Behaviour of footings on reinforced sand subjected to repeated loading – Comparing use of 3D and planar geotextile

Geotextiles and Geomembranes 28 (2010) 434–447

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Behaviour of footings on reinforced sand subjected to repeated loading – Comparing use of 3D and planar geotextile S.N. Moghaddas Tafreshi a, *, A.R. Dawson b,1 a b

Department of Civil Engineering, K.N. Toosi University of Technology, Valiasr St., Mirdamad Cr., Tehran, Iran Nottingham Transportation Engineering Centre, University of Nottingham, Nottingham, UK

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 May 2009 Received in revised form 17 November 2009 Accepted 3 December 2009 Available online 18 February 2010

This paper describes a series of laboratory model tests performed on strip footings supported on 3D and planar geotextile-reinforced sand beds under a combination of static and repeated loads. Footing settlement due to initial static applied load and up to 20,000 subsequent load repetitions was recorded, until its value becomes stable or failure occurred due to excessive settlement. The response under the first few cycles was found to be a significant behavioral characteristic of footings under repeated loads. The influence of various amplitudes of repeated load on foundations containing different numbers of planar geotextile layers and different heights of the 3D geotextile reinforcement were investigated. Most of the observed responses show plastic shakedown developing – that is a stable, resilient response is observed once incremental plastic strains under each load repetition have ceased to accumulate. The results show that the maximum footing settlement due to repeated loading is comparable for either planar- or 3D-reinforced sand and much improved over the settlement of unreinforced sand. The efficiency of reinforcement in reducing the maximum footing settlement was decreased by increasing the mass of reinforcement in the sand. On the whole, the results indicate that, for the same mass of geotextile material used in the tests, the 3D geotextile reinforcement system behaves more effectively than planar reinforcement as a retardant for the effects of dynamic loading. Thus, a specific improvement in footing settlement can be achieved using a lesser quantity of 3D geotextile material compared to planar geotextile. Ó 2009 Elsevier Ltd. All rights reserved.

Keywords: Laboratory test Repeated loads Strip footing 3D and planar geotextile reinforcement Footing settlement Plastic shakedown

1. Introduction Machine foundations require the special attention of a foundation engineer. In addition to static loads due to the weight of machine and the foundation, loads acting on such foundations are often dynamic in nature due to the action of the moving parts of the machine. While these dynamic loads are generally small, as compared to the static load, they are applied repetitively over a very large number of loading cycles. Therefore it is necessary that the soil behaviour is elastic, or else deformation will increase with each cycle of loading until the unstable soil behaviour develops. Research into the behaviour of unreinforced soil and shallow foundations were subjected to dynamic loads was initiated during the 1960s. Both theoretical and experimental studies of the dynamic bearing capacity of shallow foundations have been

* Corresponding author. Tel.: þ982188779473; fax: þ982188779476. E-mail addresses: [email protected] (S.N. Moghaddas [email protected] (A.R. Dawson). 1 Tel.: þ441159513902; fax: þ441159513909. 0266-1144/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2009.12.007

Tafreshi),

reported by several researchers to understand the load–settlement relationship of footings and also the relationship between footing settlement and the number of load cycles (Cunny and Sloan, 1961; Raymond and Komos, 1978; Das and Shin, 1996). In recent decades, due to its economy, ease of construction and ability to improve the visual appearance, reinforced soil has been widely exploited in geotechnical engineering applications such as the construction of roads, railway embankments, stabilization of slopes, and improvement of soft ground and so on. In the case of monotonic loads, the beneficial effects of the planar geosynthetic (Shin and Das, 2000; Dash et al., 2004. Yoon et al., 2004; Deb et al., 2005; Ghosh et al., 2005; Patra et al., 2005, 2006; Hufenus et al., 2006; El Sawwaf, 2007; Alamshahi and Hataf, 2009; Bathurst et al., 2009; Sharma et al., 2009) and 3D geosynthetic geocells (Rea and Mitchell, 1978; Mitchell et al., 1979; Shimizu and Inui, 1990; Cowland and Wong, 1993; Krishnaswamy et al., 2000; Dash et al., 2001a,b; Dash et al., 2003; Sitharam et al., 2005; Dash et al., 2007; Madhavi Latha and Rajagopal, 2007; Sireesh et al., 2009) have most often been studied in geotechnical applications.

S.N. Moghaddas Tafreshi, A.R. Dawson / Geotextiles and Geomembranes 28 (2010) 434–447

In the case of reinforced footings under repeated loads, only a few relevant studies have been found and these concentrated on planar-reinforced applications (Das and Shin, 1994; Raymond, 2002; Shin et al., 2002). Das and Maji (1994) and Das (1998) conducted laboratory model tests, observing settlement of surfacepositioned, square foundations supported by a medium dense reinforced sand bed and subjected to repeated loading of low frequency. The tests results indicated that the geogrid reinforcement can act as a settlement retardant for dynamic loadings conditions on the foundations. Mogahaddas Tafreshi and Khalaj (2008) performed an experimental study to investigate the behaviour of pipes buried in geogrid reinforced sand when subjected to repeated loads. They reported that the use of geogrid reinforcement can significantly reduce the vertical diameter change of pipe and settlement of the soil surface. The literature above indicates that there is a lack of studies into the behaviour of footings under repeated load when supported on reinforced soil. This is especially the case for 3D fabrications of planar geotextile (as opposed to 3D arrangements of geogrids). Both might be termed geocells, but the term 3D geotextile is used in this paper for the specific geotextile-based geocells that are studied. In the research described here, and in order to develop a better understanding of the behaviour of footings under a combination of static and repeated loads supported on 3D and planar geotextilereinforced sand beds with the same characteristics, a series of different laboratory, pilot-scale tests were performed. In these tests the settlement of a strip footing supported by reinforced relatively dense sand with either a three-dimensional (3D) geotextile or with planar geotextile reinforcement is evaluated. The overall goal was to investigate the response of footings built on reinforced sand and unreinforced sand to repeated loading and also, particularly, to demonstrate the benefits of 3D geotextile and to compare its behaviour to that of an equivalent, reference unreinforced case as well as to a conventional planar geotextile arrangement. Both effectiveness and economy are of interest. Also, the effect of the height of the 3D geotextile reinforcement (or the number of planar geotextile layers) below the footing base, the ratio of repeated load intensity to applied static load (for details see Table 2) and the rapidity with which steady-state (plastic shakedown) conditions arise are investigated. It should be noted that only one type of 3D and planar geotextile, one footing width, and one type of sand were used in laboratory tests. It is recognized that the results of this study may be somewhat different to full-scale foundation behaviour in the field, although the general trend is expected to be similar.

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the hydraulic actuator. The actuator may produce monotonic or repeated loads and has a maximum capacity of 10 kN, depending on the intensity of the input compressed oil. The repeated load with different amplitudes, different frequencies (up to 10 Hz) and an unlimited number of load cycles can be produced and controlled by the hydraulic jack and server control. The controlling unit consists of an electromechanical system, which can regulate the intensity of the compressed oil required to produce a repeated load with the desired amplitude and frequency. The testing tank is designed as a rigid box, 750 mm in length, 375 mm in height, and 150 mm in width, encompassing the reinforced soil and model foundation (Figs. 1, 4 and 5). The back and side faces of the tank consist of smooth ply-wood sheets of 17.5 mm thickness, which are permanently fixed to channel sections. To allow the visual observations of the sand-reinforcement system, as well as photo scanning (if desired), the front face of the tank is made of a Plexiglas sheet, 15 mm in thickness. To prevent undesirable movement of the back and front sides of the tank (so as to maintain plane strain conditions) the rigidity of the tank has been guaranteed by using two stiff steel sections of U-100 on the back face, with two stiff wedged blocks and a metallic spreader beam to retain the front face of the tank relative to the steel columns of the loading system. According to some preliminary test results (not further reported here), under a maximum applied loading stress of 1000 kPa on the soil surface, the measured deflection of the back and front faces of the tank were very small demonstrating that they would be negligible at the stress levels applied in the main test programme. The side wall friction effects on the model test results were reduced by coating the inside of the front and back walls with petroleum jelly. Also during the tests, no differential settlement between the two ends of the footing (loading plate) was observed. Taking these observations together demonstrates that plane strain conditions were sensibly achieved. The data acquisition system was developed in such a way that both load and settlement could be read and recorded automatically. An S-shape load cell with an accuracy of 0.01% full-scale was also used and placed between the loading shaft and footing to precisely measure the pattern of applied load. A linear variable differential transducer (LVDT) with an accuracy of 0.01% of full range (75 mm) was placed on the footing model to provide the value of footing settlement during the loading. To ensure an accurate reading, all of the devices were calibrated prior to each series of tests. 3. Materials 3.1. Sand

2. Laboratory model tests The general arrangement of the laboratory test is shown in Fig. 1. A physical model test was conducted in a test bed comprising a loading system, testing tank, and data acquisition system. The loading system includes a loading frame, a hydraulic actuator and a controlling unit. The loading frame consists of four stiff and heavy steel columns and a horizontal crosshead that supports Table 1 The engineering properties of the geotextile used in the tests. Description

Value

Type of geotextile Type of polymer Area weight (g/m2) Thickness under 2 kN/m2 (mm) Thickness under 200 kN/m2 (mm) Tensile strength (kN/m) Strength at 5% (kN/m)

Non-woven polymer 100% polypropylene 190 0.57 0.47 13.1 5.7

The soil used is a relatively-uniform silica sand with grain sizes between 0.85 and 2.18 mm and with a specific gravity, Gs, of 2.68. It has a Coefficient of uniformity, Cu, of 1.35, Coefficient of curvature, Cc, of 0.95, an effective grain size, D10, of 1.2 mm, and mean grain size, D50, of 1.53 which means that almost all the grains are between 1 and 2 mm in size. The maximum and minimum void ratio (emax and emin) of the sand was obtained as 0.82 and 0.54, respectively. According to the Unified Soil Classification System, the sand is classified as poorly graded sand with letter symbol SP. The angle of internal friction of sand obtained through drained triaxial compression tests on dry sand sample at a relative density of 72% was 37.5 (all tests being run on dry sand at this relative density). 3.2. Reinforcement Geocells may consist of a cellular structure manufactured from flexible, semi-flexible or strong geosynthetics such as geotextile. In the researches reported by Bush et al. (1990), Krishnaswamy et al.

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Table 2 Scheme of the tests for unreinforced and reinforced (planar and 3D) sand. Test Series

Type of reinforcement

Type of test

qdyn/qstat (%)

H/B or N

u/B

b3D/B or bplanar/B

No. of tests

Purpose of the tests

1

Unreinforced

Static

––

––

––

––

1 þ 1a

To arrive at the optimum values of u/B and value of static load, qstat

2

Unreinforced

Repeated

20%, 30% and 50%

––

––

––

3 þ 2a

To quantify the improvements due to reinforcements

3

3D-reinforced

Static

––

H/B ¼ 0.33

0, 0.1, 0.25, 0.5, 1

b3D/B ¼ 3.2

5 þ 2a

To arrive at the optimum values of u/B

4

3D-reinforced

Repeated

20%, 30% and 50%

H/B ¼ 0.33, 0.66, 1.33

0.1

b3D/B ¼ 3.2

9 þ 3a

To study the effect of the H/B and intensity of repeated load at optimum values of u/B

5

Planar-reinforced

Static

––

N¼1

0.2, 0.4, 0.6, 1, 1.2

bplanar/B ¼ 4.1

5 þ 2a

To arrive at the optimum values of u/B

6

Planar-reinforced

Repeated

20%, 30% and 50%

N ¼ 1, 2, 4

0.35

bplanar/B ¼ 4.1

9 þ 3a

To study the effect of the number of reinforced layers (N) and intensity of repeated load at optimum values of u/B

a

Indicates duplicate tests performed to verify the repeatability of the test data.

(2000), Dash et al. (2003) and Sitharam et al. (2007) the geocell mattress was prepared by cutting the geogrids to the required length and height from full rolls and placing them in transverse and diagonal directions, on the soil bed, with bodkin joints (plastic strips) inserted at the connections. This type of geocell is hand made from geogrid and could be termed ‘geocells with perforations’. In this current research, contrary to the above, the geocell used was made of a type of geotextile – an innovative approach for use in ground stabilization. They could be termed ‘geocells without perforations’. This type of geocell is named ‘3D geotextile’ by the authors. It comprises a polymeric, honeycomb-like structure with open top and bottom manufactured from strips of geotextile that are thermo-welded into a cellular system. When filled with soil or other mineral material, it provides an ideal surface for construction projects such as foundations, slopes, driveways, etc. The high tensile strength of both the weld and geotextile provide an ideal Hydraulic Actuator Loading Frame -

Load Piston

LVDT

Model Strip Footing

Load Cell

Reinforced Zone (Planar or 3D)

Loading Frame – Column

structure with high capacity that prevents infill from spreading thus hindering settlement. The pocket size (d) of the 3D geotextile used was kept constant (at d ¼ 50 mm). It was used at heights (H) of 25, 50 and 100 mm in the testing program. The 3D geotextile layer was prepared by cutting to the required length and height from a full pack. Fig. 2 shows an isometric view of the 3D geotextile used in the investigations. The 3D and planar geotextile used were both made and supplied by the same company. The type of geotextile is non-woven. The engineering properties of this geotextile, as listed by the manufacture, are presented in Table 1. The 3D geotextile is fabricated from the same geotextile material that forms the planar geotextile. 4. Preparation of model test and test procedure In order to provide experimental control and repeatability of the tests, Kolbsuzewski’s (1948) raining technique was used to deposit the soil in the testing tank at a known and uniform density. A moveable perforated steel plate was provided for raining the sand inside the testing tank (750 mm in length, 150 mm in width). It may be mounted above the testing tank to pour the sand from specified height. The height of raining to

Metallic Support Bar Wedge Block to Retain Test Box

Sand Test Box Pedestal

Fig. 1. General arrangements of tests.

Fig. 2. Isometric view of the 3D geotextile.

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a

437

Strip Footing Model 5B (375mm)

Dynamic Load Static Load

Strip Footing

u h h h

Planar Geotextile bplanar

10B (750mm)

b

Fig. 5. Geometry of the planar geotextile-reinforced foundation bed.

Applied Pressure (kPa)

qdyn.

1 sec.

qstat.

0

0

7

2

0

Time (sec.) Fig. 3. Typical time history of initial static and repeated load on footing.

achieve the desired density was determined a priori by performing a series of trials with different heights of raining. Sand was then rained from a pre-calibrated height to consistently maintain a relative density of 72% in all the tests. In the case of the planar geotextile reinforcement, by considering the position of the reinforcement layers, the inner face of the tank was marked beneath the position of footing to facilitate accurate preparation of the reinforced sand bed. The soil was rained from the prescribed height through the perforated plate in the tank and then on reaching the first reinforcement level, raining of sand was temporarily ceased. Thereafter the first geotextile layer was placed on the surface of the sand, after which the sand raining was continued until the desired level of the second geotextile layer was achieved. The preparation of the reinforced sand bed used one to four planar geotextile layers. The geotextiles extended from front to rear of the test tank and a specified length (b3D and bplanar) as described in Section 6 and Table 2. After final geotextile placing, sand raining was continued up to the footing level. In the case of the 3D geotextile-reinforced bed, sand was rained up to the predetermined depth using depth-marking on the sides of

Strip Footing Model

5B (375mm)

u

3D Geotextile

H b3D

10B (750mm) Fig. 4. Geometry of the 3D geotextile-reinforced foundation bed.

the tank as guides. Then the 3D reinforcement was placed on the top of the levelled sand bed. After that the cell pockets were filled with sand using the raining technique which continued up to the footing level. For both the planar and 3D geotextile, great care was taken to level the soil surface using a special ruler so that the relative density of the top surface was not affected. The model footing used was made of a steel rigid plate and measured, 148 mm in length, 75 mm in width (B) and 20 mm in thickness. In order to create plane strain conditions within the test arrangement, the length of the footing (148 mm) was made almost equal to the width of the tank (150 mm). At each face of the tank, a 1 mm wide gape was given to prevent contact between the footing and the side walls. The base of the model footing was made rough by covering it with epoxy glue and rolling it in sand. The two ends of the footing plate were polished to have a smooth surface and also coated with petroleum jelly to minimize the end friction effects. The model footing was placed at the desired position on the soil, with a length of the footing parallel to the width of the tank. In order to maintain a vertical loading alignment, a small hemi-spherical indentation was made at the centre of the footing model. A load cell was placed on the loading shaft to record the applied loads and its lower end equipped with a hemi-spherical protrusion that engaged with the seating on the footing. A LVDT was placed on the footing model accurately to measure the settlement of the footing during the static and repeated loadings. Regrettably, on geotextile deformation instrumentation was not feasible for the 3D geotextile, as strains are almost certainly highly variable across the height of the cell walls and also with location along them (depending on the plan angle and web connection position). As their instrumentation would have required a further study to determine best position it was decided that reliance would be made on external instrumentation. With the main study material being treated this way, instrumentation of the planar geotextile adopted the same strategy.

5. Pattern of applied load Fig. 3 shows the typical time history of applied load on the footing. As can be seen, the footing is subjected to a pre-specified static load of intensity, qstat, applied at a rate of 1.0 kPa/s, after which a repeated load having an amplitude of qdyn is superimposed on the static load. Before applying the repeated load, the static load is kept constant until no further settlement occurs or the rate of settlement becomes negligible. During the tests the static load would be permanently applied on the footing while the repeated load was returned to zero at the end of each cycle. Sinusoidal load cycles with a frequency of 1 Hz (1 cycle/s) would be continued until the rate of change of total settlement drops to an insignificant amount or, alternatively, excessive settlement and unstable behaviour is observed.

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In the practical design of machine foundations, sinusoidal, triangular or trapezoidal types of repeated loading are often of more importance than static loads. Sinusoidal repeated loadings are superimposed on the static load, which represents the weight of the machine and foundation. These repeated loadings are selected to simulate the vibrating loads applied on machine foundations, which are often time-dependent due to the action of the moving parts of the machine. As the dynamic loads are generally, relatively small compared to the weight of machine, the values of additional dynamic load, qdyn, were selected as 20, 30 and 50% of qstat. The lower two values encompassed stresses likely to be experienced in many earthquakes or due to the loading of vibrating machines resting on foundations, while the value of 50% represents an extreme value. 6. Test parameters and testing program The geometry of the test configurations for both the 3D and the planar geotextile considered in these investigations are shown in Figs. 4 and 5, respectively. Also, the details of both the 3D and planar-reinforced tests are given in Table 2. Test series 3 and 4 on the 3D geotextile-reinforced bed were conducted by varying the depth to the top of 3D geotextile layer below the footing (dimension u) in the cases of static loading and the height of the 3D reinforcement (dimension H) in the case of repeated loads. In deciding the parameters to be investigated and their values, the authors have attempted to replicate likely in-situ usage (geometry, factor of safety, stress level, etc.), albeit at reduced scale. They recognise the limitations inherent on scaling, but argue that, for dry sand, the effects are broadly proportional to the scaling. This point is discussed further in Section 8. In the case of the planar geotextile-reinforced bed, two series (test series 5 and 6) of static and repeated tests were conducted, respectively, by varying the depth to the top of first reinforcement layer from the base of the footing (u) and the number of layers (N). All the variable and constant parameters used to describe the tests are expressed in non-dimensional form with respect to footing width (B) as u/B, H/B, b3D/B and bplanar/B (where b3D and bplanar are the length of 3D and planar reinforcements, respectively, at right angles to the axis of the strip footing). Tests series 1 and 2 were carried out on unreinforced sand to provide a reference load capacity against which to quantify the improvements due to reinforcements. In test series 1 the ultimate static load capacity of unreinforced sand was found to be 262 kPa. Similar to full-scale usage, a factor of safety of a little more than 2 was adopted – thereby defining qstat as 120 kPa, being the static pre-loading applied prior to repeated loading in subsequent test series. The values of additional dynamic load, qdyn (see Fig. 3) were selected as 20, 30 and 50% of qstat (qdyn/qstat ¼ 20%, 30% and 50%) which explained in Section 5. The range of values of u/B listed in Table 2 was selected as being likely to encompass the optimum value on the basis of the results presented by previous researchers and described more in Section 6.1 of this paper. The value of lateral

extents of the geotextiles (b3D/B or bplanar/B) was selected based on preliminary tests not reported here (Moghaddas Tafreshi and Dawson, 2010). The vertical spacing (h, planar) was chosen in agreement with other researchers’ findings (see Section 7.1 of this paper) and to reinforce the same zone as occupied by the 3D geotextile available. For the 3D geotextile, the values of H/B were adopted, following preliminary assessments, as likely to achieve significant differences of response. The length and vertical heights, or number of layers, were also chosen to ensure that the masses of geotextile material in the 3D geotextile and in the planar geotextile installations were paired. Some of the tests listed in Table 2 were repeated carefully at least twice to examine the performance of the apparatus, the accuracy of the measurements, the repeatability of the system, reliability of the results and finally to verify the consistency of the test data. The results obtained depicted a close match between results of the two or three trial tests with maximum differences in results of around 10%. This difference was considered to be small and is subsequently neglected. It demonstrates that the procedure and technique adopted can produce repeatable tests within the bounds that may be expected from geotechnical testing apparatuses. The authors decided that a meaningful comparative equivalence between the planar and 3D geotextile, required that the mass of geotextile material should be matched. This definition of equivalence does have some drawbacks. Firstly the reinforcing width will differ. Secondly, there will usually need to be more than one layer of planar geotextile, necessitating a decision on inter-sheet spacing (h). The authors argue that the arrangement adopted is near optimal as it satisfies the following goals:  Close to a fair comparison between 3D and planar arrangements due to identical masses  Ensures comparable volume coverage by the two reinforcement solutions  In line with previous researchers’ observations regarding optimum spacing of planar reinforcement for best performance. Yoon et al. (2004) and Ghosh et al. (2005) obtained maximum values of bearing capacity and a minimum value of footing settlement when the vertical layer spacing, h, was constant and equal to the cover depth, u, with u/B ¼ h/B ¼ 0.35.  The width of reinforcement encompasses the likely optimal values. Although the authors have not specifically investigated optimal width under repeated loading, their earlier paper (Moghaddas Tafreshi and Dawson, 2010) on the static response of similar systems showed that the lengths of reinforcement reported in this paper cover the range in which the optimum width is expected to fall. Lengthening them further than in these experiments (at the expense of fewer layers so as to keep the overall mass constant) will not be beneficial. Hence, Table 3 shows the quantity of material used in each test relative to that used in the least reinforced test. This value, termed

Table 3 The quantity of geotextile material for the planar and 3D reinforcement used in test program. Planar reinforcement (reinforcement width to footing width, bplanar/ B ¼ 4.1)

3D reinforcement (reinforcement width to footing width, b3D/ B ¼ 3.2)

Number of reinforced layers, N (See Fig. 5)

Quantity of geotextile material regarding ‘a*’

Height of reinforcement, H/B (See Fig. 4)

Quantity of geotextile material regarding ‘a*’

1 2 4

a 2a 4a

0.33 0.66 1.33

a 2a 4a

*See text above for definition of parameter ‘a’.

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1 Planar Reinforcement bplanar/B=4.1, N=1 SSRF3D & SSRFplanar (%)

‘a’, is equivalent to the mass of one sheet of planar geotextile (N ¼ 1) of the reinforcement width of 4.1 (bplanar/B ¼ 4.1) or the identical mass of the 3D reinforcement with height of H/B ¼ 0.33 and width of 3.2 (b3D/B ¼ 3.2). The table indicates the amount of geotextile using this parameter, whether provided in the form of several layers of planar reinforcement or in the form of taller 3D geotextile inclusions (which are manufactured of the same geotextile). As can be seen, assessment of performance was undertaken for paired arrangements with planar sheet and 3D reinforcements of the same mass. For example, the experiment reinforced by 2 layers of planar geotextile has exactly the same mass of geotextile as that reinforced by the 3D reinforcement at H/B ¼ 0.66. For this pair both have 2 units ‘a’ of reinforcement. Similarly, the experiment reinforced by 4 layers of planar geotextile has exactly the same mass of geotextile as that reinforced by the 3D reinforcement at H/B ¼ 1.33, both members of this pair having 4 units ‘a’ of reinforcement. As the reinforcement width was kept constant for the planar or 3D reinforcement, hence the amount of material used in each test is a function of the number of layers of planar geotextile or of the height of 3D geotextile.

0.8

0.6

0.4 3D Reinforcement b3D/B=3.2, H/B=0.33 0.2 0

7.1. Determination of the optimum value of u/B In order to obtain the optimum value of cover over the reinforcements (ratio u/B), the decrease in footing settlement due to reinforcement under static loading was selected as an assessment criterion. The performance improvement due to the provision of reinforcement is represented using a non-dimensional improvement factor, SSRF (Static Settlement Reduction Factor), which compares the settlement of the planar or 3D reinforcement bed to that of the unreinforced bed at the same bearing pressure (Fig. 6). The values of bearing pressures selected are those that cause the indicated amount of settlement in the unreinforced case, sunrein. SSRF is defined as follows:

q

Bearing Pressure (kPa)

0

s3D Footing Settlement, s/B (%)

splanar

3D Geotextile Planar Geotextile Unreinforced

sunrein.

Fig. 6. Definition of parameters to calculate the value of improvement in footing settlement in terms of reduction in static settlement (SSRFplanar and SSRF3D).

0.2

0.4

Planar: s/B=4% Planar: s/B=8% Planar: s/B=12% 3D: s/B=12% 3D: s/B=8% 3D: s/B=4%

0.6 0.8 u/B Ratio

1

1.2

Fig. 7. Variation in the values of SSRFplanar and SSRF3D with u/B ratio at different settlements (sunrein/B ¼ 4%, 8% and 12%) of the unreinforced foundation bed.

7. Results and discussions In this section, the tests results of the laboratory model are presented with a discussion highlighting the effects of the different parameters. The presentation of all the result figures would have made the paper lengthy, so only a selection to illustrate the observed trends is presented.

439

SSRFplanar ¼ at

(1)

sunrein: ¼ 4%; 8% and 12% B

SSRF3D ¼ at

splanar sunrein:

s3D sunrein:

(2)

sunrein: ¼ 4%; 8% and 12% B

where splanar and s3D are the value of the static settlement of the planar and 3D-reinforced bed at a given bearing pressure corresponding to sunrein, respectively. These terms are illustrated in Fig. 6. The optimum cover over the top of the geotextile, expressed as the value of the ratio u/B, for both planar and 3D reinforcement is obtained from the static tests (tests series 3 and 5). For the 3D reinforcement case the tests are done at H/B ¼ 0.33 having a b3D/ B ¼ 3.2 and for the planar reinforcement one, are done for a single layer (N ¼ 1) of geotextile having a bplanar/B ¼ 4.1. Thus the geotextile material used in planar form has exactly the same mass as that used in the 3D form (see Table 3). Fig. 7 presents the variation of both SSRFplanar and SSRF3D with u/B ratio. From this figure it was found that the minimum values of SSRF3D and SSRFplanar were obtained at the u/B values of approximately 0.1 and 0.35, respectively. These minimum values appear to apply irrespective of settlement magnitude. In the case of 3D reinforcement, Fig. 7 shows the improvement factor (SSRF3D) initially slightly decreasing (corresponding to a decrease in the settlement of the 3D-reinforced bed as compared with the unreinforced one) while the depth of placement increases from u/B ¼ 0 to u/B z 0.1, but that, thereafter, with increase in the u/ B ratio, the value of SSRF3D increases. The slight increase in performance improvement until u/B ¼ 0.1 could be due to the surface sand layer, above the 3D reinforcement, acting as a cushion, preventing the direct contact of the footing base with the cell walls and distributing the footing pressure more uniformly over the cellular 3D geotextile. Sitharam and Sireesh (2005) reported somewhat similar findings, observing that the bearing capacity of a circular footing on a geogrid cell-reinforced bed improved significantly to a depth of placement of u/B ¼ 0.05. Therefore, in the present study in all the tests, the 3D reinforcement was placed at u/ B ¼ 0.1. It is interesting to note that when the depth of placement reaches approximately the dimension of the width of footing (u/

440

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a Footing Settlement (mm)

4

Continuation of this line can be viewed in Fig. 9

3

2

1

0 0

100

200

300

400

Time (Sec.) 200

Applied Stress (kPa)

160

120

7.2. The general behaviour of the 3D and planar reinforcement under repeated loads 80

40

0 0

1

2

3

4

Footing Settlement (mm) Fig. 8. Typical trend of settlement under repeated loading (a) footing settlement with time, (b) hysteresis curve.

B z 1), the influence of 3D reinforcement becomes practically negligible and the reinforced bed behaves like an unreinforced case. At this value of u/B, the stress applied by the footing is concentrated in the unreinforced soil mass above the reinforcement so that the failure mechanism tends to the unreinforced one. Sitharam and Sireesh (2005) reported similar result in the case of u/B ¼ 1 for a cellular mattress. Likewise, a similar pattern is observed for planar reinforcement (Fig. 7). From this figure, it is seen that, with an increase in u/ B ratio, the value of SSRFplanar decreases until u/B z 0.35–0.4, after which, with further increases in u/B, the value of SSRFplanar increases. Mogahaddas Tafreshi and Khalaj (2008) in their studies to investigate the beneficial effect of geogrid in decreasing the settlement of the soil surface and the deformation of small diameter pipes embedded in reinforced planar geogrid sand under repeated loading obtained similar results with u/B z 0.35. Ghosh et al. (2005) reported a similar finding for a square footing on pond ash reinforced with jute-geotextile where u/B ¼ 0.3–0.35 gave a significant improvement in bearing capacity. These depths are consistent with the values identified by many researchers as reviewed in the companion paper (Moghaddas Tafreshi and Dawson, 2010).

Except for some heavily loaded tests (described at the end of this section), the typical trend of footing settlement with the time (or number of load cycles) under loading and unloading is as shown in Fig. 8a for the first 400 s. For the result illustrated in Fig. 8a, the footing supported on a 3D-reinforced bed with H/B ¼ 0.66 had been subjected to repeated loadings of 50% of applied static load (qdyn/ qstatic ¼ 50%). This figure shows that the rate of change of peak settlement and residual settlement reduces as the number of cycles increases, and that a small reduction in amplitude (i.e. the difference between these two settlements) is also apparent. Often, the variation of settlement becomes stable after a number cycles (see Fig. 9).

25 H/B=0.66 N=2 unreinforced

qdyn/qstat= 50%

b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

20

Footing Settlement, s/B (%)

b

There are two explanations for these optimum u/B values. One is that for u/B < 0.35 the overburden was not sufficient to develop enough frictional resistance at the interface of the reinforcement and sand. The lack of sufficient confining pressure for the top reinforcement layer beyond the footing edges at low values of depth ratio is thought to be an explanation. Secondly, reference to Boussinesq’s (1885) stress distribution under a strip load on a semiinfinite continuum shows maximum shear stress at a depth of approximately 1/3rd of the width of the loaded area. Where the shear stress is maximum, the maximum shear strain is to be expected and the maximum tensile strain, which is addressed by any geotextile, can be expected to be close to this point. Increasing u/B beyond 0.30–0.4 means that the top layer of reinforcement is located out of the most effective zone, so an increase in value of SSRF was observed at all settlements until the value of u/B reaches a depth of 1.2 times of the footing width. Then, at this depth, the reinforcement layer lies outside the failure zone beneath the foundation and so the influence of planar reinforcement becomes negligible. Mogahaddas Tafreshi and Khalaj (2008) reported similar results for the settlement of the soil surface and the deformation of small diameter pipes embedded in reinforced planar geogrid sand under repeated loads at high u/B values. Also, Akinmusuru and Akinbolade (1981) and Ghosh et al. (2005) indicated similar results with a decrease in bearing capacity with increasing u/B. Therefore, in the present study, the top planar reinforcement was placed at u/B ¼ 0.35 in every case.

qdyn/qstat=30% 15

X

qdyn/qstat=50%

10

qdyn/qstat=20% qdyn/qstat=30%

qdyn/qstat=30% qdyn/qstat=50%

qdyn/qstat=20%

5

qdyn/qstat=20% 0 0

4000

8000

12000

16000

20000

Number of Applied Cycles Fig. 9. Variation of the footing settlement (s/B) with number of applied load repetitions for the unreinforced, 3D (H/B ¼ 0.66) and planar (N ¼ 2) reinforced beds. Loading amplitude of repeated loads (qdyn/qstat) was 20%, 30% and 50%.

S.N. Moghaddas Tafreshi, A.R. Dawson / Geotextiles and Geomembranes 28 (2010) 434–447

This stabilising response indicates that the early process of reorientation of particles inside the 3D geotextile, causing local fill stiffening, ceases relative rapidly and the system then reaches the ‘‘plastic shakedown’’ condition defined by Werkmeister et al. (2005) in which subsequent deformation is fully recovered in each cycle. In such a case no yield condition is reached at conventional stress levels. The final settlement value can be referred to either as the ‘‘maximum settlement’’ or the ‘‘shakedown settlement’’. The number of cycles of load application required to reach this constant, maximum, settlement value is defined by the parameter ncr. The hysteresis loop of footing settlement, shown in Fig. 8b, is derived from the same test. It is clear that a steady response condition was achieved with the load-settlement path forming a closed hysteresis loop. With increased load repetition the repeated loading and unloading loop becoming more symmetric, thus indicating less energy is lost in the system. The hysteresis curve also shows that there is an increase in the slope of the repeated pressure-settlement curve with an increase in the number of load–unload cycles. This corresponds to a reduction in the rate of change of peak settlement with number of load applications which, together, are indicative of a hardening of the reinforced system (Figs. 8 and 9). The other general observation of behaviour of the footing settlement under repeated loads is the large portion of the plastic settlement of the footing that occurs during the first cycle and also during the first 10–20 cycles of loading and unloading compared to the total deformation recorded after all cycles. In all tests the induced settlements in the first cycles are much larger than that occurring under subsequent cycles as can be shown in Fig. 8. Overall, in most of the tests performed on the reinforced sand bed, the initial rapid settlement that took place during the first ten cycles of loading gave rise to about 35%–60% of the total settlement, the actual proportion depending on the type and the mass of reinforcement and on the magnitude of the applied repeated load. Although the pattern of response just described is applicable to most of the test, in the cases of the unreinforced sand beds under cyclic loads with amplitudes of 50% and 30% of static load (Fig. 9) and the case of the sand bed reinforced with one planar geotextile layer under strong cyclic loads with amplitude of 50% of static load, excessive settlement and consequently unstable behaviour is observed. Furthermore, due to excessive footing settlement, heave of the fill surface starts. This behaviour is attributable to rupture zones developing under the strong cyclic loads locally in the region under and around the footing. According to the definition of ncr given above, it is not possible to define a value if there is no shakedown. However, to enable comparison between stabilising and non-stabilising responses, for non-stabilising behaviour the value of ncr is defined as the number of loading cycles at which the settlement rate begins to accelerate (point X in Fig. 9). 7.3. The effect of the amplitude of the repeated load The variation of the footing settlement to footing width, s/B, with number of applied load repetitions as a consequence of the

441

repeated loading pattern (as illustrated in Fig. 3), is plotted in Fig. 9. The data are presented for unreinforced, planar-reinforced and 3Dreinforced sand beds. The reinforced cases had the same mass of geotextile (N ¼ 2 and H/B ¼ 0.66, see Table 3). The curves in Fig. 9 show the cumulative plastic and resilient settlement measured at the peak of each load pulse. In order to investigate more clearly the beneficial effect of reinforcement in decreasing settlement, the variation in footing settlement (proportional to footing width), s/B, of the unreinforced, the planar-reinforced and the 3D-reinforced beds for different amplitude of repeated load is shown in Table 4. The three tests referred to at the end of Section 7.2 which exhibit rupture are shown in Table 4 in bold text. The values of s/B shown for these three cases were selected corresponding to the point at which settlement rate per cycle begins to accelerate and at which unstable behaviour is observed. Therefore these values are only used to clarify the role of the soil-reinforcement. Based on Fig. 9 and Table 4, the following general observations can be made:  Using the 3D reinforcement, or the planar reinforcement with the number of layers greater than 1, leads to stabilising behaviour, irrespective of the repeated load level, qdyn/qstat, whereas no-reinforcement (qdyn/qstat ¼ 30% and 50%) or underreinforcement (N ¼ 1 for planar geotextile at qdyn/qstat ¼ 50%) allows excessive settlement and unstable behaviour to develop. The only unreinforced bed to show a stabilising response was that loaded at qdyn/qstat ¼ 20% which became stable at a maximum (shakedown) settlement, s/B, equal to 9.11% at approximately 15 400 load cycles.  In the case of the unreinforced sand beds under repeated loading, it is apparent that the excessive settlement commenced at about 3700 cycles (e.g. point X on Fig. 9) and 170 cycles, respectively, for repeated load amplitudes that were 30% and 50% of static load (qdyn/qstat). For the experiment containing one layer of planar reinforcement (N ¼ 1) and subjected to a repeated loading amplitude that was 50% of the static load (qdyn/qstat ¼ 50%), the excessive settlement commenced at about 2220 cycles. This point of inflexion in the number of cycles versus settlement curve appears to evidence a change in internal behaviour of the sand. After this number of cycles, unstable behaviour develops and the value of s/B accelerates with further load applications.  When a non-stabilising response is observed, due to excessive footing settlement, significant heave of the fill surface starts. This response indicates that the unreinforced soil, or soilreinforcement composite material with a small mass of reinforcement, when subjected to a strong repeated loads, ruptures locally in the region under and around the footing, permitting large settlements.  In the case of the 3D reinforcement and the planar reinforcement (with N > 1), an initial, rapid settlement during the first load applications is followed by a secondary settlement at a slower rate. Finally the settlement rate of the footing is very small or insignificant.

Table 4 Summary of shakedown settlement results obtained under repeated loading, s/B (%), for test series 2, 4 and 6. qdyn/qstat (%)

20 (%) 30 (%) 50 (%) a

Planar-reinforced sand

3D-reinforced sand

Unreinforced sand

N¼1

N¼2

N¼4

H/B ¼ 0.33

H/B ¼ 0.66

H/B ¼ 1.33

7.16 11.05 17.52a

5.94 8.66 15

5.01 8.03 11.76

5.52 7.68 14.39

4.26 6.02 8.15

3.61 4.67 6.05

Excessive settlement and unstable behaviour observed.

9.11 14.56a 18.88a

S.N. Moghaddas Tafreshi, A.R. Dawson / Geotextiles and Geomembranes 28 (2010) 434–447

for the experiments with the three different heights of 3D reinforcement (H/B ¼ 0.33, 0.66, 1.33) and for the unreinforced sand bed. The figure shows the results for the repeated loading case having amplitude of 20% of applied static load (qdyn/qstat ¼ 20%). The lines show the cumulative plastic and resilient settlement measured at the peak of each load pulse. It can be noted that:

Maximum Footing Settlement, s/B (%)

22 b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

20

Unreinforced N=1

18 16

N=2

14

H/B=0.33

12

N=4

10 H/B=0.66

8

H/B=1.33 6 4 2 10

20

30

40

50

60

qdyn/qstat (%) Fig. 10. Variation of the maximum footing settlement (s/B) with amplitude of repeated loads for unreinforced and both the 3D and the planar-reinforced bed.

 As expected, the increase in the magnitude of the repeated loads directly causes the footing settlement to increase for both unreinforced and reinforced sand beds. For example, the maximum footing settlements for the 3D-reinforced sand bed with H/B ¼ 0.66 at the end of loading are 4.26%, 6.02% and 8.15% of the footing width for magnitudes of repeated load that are 20%, 30% and 50% of the initial static load, respectively (as per Fig. 3b).  For the same mass of geotextile material used, the 3D-reinforced bed system clearly has a superior ability to reduce the maximum settlement of the footing as compared with the planar-reinforced system at any given dynamic loading, qdyn/ qstat. The experimental values of footing settlement for all the cases given in Table 4 can be used to describe more fully the behaviour of the 3D reinforcement and planar reinforcement under different magnitudes of repeated load, qdyn/qstat. Fig. 10 shows the variation of the maximum footing settlement (s/B) with amplitude of repeated loads for the 3D-reinforced, planar-reinforced and unreinforced beds. From this figure it can be observed that, although there is some scatter, the footing settlement varies linearly with qdyn/qstat, irrespective of reinforcement type (3D or planar) and amount. With increase in the height of the 3D reinforcement or in the number of planar reinforcement layers the rigidity of the reinforced system increases or, to state this another way, the maximum value of footing settlement (s/B) decreases at any given qdyn/qstat. This implies that increasing the amount of reinforcement mass in sand can control (lessen) the footing settlement and provide greater stability to a footing even under strong dynamic loads. Also, Fig. 10 makes plain that, even when comprising half the mass of geotextile material (H/B ¼ 0.66 compared with N ¼ 4), the 3D-reinforced sand can deliver a greater improvement (decrease) in the maximum settlement of the footing compared with the planar-reinforced one at any given qdyn/qstat.

 The variation rate of peak footing settlement reduces as the number of cycles increase, and finally becomes stable after a certain number cycles, irrespective of the height of the 3D reinforcement (H/B) or the number of layers of planar reinforcement (N). This indicates that, where the total loading is insufficient to cause rupture within the soil system, reorientation of particles in the soil adjacent to the geotextile ceases relative rapidly, the system becomes stable and can be said to have reached a state of plastic shakedown (Werkmeister et al., 2005). On the other hand, the magnitude of footing settlement increases with number of cycles (n) and reaches a sensibly constant maximum value at the number of load cycles here defined as n ¼ ncr.  The maximum footing settlement, s/B, is considerably decreased relative to the unreinforced one as a consequence of either increase in the height of the 3D reinforcement (H/B) or in the number of layers of planar reinforcement (N),  The performance of the 3D geotextile is much improved over that of the planar geotextile for the same mass of geotextile material used. This aspect is discussed further in Section 7.6. The performance of reinforcement in decreasing the settlement of a sand bed subjected to dynamic loads of various amplitudes (either by adding 3D geotextile of increasing height (H/B) or by adding layers of the planar geotextile (N)), is the subject of Fig. 12. The variation of the maximum value of footing settlement (in terms of s/B) as a function of the number of layers of planar (N) and the height of 3D (H/B) geotextile is shown for the three repeated load amplitudes (qdyn/qstat ¼ 20%, 30% and 50%). Overall, this figure indicates that the value of maximum footing settlement decreases steadily due to additional layers of planar geotextile (N) or due to the height of the 3D geotextile (H/B), irrespective of magnitudes of the repeated loading. The reinforcement seems to have a similar effect as would an enhancement of the soil

10 b3D/B=3.2, bplanar/B=4.1 qdyn/qstat.=20% qstat.=120kPa

9

Footing Settlement, s/B (%)

442

8

Unreinforced

N=1 7 N=2

6

H/B=0.33 5

N=4 H/B=0.66

4

H/B=1.33 3 2 1

7.4. The effect of the number of layers of the planar and height of the 3D reinforcement

0 0

4000

8000

12000

16000

Number of Applied Cycles

Fig. 11 summarizes the variation in the maximum footing settlement (non-dimensionalized as s/B) with number of applied load repetitions for the three planar-reinforced cases (N ¼ 1, 2, 4),

Fig. 11. Variation of the footing settlement (s/B) with number of applied load repetitions at qdyn/qstat ¼ 20% for the unreinforced, 3D-reinforced and planar-reinforced beds.

S.N. Moghaddas Tafreshi, A.R. Dawson / Geotextiles and Geomembranes 28 (2010) 434–447

20

b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

Maximum Footing Settlement, s/B (%)

18 16 14

3D: qdyn/qstat=20% 3D: qdyn/qstat=30% 3D: qdyn/qstat=50% Planar: qdyn/qstat=20% Planar: qdyn/qstat=30% Planar: qdyn/qstat=50%

12 10 8 6 4 2 0

1 2 3 4 Number of planar layers (N) or 3 times of height of 3D reinforcement (3H/B)

5

Fig. 12. Variation of the maximum footing settlement (s/B) with number of layers of planar, or height of 3D, reinforcements under repeated loading of amplitude qdyn/ qstat ¼ 20%, 30% and 50%.

density, increasing the plastic modulus of the sand. It is probable, also, that a stiffening of the soil occurs, allowing greater load sharing than in the unreinforced sand, but this aspect requires more detailed consideration than is possible in this paper. Fig. 12 shows that the rate of reduction in footing settlement reduces with increase in the value of H/B or N (i.e. the slope of the curves decrease with increase in the value of H/B or N) as no marked further decrease in footing settlement occurs when the fourth layer of planar reinforcement is added or when the height of 3D reinforcement increases to H/B ¼ 1.33, especially at the lower magnitudes of the repeated loads (20% and 30% of static load). This means that, for heavy dynamic loading (greater than 30% of static load) further layers of planar or higher 3D reinforcement might still be effective. In such a situation, the generated stress bowl will extend further into the soil and reinforcement may, therefore, be expected to function to a greater depth. Consider, for example, the maximum settlement (s/B) of a footing supported by unreinforced sand and subjected to a repeated load equal to 20% of the static load value. At the end of loading, the total settlement (s/B) is 9.11%. This value can be compared with the settlement of the footing supported on the 3D-reinforced sand, which decreases to 5.52%, 4.26% and 3.61% for H/ B of 0.33, 0.66 and 1.33, respectively. These values imply that the relative decrease in footing settlement for a variation of H/B between 0.33 and 0.66 is substantially greater than those for variation of H/B between 0.66 and 1.33 (even though the mass used for H/B ¼ 0.66 and H/B ¼ 1.33 are, respectively, two and four times of H/B ¼ 0.33), confirming that with increase in the value of H/B beyond 1.33–1.5 is not likely to deliver further substantial reduction in footing settlement. A similar pattern can be observed for the variation of footing settlement with increase in the number of planar geotextile reinforcing layers. Such a finding is not unexpected as a simple stress analysis (e.g. according to Boussinesq (1885)) will show that the zone of soil influenced by the footing loading only extends to a depth of z1–2 times the footing width. Therefore marginal performance improvement in footing settlement would be expected when the value of H/B reaches around 1.5 or the value of N increase beyond 4 or 5 layers (i.e. when the lowest layer is below 1.4B–1.75B). Mogahaddas Tafreshi and Khalaj (2008) reported that the reduction in vertical diameter of a buried pipe and the settlement of

443

the overlying soil surface under repeated loads can be reduced significantly by using geogrid reinforcement whereas the efficiency of the reinforcement was decreased by increasing the number of reinforcement layers. Also, Sitharam and Sireesh (2005) and Sitharam et al. (2007) have observed the marginal performance improvement when the height of a geocell increased to around 1.8 times of the diameter of a circular footing supported on a reinforced clay bed. A further observation is that, with increase in the height of the 3D reinforcement or the number of planar-reinforced layers, the rigidity of the reinforced system increases, which restrains the soil against heave thereby reducing heave of the fill surface. In the case of increasing mass of 3D geotextile, and with magnitudes of the repeated load being equal to, or less than, 30% of the static load, the heave of the soil surface besides the footing is completely restrained and the 3D geotextile behaves like a slab, spreading the load far more effectively than does the unreinforced soil. This effect is only partially observed for the planar geotextile reinforced systems. 7.5. Rate of establishment of plastic shakedown Plastic shakedown occurs in all, except the weakest arrangements under the higher loadings (Section 7.3 and Table 4). When plastic shakedown does occur, the number of cycles required before a steady-state response is observed (ncr) varies widely with the reinforcement arrangements and the load level. The figures already presented show that:  The value of ncr increases with increase in the repeated load level, qdyn/qstat (see Fig. 9). Although not illustrated here, this increase in ncr with increasing load level is true for all masses of geotextile,  The value of ncr decreases with increase in the height of the 3D reinforcement (H/B) or in the number of layers of planar reinforcement (N),  The magnitude of ncr for the tests performed on unreinforced and reinforced beds is always more than 10,000 and does not exceeded about 18,800 cycles (see Fig. 9),  Despite 3D reinforcement acting more efficiently than planar reinforcement to reduce the footing settlement, the value of ncr is only a little lower for 3D reinforced foundations than for planar ones, so it appears that the form of the geotextile does not affect the rate of stabilization very much. This appears to be true at all load levels and not just those illustrated in this paper, and  The deformation response of the unreinforced system is approximately the same for both static loading and for the first cycle of repeated loading at the same magnitude of post120 kPa loading (qstat > 120 kPa). Reinforcement usage was also found to reduce the plastic deformation under the first cycle of repeated loading compared to that under a similar static loading, with the reduction being greatest when more reinforcement was present and when the loading rate was fastest.

7.6. Comparison of the performance of 3D and planar reinforcement under dynamic loads From the results presented in Figs. 9–12, it is seen clearly that, for all the cases with the same mass of geotextile material (see Table 3 to compare the mass of the 3D and planar reinforcement), the 3D-reinforced bed system has greater efficiency – i.e. less footing settlement because the curves for the 3D reinforcement are lower than the planar one having the same mass of geotextile – at

444

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1

a

b

b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

0.8 b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

3D: qdyn/qstat=50%

3D: qdyn/qstat=30%

Planar: qdyn/qstat=50%

RSRF3D & RSRFplanar

RSRF3D & RSRFplanar

0.8

0.6

Planar: qdyn/qstat=30%

0.6

0.4

0.4

0.2

0.2 0

1 2 3 4 Amount of geotextile material used in terms of parameter 'a'

c

5

0

1 2 3 4 Amount of geotextile material used in terms of parameter 'a'

5

1 b3D/B=3.2, bplanar/B=4.1 qstat.=120kPa

RSRF3D & RSRFplanar

0.8 3D: qdyn/qstat=20% Planar: qdyn/qstat=20% 0.6

0.4

0.2 0

1 2 3 4 Amount of geotextile material used in terms of parameter 'a'

5

Fig. 13. Variation of Repeated Load-Settlement Reduction Factor (RSRF) with amount of geotextile material used in the 3D and planar reinforcements for three amplitude of dynamic loads (a) qdyn/qstat ¼ 50%, (b) qdyn/qstat ¼ 30%, and (c) qdyn/qstat ¼ 20%.

any given magnitude of repeated load or any selected number of load applications. In order to show more clearly the performance of the 3D reinforcement compared to that of the planar reinforcement at the same (or lesser) quantity of material, the improvement in footing settlement in terms of a Repeated Load-Settlement Reduction Factor (RSRF) is introduced. The RSRF is defined as follows.

 RSRFplanar ¼

splanar

 max

ðsunrein: Þmax

(3)

at qdyn/qstat ¼ 20%, 30% and 50%

RSRF3D ¼

ðs3D Þmax ðsunrein: Þmax

at qdyn =qstat ¼ 20%; 30% and 50%

(4)

where (splanar)max, (s3D)max and (sunrein)max are the maximum (final) values of the settlement of the planar-reinforced, 3D reinforced and unreinforced beds, respectively, at a given amplitude of repeated

load (qdyn/qstat ¼ 20%, 30% and 50%). If the failure takes place due to excessive settlement of the footing, the footing settlement at failure is taken as its value at ncr while calculating the RSRF. Fig. 13a–c plots this factor against the amount of geotextile material used (in terms of parameter ‘a’, as explained earlier in Table 3) for the three amplitudes of dynamic loads. For example, from Fig. 13c, in the case of the magnitude of the additional repeated loads equalling 20% of the qstat value, the maximum settlement of footing (s/B) compared with unreinforced sand decreases 54% (RSRF ¼ 0.46) due to the use of 2 units of 3D reinforcement (2a arranged as H/B ¼ 0.66), whereas there is only a 35% reduction (RSRF ¼ 0.65) for the planar reinforcement (2a arranged as N ¼ 2) even though both arrangements have the same mass. For this amount of geotextile material the performance of the 3D geotextile is about 20% better as regards footing settlement than that of the planar geotextile. Furthermore the maximum settlement of the footing decreases about 30% due to the 3D reinforcement, compared with planar-reinforced sand. From this comparison, it can be concluded that the 3D reinforced footing bed behaves as a much less plastic system and is consistently more

S.N. Moghaddas Tafreshi, A.R. Dawson / Geotextiles and Geomembranes 28 (2010) 434–447

efficient at limiting the footing settlement under repeated loading compared to the planar-reinforced case for the same mass of geotextile. Similar comparisons can be made for other load levels and amounts of geotextile material using Fig. 13a–c. In every situation the 3D geotextile gives a much greater improvement in settlement behaviour, relative to the unreinforced case, than does the same mass of geotextile used in a planar implementation. It is also evident that the lowest mass of geotextile (1a), when installed in a single, planar sheet, and subjected to relatively high loading (qdyn/ qstat ¼ 50% – see Fig. 13a and b) has a small or even an insignificant benefit as regards settlement. Figs. 9–13 also show that reinforcement using 3D inclusion results in a better performance compared to that of the planar geotextile even when comprising a lesser quantity of geotextile material. For example, under repeated loading equal to 20% of qstat, Fig. 13c shows that, to achieve a 45% reduction in footing settlement (RSRF ¼ 0.55) over the unreinforced case, there are two choices: (1) Four layers (N ¼ 4) of planar geotextile with the amount of geotextile material used equal to ‘4a’ (see Table 3). (2) The 3D geotextile with H/B ¼ 0.46 and the amount of geotextile material used equal to ‘1.4a’ (H/B and ‘a’ values interpolated from Fig. 13c). However, Fig. 13c shows that to achieve a 60% reduction in footing settlement (RSRF ¼ 0.40) only a 3D reinforcement will suffice – being the installation with ‘4a’ units of mass (H/B ¼ 1.33). Given the slope of the upper line in this figure, it appears that use of planar geotextile can never achieve this benefit, regardless of number of layers installed. These comparisons indicate that:  3D geotextile, subjected to the combination of static and repeated loading studied here, offers a significant improvement over that of the planar geotextile incorporating the same mass of geotextile material. Putting this another way, the same reduction in footing settlement can always be achieved by significantly less geotextile employed in a 3D arrangement that when employed in planar sheets. Therefore, use of 3D reinforcement is expected to be a much more economic means of providing improved footing settlement than is a planar reinforcement scheme (dependent only on the additional fabrication costs for the 3D material).  For the example discussed, a 3D geotextile achieved a similar performance to a planar reinforcement arrangement that contained 2.85 times as much mass of geotextile material. It is; therefore, inferred that use of the 3D geotextile could be compared to that of the planar geotextile even were less material to be used in the 3D arrangement. There is insufficient evidence to conclusively determine the reasons for the significantly improved performance of the 3D reinforcement compared to that of the planar geotextile. However it is suggested that it may be attributed to the following reasons:  In the case of a planar reinforcement system, the reinforcing action is solely dependent on the frictional bond between the two successive horizontal planar reinforcements and on the shear strength of the soil between two planar sheets. Hence, when the applied load on the footing transfers downwards, the soil mass between two adjacent layers can ratchet out when the frictional resistance with the reinforcement surface reduces upon unloading, once in each loading cycle. Such

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movement limits the ability of the total system to act compositely, thereby permitting more footing settlement under the constant combination of static and repeated loads.  Due to its three-dimensional mechanism, the cell walls of 3D geotextile reinforcement keep the encapsulated soil from being displaced laterally by the applied loading. They act to confine the material by hoop action, thereby increasing the shear strength of the composite system. Ratchetting is only possible for a few cycles before the cell walls prevent further net movement. Thus repeated loading tends to generate compaction and consequential improved load distribution capacity – something that cannot develop much between planar geotextile layers as there will be no limiting confinement. It is anticipated that load redistribution occurs within the confined zone involving a three-dimensional interaction between the infill materials and the cellular structure. Vertical stress applied to the infill will induce a horizontal active pressure at the perimeter of the cell. An effect of the horizontal confining stresses is likely to be the formation of a composite slab with high flexural stiffness and load support capabilities within the geocell layer. Consequently the foundation will experience a decreasing settlement with greater overall stability under a combination of static and dynamic loads.  The second moment of inertia, and hence shear and bending rigidity, of the 3D geotextile is significantly greater than that of the planar reinforcement with the same mass. With the sand in its pockets a composite material is formed and the 3D geotextile behaves as a stiff bed that redistributes stress over a wider area giving a decrease in the settlement of the footing. Such composite action is unlikely to be possible for a planar arrangement as the sand can, relatively easily, move out from between geotextile sheets as it is only retained by friction and not also by hoop action of the geocells. 8. Applicability and limitations The efficiency of 3D geotextile reinforcement instead of conventional layered geotextile reinforcement for foundations on soil subjected to repeated loads is demonstrated by the results presented herein. This should provide encouragement for their application, but it should be noted that the experimental results are obtained for only one type of geotextile, one pocket size of the 3D geotextile, one size of footing width, and one type of sand. Thus, specific applications should only be made after considering the above limitations. Likewise, the present test results are based on tests conducted on a small model strip foundation in plane strain conditions. For other conditions, such as for square or circular footings, a threedimensional physical model would be very useful. Furthermore, although Milligan et al. (1986) and Adams and Collin (1997) in their studies on large- and small-scale tests on the behaviour of granular layers with geogrid reinforcement showed that the general mechanisms and behaviour observed in the small model tests could be reproduced at large-scale, future tests need to be conducted with larger scale model foundations at various conditions. For example, different footings (in size, shape and depth) and different characteristics and pocket size of the 3D geotextile should be studied to validate the present findings and to determine the existence of a scale effect, if any. Scale effects on optimal geometry and on strain response are expected to be small for dry sandy soils where properties are dominated by frictional effects consequent on applied loading, the stress levels being comparable in the model and full-size. This would not, necessarily, have been the case had damp (high suction) or cohesive soils been employed (where extrapolation of

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results to full-scale would need to recognise the non-scaling nature of these effects). Qualitatively, this study has provided insight into the basic mechanism that establishes the behaviour of footings under repeated loads supported on 3D and planar geotextile-reinforced sand beds. These results will be helpful in designing large-scale model tests, for simulation studies using numerical models and in the application of the concepts at full-scale. An implication for full-size small to medium machine foundations on granular soil is that reinforcement by a 3D geotextile is a feasible alternative to costly piled solutions, though some relevelling of the machine may be needed early in the foundation’s life due to initial bedding effects. Reinforcement by either 3D or planar geotextiles could be a valuable insurance measure against excessive settlement under earthquake-induced vibrations. A fuller understanding of the mechanisms at work within the reinforced system would require detailed strain instrumentation of the geotextile webs. This is not a simple matter given their varying angles, fixity and degree of cell opening. Nevertheless, this would be a fruitful avenue for future studies.

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9. Summary and conclusions In this current research, a series of repeated load tests of laboratory model footing was carried out to compare the potential benefits of 3D geotextile reinforcement of sand with those obtained when reinforcing with planar geotextile reinforcement. Apart from the form of the reinforcement, all other characteristics beneath the footing base remained constant, including the mass of geotextile used. Benefits were assessed in terms of the decreased settlement of a strip footing subjected to a combination of static and repeated loads. The various parameters studied in this testing program include:  The mass of geotextile material (either as height of the 3D geotextile or as the number of planar layers of geotextile) below the footing base and  Intensity of repeated load on the footing model. Based on the results obtained from the present study, the following conclusions can be made about the behaviour of a strip footing on 3D and planar geotextile: (1) The optimum depth of the topmost layer (as determined by static testing using the settlement criterion) of planar reinforcement is approximately 0.35 times the footing width while the depth to the top of the 3D geotextile should be approximately 0.1 times of the footing width. (2) The rate of footing settlement decreases significantly as the number of loading cycles increases. Consequently, a resilient response condition, known as plastic shakedown, is achieved after 10,000–20,000 cycles dependent on the type and the mass of reinforcement and the magnitude of the repeated load applied to the footing. (3) For all tests, the largest portion of the footing settlement occurred after the first ten cycles. The ratio of footing settlement during the first ten to that achieved by the last cycle varies between 0.35 and 0.6. (4) The magnitude of the maximum footing settlement and the number of cycles required to develop plastic shakedown of the footing are a function of the initial applied static load (qstat), the amplitude of the repeated load (qdyn) and the mass of reinforcement below the footing base (N and H/B). (5) For a given value of amplitude of repeated load, with increase in the number of planar reinforcement layers and in the height

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of 3D reinforcement, the footing settlement decreases. The efficiency (expressed in relation to the mass of reinforcement) was decreased by increasing the above parameters. With increase in the amplitude of repeated load, the value of footing settlement increases in a broadly linear manner, irrespective of the number of planar reinforcement layers or of the height of 3D reinforcement. The maximum footing settlement, s/B, under repeated loading that has a value 20% of static load, is reduced by using the maximum mass ‘4a’ of the planar and 3D reinforcement by approximately 45% and 60%, respectively. Thus, the provision of the 3D geotextile reinforces the sand layer more than the planar geotextile with the same characteristics and the same mass, significantly reducing the footing settlement and decreasing the surface heave of the footing bed. Also, plastic shakedown is achieved more rapidly (i.e. for a lesser number of load cycles) for the 3D geotextile than for the planar geotextile. The comparative investigations imply that in order to achieve a specified improvement in decreasing the footing settlement, less mass of material is required in a 3D geotextile implementation than in a planar geotextile one. In the example given in this paper, a 3D geotextile achieved a similar performance to a planar reinforcement arrangement that contained 2.85 times as much mass of geotextile material. Compared to planar-reinforced sand beds, deformation of the foundation bed containing the 3D geotextile appears to develop horizontal confining stresses that act to strengthen the sand within the cells. This response of the system then delivers greater resistance to subsequent plastic deformation at all stages. Compared to static loading, the footing settlement under the first cycle of repeated loading due to post-120 kPa loading (qstat > 120 kPa) is approximately the same for the unreinforced sand bed. For the reinforced case, its value is less, with the difference increasing when using more reinforcement and using the fastest repeated loading.

Acknowledgment The authors would like to thank DuPont de Nemours, Luxembourg, and their UK agents, TDP Limited, for the 3D and planar geotextile support with the testing program. They also wish to thank the referees for their attention to detail and many helpful suggestions that have contributed to this final version of the paper.

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Nomenclature B: width of footing bplanar: reinforcement width of the planar reinforcement u: depth of the first layer of planar reinforcement and embedded depth of the 3D reinforcement beneath the footing h: vertical spacing between layers of planar reinforcement N: number of layers of planar reinforcement b3D: reinforcement width of the 3D reinforcement H: height of the reinforced zone by the 3D geotextile reinforcement d: pocket size of the 3D geotextile Dr: relative density of soil (sunrein)max: value of settlement of the unreinforced sand at a given bearing pressure in static test (splanar)max: value of settlement of the planar-reinforced sand at a given bearing pressure in static test corresponding to sunrein (s3D)max: value of settlement of the 3D-reinforced sand at a given bearing pressure in static test corresponding to sunrein SSRF: static settlement reduction factor qstat: intensity of pre-specified static load qdyn: amplitude of repeated load sunrein: maximum value of settlement of footing supported on unreinforced sand under combination of static and repeated loads splanar: maximum value of settlement of footing supported on planar-reinforced sand under combination of static and repeated loads s3D: Maximum value of settlement of footing supported on 3D-reinforced sand under combination of static and repeated loads RSRF: repeated load-settlement reduction factor