J. Cent. South Univ. (2012) 19: 1116-1124
DOI: 10.1007/s11771-012-1117-z
Bearing capacity and settlement of strip footing on
geosynthetic reinforced clayey slopes
S. A. Naeini, B. Khadem Rabe, E. Mahmoodi
Department of Civil Engineering, Imam Khomeini International University, Qazvin 16818-34149, Iran
? Central South University Press and Springer-Verlag Berlin Heidelberg 2012
Abstract: The effect of geosynthetic reinforcing on bearing capacity of a strip footing resting on georeinforced clayey slopes was investigated. The results of a series of numerical study using finite element analyses on strip footing upon both reinforced and unreinforced clayey slopes were presented. The objectives of this work are to: 1) determine the influence of reinforcement on the bearing-capacity of the strip footings adjacent slopes, 2) suggest an optimum number of reinforcement and 3) survey the effect of friction angle in clayey soils reinforced by geogrids. The investigations were carried out by varying the edge distance of the footing from slope. Also different numbers of geosynthetic layers were applied to obtaining the maximum bearing capacity and minimum settlement. To achieve the third objective, two different friction angles were used. The results show that the load-settlement behavior and ultimate bearing capacity of footing can be considerably improved by the inclusion of reinforcing layer. But using more than one layer reinforcement, the ultimate bearing capacity does not change considerably. It is also shown that for both reinforced and unreinforced slopes, the bearing capacity increases with an increase in edge distance. In addition, as the soil friction angle is increased, the efficiency of reinforcing reduces.
Key words: geosynthetic reinforcing; numerical analysis; bearing capacity; strip footing; clayey slope; friction angle
1 Introduction
Foundations are sometimes built near the edges of slopes. Examples of such practice are buildings or roads constructed in hilly regions and foundations for bridge abutments resting close to slopes. The bearing capacity of a foundation constructed near the edge of a slope assumes its importance in view of the fact that performance of the structure depends on the stability of the slope and the soil bearing capacity. When a shallow footing is placed in the vicinity on the edge of slope and subjected to axial loading, it results in a reduction of ultimate bearing capacity compared to that constructed on a horizontal ground surface. The stability of a foundation located on top of a slope is further affected by the edge distance and the slope angle, as SHIELDS et al [1] reported. Therefore, the investigation of the means to improve the bearing capacity and stability of foundations near the edges of slopes is one of the major aspects in the design of such structures, as they are more liable to failure than other types of structures. However, very little researches has been carried out for calculating the bearing capacity of the footings embedded near sloping ground [2-5], but all of them have introduced some parameters that can be just used for sandy soils, and if they are applied for clayey soil, the ground must have gradual steep as slope less than friction angle of soil.
Nowadays, using reinforcement for improving the stability and settlement characteristics is common. There are many types of reinforcements like geomembranes, geosynthetics, and geotextiles. Introduction of high tensile strength reinforcing materials to stabilize embankments or existing slopes to sustain loads from traffic or heavy structures has been widely adopted in practice. An understanding of the behavior of reinforced slopes loaded with a surface footing is of practical importance for geotechnical engineers. Although there are several research studies on reinforced level ground [6-10], most of these researches are based on reinforced sandy soils, but there are many situations that building structures on clayey soils even on clayey slopes is unavoidable.
Thus, some researches for analyzing the treatment of reinforced clayey soils were carried out, and the behavior of strip footing resting on reinforced clayey soil was analyzed [11-17]. Some results were obtained from these studies, for instance, they found that settlement under footing was reduced by increasing the number of layer, stiffness and size of reinforcements. OTANI et al [11] concluded that bearing capacity of the reinforced ground was improved as the depth and length of geosynthetics were increased, but there was an optimum depth for maximum reinforcing effect. In addition, they found that there was an optimum number of geosynthetic layers.
Investigations of footings on reinforced slopes are rather limited [18-19]. These are the same reinforced ground investigations just focusing on sandy slopes, but as mentioned above, there are many inevitable sites that footing are rested on clayey slopes. Thus, BAHLOUL [20], SAWWAF [21] and YETIMOGLU et al [22] carried out some studies on these situations. A conventional solution is removing a part of weak soil and replacing it with sandy soil. This method is so expensive and the main aim of engineering is to build safe and cost effective structures. For this reason, SAWWAF [21] combined this method with reinforcing and used a reinforced sand layer over clayey soil adjacent slope. So, BAHLOUL [20] used randomly fiber reinforced sand cushions upon clayey slopes. In this work, we focus on just clayey soils next to slopes and inclinations which are reinforced with geosynthetics in one or more layers.
The main purposes of this work are to examine some salient aspects that influence the performance of a strip footing resting on a clayey slope, by the inclusion of layers of geogrid reinforcement, to understand the reinforcement mechanisms, and to recommend an optimal number of reinforcement. The parameters which varied in this work are the edge distance between the footing and the crest of the slope, numbers of reinforced layers and also two friction angles.
2 Material properties
The plane strain elastoplastic finite element analysis was carried out using the program PLAXIS. All the finite element calculations were based on six-nodded triangular elements with a three-point Gaussian integration rule to calculate the element stiffness matrices. In this work, the clay was modeled using Mohr-Coulomb criterion. Five material parameters were required to specify the soil model in each analysis, including effective cohesion (c'), effective angle of internal friction (φ'), elastic modulus (E) and Poisson ratio (υ). In addition, it was necessary to specify the dry unit weight of the soil (γdry), reinforced layer properties and reduction factor (Rinter). Note that the soil modeled in this work was assumed complete dry, because the level of ground water was assumed at the lower boundary of the soil mass. The material parameters adopted in the analysis are presented in Table 1.
The geosynthetic reinforcement was modeled by using elastic “geotextile elements”. A geogrid CE121 with high density polyethylene of 8 mm × 10 mm mesh size was used. The physical and mechanical properties of reinforcement are given in Table 2. The geogrid CE121 which is used in the model is shown in Fig. 1.
Table 1 Properties of soil used in modeling
Table 2 Physical and mechanical properties of reinforcement
Fig. 1 Geosynthetic used in model (geogrid CE 121)
3 Analysis considerations
For modeling and investigating the scope in this work, there are many methods such as upper bound method, lower bound method, slip line method, limit equilibrium method and finite element method. As mentioned by OTANI et al [11] for obtaining the bearing capacity of footing, there are five conditions that should be satisfied, most of them are unknown for the limit equilibrium method that is used widely in practical engineering, and they are known for finite element method. So, KOATAKE et al [23] modeled the result of compression tests on reinforced sand by elastoplastic finite element method. This method is greatly available in literatures, such as MOAVENI [24]. Finite element method is commonly accepted for analyzing in both practical and theoretic contents. Hence, finite element method was used and analysis was performed by the finite element software PLAXIS, which can manage and expedite a wide range of geotechnical problems.
The soil mass which was modeled by PLAXIS software, has the length of 50B and the height of 12B, where B is the width of the strip footing including a slope with inclination 1H:1V in one corner. Distance between edge of slope and corner of footing (D) is one of variables as well as footing width B and number of geosynthetic layers.
The geometry of a typical finite element model adopted for the analysis is shown in Fig. 2. The left vertical line and the right vertical side of the model were constrained horizontally, and the bottom horizontal boundary was constrained in both the horizontal and vertical directions. The interaction between the geosynthetic and the surrounding soil was simulated by interface elements located between the reinforcement and the soil surfaces. The interface elements were connected to soil elements by three pairs of nodes. The stiffness matrix for interface elements was obtained using Newton–Cotes integration points. The interface friction angle and adhesion between the contact surfaces were modeled by assigning a suitable value for the strength reduction factor at the interface compared with the corresponding soil strengths.
Fig. 2 Schematic diagram of model test configuration (B is width of footing and D is edge distance of footing)
In all the calculations described in this work, the footing was considered to be very stiff and rough. To carry out this calculation, the settlement of the footing was simulated by means of a uniform prescribed displacement at the top of the clay layer instead of modeling the footing itself.
The adopted soil parameters were assumed to remain the same in all the finite element analyses for the unreinforced system. For the reinforced case, a reinforcement layer was introduced at the required depth with appropriate strength reduction factors, then another reinforced layer was added and analysis was repeated, and finally the third reinforced layer was added and again analysis was repeated. Distance between reinforcement layers and first layer of ground level was assumed the same and equal to footing width B. The width and length of reinforcements were assumed large enough so that they do not have any effect on the bearing capacity.
Finite element analyses were carried out by applying vertical prescribed displacements and zero horizontal prescribed displacements to the nodes at the base of the footing.
4 Results of finite element analysis
4.1 Comparison between different methods of bearing capacity calculations
For making sure the results of PLAXIS software and comparing the finite element method findings with results obtained from some methods with experimental bases, a soil mass without any slope was modeled and then ultimate bearing capacities were compared.
TERZAGHI [25] used former equations and extended them to take into account the weight of soil and the effect of soil above the base of the foundation on the bearing capacity. TERZAGHI’s equation has many assumptions: 1) The soil is semi-infinite, homogeneous and isotropic; 2) The problem is two-dimensional; 3) The base of the footing is rough; 4) Mohr-Coloumb criteria; 5) The ground surface is horizontal; 6) The failure is caused by general shear; 7) The overburden pressure at foundation level is equal to a surcharge load (γDf, where γ is the effective unit weight of soil, and Df is the depth of foundation less than the width B of the foundation). Terzaghi’s equation is:
(1)
where qult is the ultimate load per unit length of footing; c is the unit cohesion; γ is the effective unit weight of soil; B is the width of footing; Df is the depth of foundation; Nc, Nq and Nγ are the bearing capacity factors. They are functions of the angle of friction, Ф.
Since TERZAGHI’s method is limited to strip footing, MEYERHOF [26] presented a general bearing capacity equation which takes into account the shape and the inclination of load. The general form of equation suggested by MEYERHOF for bearing capacity is
(2)
where c is the cohesion; 
γ′ is the effective unit weight above the base level of foundation; Sc, Sq and Sγ are the shape factors; dc, dγ and dq are the depth factors; ic, iq and iγ are the load inclination factors; B is the width of foundation; Nc, Nq and Nγ are the bearing capacity factors.
HANSEN [2] extended MEYERHOF’s equation with two additional factors to take care of base tilt and foundations on slopes. VESIC [3] used the same form of equation suggested by HANSEN. All three investigators computed the values of Nc and Nq, but the equations used by them for computing the values of Nγ were different.
Nγ=(Nq-1)tan (1.4Ф) (MEYERHOF) (3)
Nγ=l.5(Nq-1)tanФ (HANSEN) (4)
Nγ=2(Nq+l)tanФ (VESIC) (5)
In this work, there were not any inclinations in loading and type of footing same as TERZAGHI’s assumption is assumed strip, therefore the main cause of results variation is related to Nγ. The results of four methods are summarized in Table 3.
Table 3 Comparison of different methods in bearing capacity calculation
As Table 3 shows clearly, the bearing capacity obtained from experimental methods is near to that from finite element method. The difference of TERZAGHI’s method is relatively large, which is related to the assuming sinking zone, because experimental investigations show that this zone has different shapes.
Load-settlement curves were obtained for the test models. Since there was no definite failure point observed on the load-settlement curves, the ultimate bearing capacity was determined by the following method. Tangent lines were drawn from the initial and end points of the load-settlement curve and the point of intersection of these tangents was produced back to the x-axis to obtain the ultimate bearing capacity (Fig. 3).
The load-transfer mechanism for the reinforced slope can be shown by the results of finite element analysis. The plastic points obtained from the analysis are shown in Fig. 4. The plastic failure zone of the clayey slope is intercepted by the geogrid layer and the stress distribution is extended much below it. This, in fact, results in spreading of the footing load into a wider area beneath the reinforced zone, which is formed by a relatively rigid region of soil and reinforcement directly underneath the loaded area. This deep footing effect leads to an improved load-carrying capacity of the footing.
Fig. 3 Bearing capacity calculation
Fig. 4 Plastic points
These results correspond with the findings of OTANI et al [13] obtained in clayey soils, and a special method of finite element named RPEEM was used.
4.2 Effect of edge distance of footing
A main parameter which was indicated by other studies on sandy slopes is the footing edge distance. In this work, for identifying the effect of it on bearing capacity, a series of numerical analysis were performed for eleven different edge distances of the footing on both reinforced and unreinforced slope (1H:1V), corresponding to D/B=0, 1.0, 2.0, 3.0, 4.0 and 10.0. The variations of ultimate bearing capacity (expressed as non dimensional ratio qu/γB, where qu is the ultimate bearing capacity and γ is the unit weight of the soil) at different edge distances for one layer reinforcement are shown in Fig. 5. The results clearly indicate that, for both reinforced and unreinforced slopes, the ultimate bearing capacity increases with increasing edge distance. At an edge distance of 10B, the ultimate bearing capacity of a footing on sloping unreinforced ground approaches that of a footing on a level surface. The effect of slope is minimized when the footing is placed at an edge distance beyond ten times of the width of the footing. This change in ultimate bearing capacity of footing with its distance to slope edge can be explained by increasing the passive earth pressure with increasing distance from slope. More passive pressure causes wider and deeper failure zone, failure zone, thus bearing capacity increases.
Fig. 5 Variation of qu/γB with edge distance
Furthermore, Fig. 5 shows that at any given edge distance, the ultimate bearing capacity of a footing on a reinforced slope is considerably higher than that of a footing on an unreinforced slope, thus reflecting the beneficial effect of reinforcement in improving the bearing capacity of the footing on a slope, and by using one-layer reinforcement, the ultimate bearing capacity of a footing corresponding to D/B=3 is equal to a footing on a level surface without reinforcement.
4.3 Effect of multi-layering reinforcement on bearing capacity
The second series of numerical tests were performed for eleven different edge distances of the footing on multi-layer reinforcement, corresponding to D/B=0-10. The variations of ultimate bearing capacity at different edge distances are shown in Fig. 6. For comparison, parameter of bearing capacity ratio (BCR) was introduced equal to the ratio of footing bearing capacity with reinforcements to the footing bearing capacity without any reinforcement. The results of tests are given with this parameter in Fig. 7.
The results clearly indicate that, by use of more than one layer reinforcement, the ultimate bearing capacity does not change considerably. It reduces a little even by 3-layer reinforcement compared with one or two layerings. This phenomenon is in contrast with all findings about reinforced sandy soils or clayey soils reinforced by sand cushions or a layer of reinforced sand. And this is because of increment of plastic points which are produced between layers in confined soil (Fig. 8).
When more than one layer of reinforcement was used, some plastic sheets were formed, in which soft clayey soil between them failed in tension, as shown in Fig. 8. This mode of failing in adjacent slope increases because of smaller settlement in this zone. With receding from edge of slope as settlement increases, this reducing in bearing capacity is omitted gently, and for D>4B this effect of slope is totally omitted. At distance more than four times of footing width from slope edge, bearing capacity of footing with three-layer geogrid is increased by 25% as compared with one layer reinforcement.
Fig. 6 Variation of qu/γB with edge distance and effect of multi- layer reinforcement
Fig. 7 Variation of bearing capacity ratio with number of multi- layering reinforcement
Fig. 8 Increment of tension failed points (filled ones) due to multilayer reinforcing
Load-settlement curves for six different D/B ratios of 0, 2, 4, 6, 8 and 10 are presented in Fig. 9. In these plots, effect of edge distance is so clear, and in both of unreinforced and reinforced soil masses, distance of slope edge (D/B ratio) is increased, and bearing capacity is increased.
Fig. 9 Load-settlement curves for different D/B ratios at Ф′=15°: (a) D/B=0; (b) D/B=2; (c) D/B=4; (d) D/B=6; (e) D/B=8; (f) D/B= 10
4.4 Effect of friction angle, Φ'
For investigation of the effect of friction angle on bearing capacity for reinforced clayey soils, a series of tests were performed with the same conditions as other tests, just the friction angle Φ′ of soil was changed to 25°. The results are presented in Figs. 10 and 11.
By comparing Fig. 10 with Fig. 7, it is clear that in unreinforced soils, the ultimate bearing capacity increases with increasing effective friction angle from 15° to 25°. But as shown in Fig. 11, in case of reinforced soils with geosynthetic reinforcement, increasing friction angle will decrease the ultimate bearing capacity. This fact is explained by Mohr-Coloumb criterion. As the effective friction angle Φ′ of soil increases in this criterion, and peak of 3D failure prism that corresponds to σ1=σ2=σ3=c×cotg Φ′ (σ1, σ2 and σ3 are principal stresses) tension zone (negative stress) dwindles, with increasing Φ′, the soil becomes weaker for tension stresses. Then, more plastic points are formed by high tension, and failure of soil mass happens earlier. Multilayer reinforcing and its role in forming plastic sheets and increasing the tension failed point, as shown in Fig. 8, intensify this phenomenon (Fig. 12). As friction angle increases, bearing capacity due to multilayer reinforcing decreases.
Fig. 10 Variation of qu/γB with number of multi-layer reinforcement for Φ′=25°
Fig. 11 Variation of bearing capacity ratios with number of multi-layer reinforcement at Φ′=25° and 15°
4.5 Effect of multi-layering reinforcement on settlement
The efficiency of reinforcing on settlement of footing foundation is investigated. In Fig. 9, we can clearly see the differences between load-settlement curves of unreinforced and reinforced soil mass. The difference in ultimate bearing capacity is due to the difference in the slope at the near end of curves, which results in the increase in settlement by the increment of reinforced layers.
Fig. 12 Comparison in tension fail points (filled ones) in two cases, unreinforced and multilayer reinforced mass
The method of settlement calculated by load settlement curve is shown in Fig. 3. Table 4 gives the results obtained for D/B=1 and Φ′=15°.
Table 4 Variation of footing settlement and bearing capacity for D/B=1 and Φ′=15°
As shown in Table 4, with reinforcements, settlement of foundation increases, but in case of one layer reinforcement when increasing of bearing capacity and allowable quantities of settlement are considered, utilizing one layer reinforcement seems logical. In relation to other situations, utilizing reinforcing is not necessary since settlement of footing increases and bearing capacity decreases. For example, bearing capacity of soil mass with three layer reinforcements and unreinforced soil was obtained equally. However, settlement was increased in case of three layer reinforcings. This is because of tension rupture of soil which is confined between geogrid layers.
Soft clayey soil investigations are repeated for soil with higher effective friction angle (Φ′=25°), and results are represented in Table 5.
Table 5 Variation of footing settlement and bearing capacity for D/B=1 and Φ′=25°
Comparisons of Tables 4 and 5 obviously show that the results of these two types of soil are opposite. Therefore, using of reinforcement in clayey soil with high friction angle is not so beneficial since bearing capacity is decreased. Though in comparison with unreinforced soil the settlement is decreased, increasing settlement process with adding reinforcement layers still exists.
5 Conclusions
1) The results of numerical analyses show that the provision of a reinforcement layer results in a significant increase in the bearing capacity of footings.
2) The ultimate bearing capacity of the footing on both reinforced and unreinforced slopes increases with an increase in edge distance of 0–10B. However, at an edge distance larger than 10B, the ultimate bearing capacity of the footing does not seem to be affected by the presence of the slope.
3) By using one layer reinforcement, the ultimate bearing capacity of a footing corresponding to D/B=3 is equal to that of a footing on a level surface without reinforcement.
4) By use of more than one layer reinforcement, the ultimate bearing capacity does not change considerably. It decreases a little even by three-layer reinforcement compared with one or two layers. This happens because of creating some plastic points between multilayer reinforcement.
5) In spite of unreinforced soils, the ultimate bearing capacity increases with increasing friction angle in case of reinforced soils. This phenomenon is because of forming more tension fail points due to increment in effective friction angle Φ′ and shrinking in failure surface.
6) Although in soft clayey soils, as reinforced layer increases, settlement of footing increases, increasing the bearing capacity can eliminate this bad effect. In clayey soil with high friction angle, footing settlement decreases, but decreasing of bearing capacity also occurs. Thus, use of reinforcement in this type of soil near slopes is not recommended.
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(Edited by HE Yun-bin)
Received date: 2011-05-20; Accepted date: 2011-11-10
Corresponding author: S. A. Naeini, Associate Professor; Tel: +98-281-837-1102; E-mail: Naeini.Hasan@yahoo.com
