Ultimate bearing capacity of strip footing resting on clay soil mixed with tire-derived aggregates

Abstract

This study investigated the use of recycled tire-derived aggregate (TDA) mixed with kaolin as a method of increasing the ultimate bearing capacity ( UBC) of a strip footing. Thirteen 1g physical modeling tests were prepared in a rigid box of 0.6 m × 0.9 m in plan and 0.6 m in height. During sample preparation, 0%, 20%, 40%, or 60% (by weight) of powdery, shredded, small-sized granular (G 1–4 mm) or large-sized granular (G 5–8 mm) TDA was mixed with the kaolin. A strip footing was then placed on the stabilized kaolin and was caused to fail under stress-controlled conditions to determine the UBC. A rigorous 3D finite element analysis was developed in Optum G-3 to determine the UBC values based on the experimental test results. The experimental results showed that, except for the 20% powdery TDA, the TDA showed an increase in the UBC of the strip footing. When kaolin mixed with 20% G (5–8 mm), the UBC showed a threefold increase over that for the unreinforced case. The test with 20% G (1–4 mm) recorded the highest subgrade modulus. It was observed that the UBC calculated using finite element modeling overestimated the experimental UBC by an average of 9%.

Graphical abstract

Keywords

kaolin / physical modeling tests / stabilization / numerical modeling

1 Introduction

The ultimate bearing capacity ( UBC) of soft clay is a critical factor in its stability as a footing. Determining the UBC of soft clay requires an exact experimental apparatus and depends on effective parameters such as the geotechnical properties of the basic soil, loading conditions, and footing dimensions [ 1]. Generally, problems will be experienced during the construction of any structure on soft soil related to the UBC and settlement. In this regard, soil stabilization techniques in which the soil is mixed with different types of binder can improve the geotechnical properties of soft clay. There are numerous reports on the effectiveness of this technique for improving the engineering properties of soft soil [ 2– 5]. In the mixing process, traditional binders, such as cement, lime, and gypsum, have shown positive effects on increasing the UBC of soft soil [ 6]. However, because producing such binders can have economic and environmental consequences, it may be necessary to use alternative materials to increase the UBC of soft clay.

The use of materials such as wire rope and steel powder waste [ 7– 9], waste glass [ 10], and industrial waste [ 11, 12] has been studied extensively in civil engineering. Scrap tires are major manufactured waste materials that can accumulate in nature and pollute the environment. This type of waste material can pose health hazards and increase the risk of fire. The Rubber Manufacturers Association has estimated that 242.8 million scrap tires were produced in the USA in 2015 [ 13]. By reducing the size of scrap tires through cryogenic processing or mechanical grinding, tire-derived aggregate (TDA) can be produced [ 14].

The TDA material has been used in geotechnical engineering as a liquefaction countermeasure [ 15], reinforcement element for mechanically stabilized earth walls [ 16], embankments, and road construction [ 17], to increase the pullout strength [ 18], as railway subgrades [ 19, 20], and in retaining walls and rail lines subject to dynamic loading [ 21– 23].

The geotechnical properties of TDA-sand in element tests have been widely studied [ 24– 29]. Gill et al. [ 30] evaluated the UBC of sandy soil mixed with TDA in physical modeling tests. They examined the UBC of a shallow square footing (75 mm × 75 mm) resting on sandy soil mixed with different percentages of TDA. The effect of eccentric loading on the UBC also was investigated. They reported that the UBC of the sand increased significantly with the addition of TDA. They also found that a maximum TDA content of 30% (by weight of sand) is recommended for increasing the UBC. The improvement in UBC was more significant at higher load eccentricities with an improvement ratio of 7.46.

Khan et al. [ 18] evaluated the effects of TDA on the pull-out strength of steel bars inside of TDA-sandy soil in physical modeming tests. Percentages of 20%, 30%, and 40% shredded TDA of 50, 75, and 100 mm in size were used. Their results showed that the inclusion of 30% shredded TDA increased the pull-out strength from pure sand up to 87%.

Bandyopadhyay et al. [ 31] studied the dynamic UBC of a footing (200 mm × 200 mm) resting on TDA-sand. The treated soil was mounted on a shaking table and was subjected to sinusoidal motions of varying amplitude and frequency. They reported that the dynamic UBC of the footing increased significantly with the use of 50% TDA.

Hataf and Rahimi [ 32] determined the bearing capacity of a shallow footing on sandy soil mixed with different percentages of TDA. The TDA was added to the sand at 10%, 20%, 30%, 40%, and 50% by volume. Their results indicated that the maximum UBC ratio was attained at a TDA content of 40. This optimum content increased the UBC by 83% compared to pure sand. Mittal and Gill [ 33] evaluated the UBC of a square footing (75 mm × 75 mm) resting on TDA-sand. They found that the effects of TDA on the UBC depended on s/ B (%, where s is the vertical settlement of the footing and B is the width of the footing). They indicated that, at 20% TDA at a low strain ( s/ B = 2% to 5%), the UBC of untreated sand increased 282%. On the other hand, at a high strain ( s/ B = 10% to 20%), 40% TDA recorded the most remarkable improvement (780%) compared to pure sand.

In civil engineering, numerical modeling, such as finite element (FE) analysis, has been utilized extensively [ 34– 43]. The results of this type of modeling can be compared with experimental results to validate them. In addition, since FE modeling is convenient and economical, it can be used after validation to produce new results. For example, the load-carrying capacity of the beam of reinforced concrete (RC) frame under static loading was experimentally and numerically investigated by Shishegaran et al. [ 35]. They aimed to develop a transferred stress system (TSS) on the longitudinal reinforcement bars to increase the RC frames’ bending capacity. In their study, the FE modeling validated the stress distribution on the ordinary and TSS bars.

The application of FE modeling for solving geotechnical problems has been thoroughly discussed [ 44]. For example, the determination of the UBC of footings resting on an improved ground has been numerically simulated using FE methods [ 10, 45, 46]. The stress-displacement trends and the corresponded UBCs of these footings were generated and determined using FE modeling.

The literature suggests that TDA is a positive stabilizer for increasing the UBC of treated soil. Most studies have considered a mixture of sand-TDA, although the behavior of kaolin-TDA is significantly different. Only a few studies have considered increasing the UBC of clay containing TDA in 1g physical modeling tests. The present study aimed to determine whether or not the use of TDA can increase the UBC of TDA-clay mixtures. A series of physical modeling tests were conducted on the mixtures, and the UBC of a strip footing resting on soil close to a retaining wall was determined. The response was further compared with locally available clay. The subgrade modulus of the treated clay also was determined. Similar 1g physical modeling tests were done in 3D FE modeling in Optum G-3 software.

2 Materials

Industrial kaolin clay (rated MH according to the Unified Soil Classification System) was selected as the base material and was purchased from Kaolin (Malaysia) Sdn. Bhd. The geotechnical properties of the soil are shown in Table 1. To investigate the performance of the TDA-kaolin mixture in physical modeling tests, several types of TDA were obtained from Yong Fong Rubber Industries Sdn. Bhd. The types of TDA used were: a) large-sized granular (5–8 mm), b) small-sized granular (1–4 mm), c) shredded (0.9 to 3.36 mm or 6–19 mesh), and d) powdery (0.18 mm or 80 mesh). The details of the engineering properties of TDAs can be found in previous publications [ 47, 48].

3 Test setup and experimental program

A series of large-scale experiments were carried out in a model box with inner dimensions of 0.6 m × 0.9 m in plan and 0.6 m in height. The box was made sufficiently rigid to simulate plane-strain conditions more accurately. To ensure the rigidity of the box, it was stiffened at the appropriate points throughout the depth. In the physical modeling tests, the samples were prepared with reference to the maximum dry unit weight and optimum moisture content of the individual TDA-kaolin mixture. This mixing process was based on BS 1377−1 [ 50]. The mass of soil required in each test for a given box volume was calculated, and compaction of the TDA-kaolin was done in five layers using 27 blows.

A total of 13 physical model tests were prepared. Powdery (P), shredded (SH), small-sized granular G (1–4), and large-sized granular G (5–8) TDA were mixed with kaolin at contents of 0%, 20%, 40%, and 60% by weight. The tests were denoted as TDA K(α)-TDA(β) where α is the percentage of kaolin and β is the percentage of TDA. The basic geotechnical properties of the kaolin-TDA of void ratio, optimum moisture content, and maximum dry density are shown in Fig. 1.

The strip footing was constructed as a steel box of 580 mm in length and 75 mm in width with a thickness of 25 mm. The footing length was almost equal to the box’s width to maintain optimal plane-strain conditions. The ends of the footing plate were polished to reduce friction. Static loading was applied concentrically to the footing using an air jack, and the displacement was measured by two dial gauges, one on each side of the footing. The average of the two readings was taken as the net settlement of the footing.

Loading was conducted under stress-controlled conditions at increments of 10 kPa per minute. A load cell was positioned on the strip foundation to control loading. It should be noted that there should be no interference between the walls of the tank and the failure zone of the strip footing. Prandtl [ 49] stated that, in the undrained condition, the critical distance required from the edge of the footing depends on the width of the footing and should be at least be equal to the width of the footing ( B). In this study, this critical distance was selected as 1.13 B.

4 Numerical modeling

In this study, Optum G3 2D FE software was used to determine the UBC of the strip footing under laboratory model-testing conditions. This software allows for static loads in elastoplastic and limits analyses. For the determination of the UBC, limit analysis was used as recommended by the software. FE modeling was used to simulate a cantilever retaining wall backfilled with TDA-kaolin or pure kaolin and the strip footing. Both the kaolin and TDA-kaolin backfills were modeled using a Mohr−Coulomb (MC) material model. The internal friction angle, cohesion, and dry and saturated unit weights should be determined in the MC model.

To accurately determine the cohesion of kaolin, which is an important input parameter for MC material modeling, several in situ vane shear tests were performed, and the average cohesion was calculated. The friction angle of the pure kaolin was considered to be zero. In the loading stage, the unit vertical stress was applied as the multiplier distribution stress along the footing, and Optum G3 determined the multiplier coefficient at which the footing failed. Any additional geotechnical properties required for the TDA-kaolin samples were determined using basic geotechnical tests. The densities of the TDA-kaolin samples were obtained from laboratory compaction tests. The elastic modulus and shear strength parameters were obtained from consolidated undrained tests. Figures 2(a) and 2(b) show the shear strength properties of each test as inputs of FE modeling.

For all models, standard fixities were applied to prevent translation of the sides of the model. The size and fineness of the model and FE mesh were determined through mesh sensitivity and size sensitivity analysis. This analysis was conducted in four phases:

Phase (a): geometric modeling of retaining wall, strip footing, and backfill;

Phase (b): assignment of material properties;

Phase (c): meshing;

Phase (d): loading during limit analysis.

The UBC of the footing was determined by limit analysis of the upper, lower, and mixed modes. Figures 3(a) and 3(b) show the experimental physical modeling test and numerical simulation, respectively.

5 Results and discussion

5.1 Stress−settlement behavior of the samples

The stress–settlement results for unreinforced kaolin and the TDA-kaolin mixtures are shown in Fig. 4. The results indicate that the UBC of the strip footing resting on unreinforced kaolin was 103.4 kPa.

It is evident from the stress-settlement curve that the behaviors of the TDA-kaolin mixes were different from one another, and no similar trend can be observed. In the case of pure kaolin, the footing failed at a small vertical displacement of approximately 5 mm. Because of the texture of TDA and because the TDA-kaolin was much more compressible than the pure kaolin, the addition of all types of TDA increased the ductility of the mixtures (Fig. 4). This increase in the ductility of the TDA-soil mixtures has been demonstrated and discussed in previous studies [ 18, 50]. In the case of pure kaolin, the area below the footing suddenly dropped vertically, and no heave occurred along the footing. In the other tests, different failure patterns were observed. No sudden failure was seen, and the failure patterns were gradual because of the elastic behavior of the TDA in the mixture. In some tests (G-TDA), the footing also experienced a slight tilt. The deviator strain of unreinforced kaolin is numerically shown in Fig. 5.

5.2 Bearing capacity ratio

For ease of interpretation of the results, the UBC has been converted to the bearing capacity ratio ( BCR), which is expressed as:

(1) B C R = \frac{UB{C}_{\mathrm{T}\mathrm{D}\mathrm{A}-\mathrm{k}\mathrm{a}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}}}{UB{C}_{\mathrm{p}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{k}\mathrm{a}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{n}}} ,

where UBC _TDA−kaolin and UBC _{pure−kaolin} are the UBC of the stabilized samples and of the untreated soil, respectively. A BCR of greater than 1 denotes the positive effect of TDA on UBC, while a BCR value of less than 1 indicates that the TDA had a negative effect on the UBC.

Figure 6(a) shows the experimental BCR values for different percentages of powdery TDA. As seen, the addition of 20% powdery TDA (K80-P20) increased the UBC of the strip footing resting on pure kaolin 38%. An increase in the TDA content (K60-P40) caused a slight improvement of about 2%. With a further increase in the TDA content (K60-P40), the UBC decreased 44%. The main cause of this decrease in UBC likely was that the high TDA content (60%) significantly decreased the cohesion of the mixture.

The trend for shredded TDA differed from that of powdery TDA. In this case, all the TDA contents caused an increase in the UBC. Figure 6(b) shows that the TDA mixture K80-SH20 increased the UBC over that of the pure kaolin 233%. Similar improvements (284%) were observed for both the K60-SH40 and K40-SH60 mixtures. Figure 6(c) shows the effects of granular TDA on the BCR. As with the shredded TDA, the TDA content of G(1–4) increased the UBC. Samples K80-G(1–4)20, K60-G(1–4)40, and K40-G(1–4)60 increased the UBC 291%, 271%, and 153%, respectively. Figure 6(c) compares the effects of large granular (5–8 mm) TDA on the UBC. Clearly, the inclusion of this type of TDA showed a positive effect on the BCR.

The tests of K80-G(5–8)20, K60-G(5–8)40, and K40-G(5–8)60 increased the UBC 300%, 262%, and 216%, respectively. Overall, compared to all physical modeling tests, the tests on K80-G(5–8)20 with a UBC of 310 kPa and BCR of 3 were the most effective in increasing the UBC. Figure 7 compares the experimental UBC values of each test.

5.3 Comparison with FE modeling

Figures 8(a)–8(d) compares the calculated experimental and numerical UBC values from the tests for lower bound (LB), upper bound (UB), and mixed-mode (mixed) elements. Only the final UBC has been presented because the limit analysis was used to calculate the UBC. The stress-displacement trend from FE modeling has not been presented. Figures 8(a)–8(d) indicate that the experimental UBCs were approximately consistent with the mixed-mode FE modeling for the four types of TDA. However, when the experimental UBC and FE UBC were compared in mixed mode, the FE modeling overestimated the experimental UBC. Therefore, it was decided to introduce a reduction factor (RF) for the estimation of experimental UBCs from FE modeling as:

(2) \mathrm{R}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r} \mathrm{f}\mathrm{o}\mathrm{r} U B C = \frac{UB{C}_{\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l}}}{UB{C}_{\mathrm{F}\mathrm{E}\mathrm{M}}} .

This RF for the UBC converted the FE UBC for the new experimental tests. Because the positive effect of the TDA on the UBCs was observed in the shredded, small-sized granular (1–4 mm), and large-sized granular (5–8 mm) TDA, the RFs were determined only for the experimental TDA. Figures 9 shows the calculated RFs for the UBCs. As seen, the RF ranged from 87% to 96%.

5.4 Subgrade modulus of reinforced samples

The soil’s subgrade modulus ( K _s) is a key parameter in analysis and design programs such as SAP and SAFE. Generally, the K _s of the soil is defined as (Terzaghi [ 52]):

(3) K_{\mathrm{s}} = \frac{{\sigma }_{\mathrm{u}}}{\mathrm{\Delta }} ,

where K _s (kN/m ²/m) is the modulus of subgrade reaction of the soil and {\sigma }_{\mathrm{u}} (kN/m ²) and \mathrm{\Delta } (m) is the stress applied to the foundation and settlement, respectively. Equation (1) assumes that the elastic soil compressed by {\sigma }_{\mathrm{u}} can be replaced by a bed of discrete linear springs. In this study, where the kaolin soil was improved with a different type of TDA, K _s in Eq. (1) can be modified as:

(4) K_{\mathrm{s}} = \frac{UBC}{D} ,

where UBC is the ultimate bearing capacity of the strip footing and D is the vertical displacement of the improved soil at the moment of failure.

Figure 10(a) shows the calculated subgrade modulus of the reinforced samples. As can be seen, the highest K_s of 25.87 (MN/m ²/m) was for K80-G(1–4)20. Figure 10(b) compares the K_s values for the different types of TDA. As seen, the UBC and vertical displacement of K80-G(1–4)20 were 301 kPa and 11.4 mm, respectively. When the highest UBC value (K80-G(5–8)20 of 310 kPa is compared with that of K80-G(1–4)20 (301 kPa), it can be seen that K80-G(1–4)20 performed better for K_s. This confirms that, even with a lower UBC, because the corresponding vertical displacement at failure occurred at a lower level, the K_s values for K80-G(1–4)20 were higher than for K80-G(1–5)20. In Fig. 10(b), the 20% TDA recorded the highest K_s of all TDA types. This suggests that increasing the TDA content in the mixture increased the UBC and subgrade modulus of the footing up to a specific TDA limit in the mixture. The general TDA trends indicate that further addition of TDA decrease the strength and the UBC of the mixtures.

6 Conclusions

In this study, the effects of four types of TDA mixed with kaolin on the UBC of a strip footing were investigated. The samples were prepared with reference to the individual TDA-kaolin mixtures’ maximum dry unit weight and optimum moisture content. A total of 13 physical model tests were prepared and tested. This stabilization process was simulated and compared with the results of FE modeling in Optum-G3. Limit analysis was utilized in FE modeling to find the UBC. The following conclusions can be drawn from the present study.

1) The inclusion of all types of TDA increased the elastic properties of the mixtures, which caused the footing to fail at larger vertical displacement values than for pure kaolin.

2) The addition of shredded, small-sized granular (1–4 mm) and large-sized granular (5–8 mm) TDA increased the UBC of the strip footing. The addition of 60% powdery TDA, however, decreased the UBC. The highest UBC was achieved by kaolin mixed with 20% G (5–8 mm) at 310 kPa.

3) When the kaolin was mixed with 20% G (1–4 mm), the highest subgrade modulus of the reinforced samples of 25.87 MN/m ²/m was achieved.

4) FE modeling in Optum-G3 software showed acceptable accuracy for modeling of the experimental UBC.

Overall, the addition of TDA to kaolin was efficient for reinforcement. It should be noted that the results for the UBC in this study could have been influenced by the properties of the TDA and the loading conditions. Further experimental studies examining different TDA properties for different footing sizes and loading conditions are required to develop general conclusions.

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