact. It provides a composite soil/reinforcement slab with higher flexural stiffness (Dash et al., 2003;Thakur et al., 2012), higher modulus and load support capabilities within the zone that is significantly stressed by the foundation loadingconsequently decreasing the magnitude of the distributed pressure on the vertical axis beneath the foundation.

Numerical analysis
The numerical simulations for the analysis of multi-layered rubber-reinforced foundation were performed using the finite difference code FLAC-3D (2002). The geometry of the model, its calibration, its verification and a parametric study are discussed in the following sections.

Model geometry
To calibrate and verify the multi-layered soil-rubber system, two different geometries were used. A cylindrical pattern was used to simulate the triaxial test in a calibration stage. Thereafter, the obtained material properties were applied to a numerical model representing the experimental model (see Figure 3). Figure 9 shows the meshing area of numerical model (in this example for a bed with three layers of RSM). The domain was divided into 17200 elements and 19866 grid points. The displacement of the outer boundary was restrained only in the direction at 90°to the boundary while that of the base was restricted in all directions.

Model calibration
As part of the calibration, several triaxial tests were performed to assess the properties of the unreinforced and rubber-reinforced soil layers. The soil, rubber material and the density of the unreinforced and rubber-reinforced soil used in the plate loading tests were replicated in the triaxial tests. Six triaxial tests on unreinforced and rubber reinforced soil samples with 8% rubber (as optimal rubber content), at three confining pressures of 50, 100 and 150 kPa were conducted. The triaxial samples had a diameter  of 100 mm and a height of 200 mm. An elastic-perfectly plastic associative Mohr-Coulomb constitutive model was used to simulate the observed behaviour of unreinforced and rubber-reinforced layers. Even though more sophisticated elasto-plastic constitutive models exist, the Mohr-Coulomb model was deemed satisfactory in the present case as the anticipated stress paths are mainly dominated by shear failure when Table 3. Details of material properties used in the present study obtained from calibration (triaxial test). Backfill Unreinforced soil 9.7 3.9 6.5 34 7 1. significant load is applied to the soil. To calibrate the parameters of the chosen plasticity model, the following points were considered: (a) Gotteland, Lambert, and Balachowski (2005) investigated some triaxial tests on rubber-soil mixture and found that, with an increasing proportion of rubber volume in samples, the trend of most specimens was to yield a decrease in both cohesion and friction angle. (b) The dilation angle of all composites was assumed to be two-third of the value of friction angle in the corresponding composite material as suggested by Alimardani Lavason and Ghazavi (2008).
To obtain the appropriate parameters, the numerical model was used to replicate the triaxial tests on the unreinforced and rubber-reinforced samples. By using a trial-anderror technique, adjusting the input parameters until the results of the numerical analysis closely matched those obtained from the triaxial tests, representative values of bulk modulus (K), shear modulus (G), cohesion (c), friction angle (φ), dilation angle (ψ) and density (ρ), were obtained. Figure 10 compares the stress-strain responses of unreinforced and rubber-reinforced samples obtained from the calibration of numerical simulations and the experimental data measured from the same test configurations. As can be seen, there is, generally, a favourable match between the numerical results and the triaxial tests for both backfills. The soil properties (unreinforced and with 8% rubber inclusions by weight), as adopted for the numerical analysis of the unreinforced and multi-layered rubber-reinforced foundations, are presented in Table 3.

Model verification
After calibration, models (incorporating the materials with the characteristics presented in Table 3 were used to simulate the unreinforced and multi-layered rubber-soil foundations. The loading was applied at a constant, low rate of 1.5 kPa per second in the vertical direction to simulate the non-dynamic, monotonically applied, plate-loading process. Figure 11 illustrates a small part of results at this stage of the study, comparing the pressure-settlement of the unreinforced bed and of the multiple-layer reinforced beds, as obtained from numerical analysis and from the experimental tests. A relatively good match can be observed between the numerical and experimental results. Figure 12 is presented to compare pressure through the depth of the foundation beds, at applied pressures of 280 and 560 kPa, obtained from the numerical and experimental results for Figure 13. Vertical stress distribution in foundation bed obtained from numerical results.
both unreinforced and reinforced beds. Clearly, the numerical model is able to simulate the physical tests results with a high accuracy and, therefore, provides a reliable means of performing analyses additional to those performed experimentally.
To help assess the stress and deformation distribution across the depth of the foundation bed, Figures 13 and 14 illustrate the results of an applied pressure of 560 kPa. Figure 14 shows that the presence of soil-rubber layers resulted in heaving around the footing. This may be because of expansion of the passive zones in the reinforced foundation due to the effectiveness of the confinement provided by rubber inclusions. In the unreinforced condition, part of the passive zone provided by the backfill has been lost, resulting in a reduction in bearing capacity compared with that of the reinforced bed (see Figure 7(a)). This can be expected to make the bed deflect more. Tavakoli Mehrjardi, Ghanbari, and Mehdizadeh (2016) observed that the failure zones in a reinforced slope formed after a greater volume than in an unreinforced slope which might increase the likelihood that confinement be increased by the reinforcement.
As can be seen from Figure 15, the intensity of shear strains beneath the footing has been reduced using soil-rubber layers in the foundation. This might be due to reduction in surface soil settlements, leading to an attenuation of the the observed shear strains beneath the footing. Also, it can be concluded that the failure mechanism has been changed from shear punching to global shear failure by reinforcing the foundation and having an increased number of reinforcement layers. Ebrahimian and Nourzad (2013) Figure 14. Vertical settlements contours in foundation bed obtained from numerical results. similarly concluded that, in triaxial tests, large shear deformations were associated with a narrow band at the middle of the sample's layer, where failure may start.
To gain a better assessment of the stress distribution within both the unreinforced and RSM beds, Figure 16 was presented. This figure shows the vertical stress distribution on horizontal planes at depths of 60, 210, 390 and 570 mm from the ground surface, respectively. The applied surface pressure in all cases remained 560 kPa. Regardless of the number of RSM layers, the variation in vertical stress on a specified plane formed a ring-shaped stress distribution with its maximum on the centreline of loading, reducing with radial distance. For example, for a foundation bed containing three layers of RSM (N = 3), the pressure measured at the centreline of the loading surface and at depths of 60, 210, 390 and 570 mm were about 553, 355, 158 and 98 kPa, respectively. Pancar and Akpinar (2016) using some pressure cells in a foundation, also found out that the stress distribution was ring-shaped, having its maximum on the centreline. Table 4 shows the stress distribution angle (the angle of the stress shadow to the vertical), calculated from Figure 16, for each sort of foundation. Although, the stress spreads in different sorts of reinforced foundations are similar, but it shows that the RSM system can reduce the vertical stress at depth by increasing the stress distribution angle. In respect of the stress distribution angle presented in Table 4, the stress is considered to be distributed over a circular area with a diameter estimated by Equation (1).   n: load-spreading factor which ≈1.92, 1.98, 2.24 and 2.27 for unreinforced foundation, RSM (N = 1), RSM (N = 2) and RSM (N = 3), respectively. In the line with the presented findings, Tavakoli Mehrjardi et al. (2015) proposed a load-spreading factor of n = 1.5 for unreinforced backfill.

Conclusion
A series of circular plate load tests were conducted to assess the ability of rubber-soil mixture (RSM) layers to provide potential foundation improvement. Benefits were assessed in terms of increased bearing capacity, decreased settlement of footings and reduced pressure profile. Based on the results described, the following conclusions can be made: (1) The optimum percentage of waste tire rubber is around 8% of weight of the mixture matrix.
(2) The optimum thickness of RSM layer, to achieve the maximum improvement in bearing pressure and settlement of a footing, is approximately 0.4 times footing diameter.
(3) With increase in the number of RSM layers, the bearing pressure of the footing increases and the footing settlement decreases due, in part, to better load spreading of the composite system. The values of bearing pressure for the RSM beds with one, two, three and four layers of RSM, at a settlement ratio of s/D = 4%, are about 1.26, 1.47. 1.52, and 1.54 times greater, respectively, than for the reference, unreinforced bed. The rate of enhancement in load carrying capacity of the footing was reduced with increase in the number of RSM layers. Performance improvement became almost insignificant beyond three RSM layers, particularly at low settlement ratios. (4) The inclusion of a RSM layer beneath the loading plate leads to a significant reduction in the vertical stress transferred down through the foundation bed by distributing the load over a wider area. However, adding further RSM layers gives substantially less additional load spreading benefit such that a fourth layer is unlikely to give any additional benefit. For the pressure of 560 kPa applied on the footing, the transferred pressures at the depth of 570 mm are about 58, 45 and 35% for the RSM bed with one, two and three layers of RSM, respectively, compared to the pressure in the unreinforced bed. (5) The pressure transferred to a given depth in the foundation bed varies nonlinearly with applied pressure on the footing surface. For the foundation bed with two layers of RSM, the pressure values at the level of 390 mm beneath the centre of footing grew by a factor of 2.35 when the level of the applied pressure only doubled. (6) Numerical analysis shows that the presence of soil-rubber layers resulted in expansion of the passive zones due to the effectiveness of the confinement provided by the rubber inclusions and that this tends to make the bed deflect less. In addition, the RSM system reduces the vertical stress at any particular depth by increasing the effective stress distribution angle.
Generally, the results of this study provide considerable encouragement for the application of multiple layers of RSM (with optimum rubber content (R c ), optimum thickness of RSM layers (h rs /D), optimum embedded depth of the first layer of RSM (u/D) and optimum thickness of the soil layer between the RSM layers (h/D)) for filed-scale footings. However, the tests results are obtained for only one type of soil, one type and size of rubber and one size of footing diameter. Thus, specific applications using the quantitative results should only be made after considering these limitations. In studies on large-and small-scale tests of the behaviour of granular soil reinforced by planar reinforcement, Adams and Collin (1997) and Milligan, Fannin, and Farrar (1986) showed that the general mechanisms and behaviour observed in the small tests could be reproduced at large scale. Therefore, insights into the basic mechanism of a foundation bed protected by RSM layers may be used to guide further studies on larger scale tests and centrifugal model tests. However, the results will aid planning of tests using different types and sizes of rubber, different sizes and shapes of footing, and different types and sizes of soil could be useful for future study. Also, the numerical studies have increased understanding of behaviour and will aid the development of design guidance in the application of multilayered RSM. To gain a better understanding of the system, the rubber particles between the soil particles should be simulated more realistically or a more compatible constitutive model of the rubber-soil mixture should be developed, in any future study.

Nomenclature b
Width of the RSM layers c Cohesion of soil C u Coefficient of uniformity C c Coefficient of curvature D Loading plate diameter D d Assumed equivalent diameter of stress distribution area in a specified depth of foundation D 10 Effective grain size (mm) D 30 Diameter through which 30% of the total soil mass is passing (mm) D 60 Diameter through which 60% of the total soil mass is passing (