Loading Rate Effects on Pile Groups in Clay
Associate Professor of Geotechnical Engineering
Department of Civil Engineering, King Saud University,
Riyadh, Saudi Arabia
e-mail: muhaidib@ksu.edu.sa
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Loading Rate Effects on Pile Groups in Clay
Associate Professor of Geotechnical Engineering |
ABSTRACT
This paper describes the results of an experimental study conducted to investigate the influence of loading rate on the behavior of pile groups in clay. The pile groups have a symmetrical plan layout consisting of 2×1, 3×1, 2×2, 2×3, and 3×3 piles with a center-to-center spacing of three or nine times the pile diameter. The model pile groups were subjected to axial compressive loads at different loading rates. The load-displacement response, axial capacity, and group efficiency have been investigated. The rate of loading was found to markedly affect the value of the compressive axial capacity of the model piles. The change in the capacity caused by 100-fold change in loading rate, expressed as percentage of the axial capacity measured at a loading rate of 0.01 mm/min, was about 30%. The relationship between logarithm of loading rate and measured axial pile capacity was linear in a semi-logarithmic plot. The slope of the fitted line varied between 0.078 and 0.591 depending on the pile group configuration and center-to-center spacing of piles in a group. Group efficiency decreases with an increase in the number of piles in a group, and it increases with an increase in spacing between piles in a group.
Keywords: Loading Rate, Pile Group, Pile Capacity, Group Efficiency, Clay, Compressive Loads.
INTRODUCTION
Many factors affect the behavior of pile groups. These include soil type, number of piles in a group (configuration of pile groups), center to center spacing between the piles in a group, method of pile installation, type of loading (static or cyclic), and the rate of loading. A review of the literature indicates that the behavior of piles and pile groups under axial, inclined, or lateral loads has perhaps received the greatest attention of numerous investigators over the last few decades. However, studies regarding the effects of rate of loading on the ultimate capacity of piles and pile groups are scanty. Previous studies on loading rate effects have in general been confined to undrained shear strength of soils with some limited studies on pile foundations. A brief presentation of these studies is given below.
Loading rate has been found to significantly affect the strength of cohesive soils. Laboratory studies have shown that the undrained shear strength of clays increases as the rate of loading increases (Casagrande and Wilson, 1951; Richardson and Whitman, 1963; Vaid et al., 1979, Graham et al., 1983; Kimura and Saitoh, 1983; Nakase and Kamei, 1986; Kulhawy and Mayne, 1990; Awoleye et al. 1991; Lacasse, 1995; Sheahan et al., 1996; Matesic and Vucetic, 2003). Results by Vaid et al. (1979) showed that a 25% increase in undrained shear strength for 100 times increase in strain rate. Graham et al. (1983) found from triaxial compression tests that undrained shear strength increased by about 10 to 20% per each log cycle of strain rate. Nakase and Kamei (1986) reported that undrained shear strength of k0-consolidated specimens, sheared in triaxial compression and extension, increased by 90% for a logarithm cycle of strain rate. Based on compiled data from 26 different normally and overconsolidated clays, Kulhawy and Mayne (1990) found an increase in undrained shear strength about 10% per a cycle of logarithm of strain rate. Results by Awoleye et al. (1991) showed that the undrained shear strength increased by about 30% for undisturbed samples and 20% for remolded specimens for a 25-fold increase in strain rate. Lacasse (1995) found that undrained shear strength of normally consolidated clay is increased by 55% when the time to failure was reduced from 140 minutes to 5 seconds. Matesic and Vucetic (2003) concluded, from the results of simple shear tests on clays and sands, that when the strain rate increased tenfold the secant shear modulus in clays at small strains increased by a factor of 1.02 to 1.11, while in sands it increased by a factor of 1.002 to 1.06.
The limited studies on the effect of loading rate on axial capacity of single piles in clay have shown that the capacity increases as the loading rate increases (Kraft et. al, 1981; Horvath, 1995; Al-Mhaidib, 2001). Results of field tests on piles in clay reported by Kraft et. al (1981) showed that the ultimate bearing capacity of piles increased by 40% to 75% when the loading rate was increased by about three orders of magnitude. Horvath (1995) found that the ultimate pile capacity of model piles in clay increases with increasing loading rate. Al-Mhaidib (2001) found that the axial capacity of model single piles in compression and tension in clay increased by about 48% and 44%, respectively, for a 100-fold increase in loading rate.
The behavior of pile groups under the applied loads is generally different from that of a single pile due to the interaction of neighboring piles. The literature on the effect of loading rate contains no known published data that correlate capacity of pile groups with the speed of loading in clay. It is, therefore, of practical importance to investigate the influence of the rate of loading on the axial capacity of pile groups and examine the behavior of such piles under different loading rates.
This paper presents the results of a series of model pile group tests performed in the geotechnical laboratory at King Saud University, Riyadh, Saudi Arabia. The model piles were subjected to axial compressive loads at different loading rates. The load-displacement response, axial capacity, and group efficiency with number of piles and spacing in a group have been investigated.
TESTING PROGRAM
The following parameters have been considered as variables in the present study:
Along with the pile groups, a single pile was also tested.
Number of Tests Performed
For each pile group configuration, four model tests were performed at constant loading rates of 0.01, 0.05, 0.1, and 1 mm/min. The tests performed are:
Number of tests for single pile: 1 × 4 = 4
Number of tests for pile group configuration (2×1): 2 × 4 = 8
Number of tests for pile group configuration (3×1): 2 × 4 = 8
Number of tests for pile group configuration (2×2): 2 × 4 = 8
Number of tests for pile group configuration (2×3): 2 × 4 = 8
Number of tests for pile group configuration (3×3): 1 × 4 = 4
The tests for 3×3 pile group with the space between the piles of 9 times the pile diameter could not be performed with the available setup because of the width of the soil tank. The total number of tests performed in this study = 4 + 8 + 8 + 8 + 8 + 4 = 40.
Repeatability of Tests
Few tests have been repeated to ascertain the variations in test results, if any. It was observed that there was practically no variation in the results of the replicate tests.
SOIL DESCRIPTION
The soil used in this study was a homogeneous soil with a brown color obtained from a brick factory in Riyadh, capital of Saudi Arabia. It is sold in a powder form under the trade name "fire clay". The soil grain-size distribution curve is presented in Fig. 1. Specific gravity, Atterberg limits, and grain size analysis were determined in accordance with ASTM test standards. The average properties of the clay are shown in Table 1. Based on the Unified Soil Classification System (USCS), the clay is classified as CL.
Figure 1. Grain size distribution curve for the tested soil
Table 1. Average geotechnical properties of the clay
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| Parameter | Value |
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| Specific gravity of solids Sand content (%) Silt content (%) Clay content (%) Liquid limit (%) Plastic limit (%) Plasticity index (%) Unified Soil Classification System |
2.80 22 30 48 36 22 14 CL |
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EXPERIMENTAL PROCEDURE
The clay soil was received from the factory in a powder form. The clay sample was air-dried and an amount of water equal to 30% of the dry weight of the soil was added. The moist clay was thoroughly mixed and then stored in air-tight plastic bags, sealed in plastic wrap to avoid loss in moisture content. It was allowed to cure at room temperature for about 24 hours to allow uniform distribution of moisture content.
The soil samples were consolidated in a steel tank of 0.8 m length, 0.5 m width, and 0.8 m height supported by a relatively rigid steel framework. At a distance of 25 mm from the bottom of the tank, four drainage holes were drilled, two in each side. In each drainage hole, a valve was installed to control water drain during consolidation and testing stages. Before placing the soil into the test tank, a 50-mm layer of poorly graded sand was placed on the bottom of the test tank, which serves as a pervious base for reducing the consolidation time. Above this layer, a geotextile sheet was placed to separate the clay from the sand layer. Thereafter, the clay was placed by hand in the test tank in three layers. The weight of clay required for the first layer to obtain a unit weight of 19 kN/m3 was packed into the test tank by hand in lifts, with the interface between the lifts being made uneven, to reduce the bedding effects.. A thick rigid steel plate with a thickness of 6 mm, covering the entire length and width of the test tank, was placed on the top of the clay. Several holes with diameters of about 5 mm were punched into the plate to allow for drainage a long the upper surface of the clay layer. Sheets of filter paper were placed along the sides of the test tank and between the clay and the loading plate to speed up the consolidation process.
In order to reach the specified consolidation pressure, a high stack of dead weights was required. This makes them unstable since they would extend far above the top of the test tank. It was therefore, decided to construct the consolidation frame (shown in Fig. 2) with a lever arm ratio of 1:10. It is possible to apply a quite large consolidation pressure using this frame. The test tank rests on a 20-mm thick steel plate that is supported by I-beams. The load is transferred to the soil by a weight hanger with a lever arm. The hanger consists of a lower and upper cross beams and a cantilevered beam with a pin connection at one end and a cradle for weights at the free end. The load is applied by placing slotted dead weights on the cradle.
Figure 2. Schematic diagram of consolidation frame
After the test tank was mounted in the consolidation frame, a consolidation pressure of 20 kPa was applied. Soil deformation was monitored and readings of settlement were taken at certain time intervals until the relationship between settlement and the logarithm of time became nearly horizontal. The settlement of the clay was measured by means of two dial gauges, which were connected to the upper plate (Fig. 2). The load was then doubled to 40 kPa. The settlement was taken with time until the time which the settlement change was insignificant.
After the completion of the consolidation of the first layer, a 6-mm rigid steel plate was placed on the top of the first layer to locate the position of the model pile groups in the test tank. This plate is similar to the plate used in the first layer, but it has several holes with diameters slightly larger than the pile diameter to prevent the piles from interfering with the plate during the consolidation process (Fig. 3). There are five different perforated plates (one for each pile configuration) depending on the number of piles in a group and on the center-to-center spacing of piles in a group. Thereafter, the model piles were placed in their positions and the steel plate was lifted up. The model piles were smooth steel piles having a diameter of 25 mm and a length of 550 mm. The clay of the second layer was then packed into the test tank around the model piles according to the procedure followed for the first layer. Thereafter, the perforated plate was place above the top of the second layer. A steel pipe was inserted to connect the plate with the loading arm to transfer the consolidation load to the soil without affecting the model piles. After that, the clay soil was subjected to the same consolidation loads (20 kPa and 40 kPa) in the same manner as done in the first layer. Finally, the third clay layer was consolidated according to the procedure followed for the second layer.
MODEL PILE TESTS
After the consolidation process of the clay had been completed, the consolidation loads were removed, and the test tank was carefully removed from the consolidation frame and immediately mounted on the testing machine. Thereafter, the drainage valves were closed and the specified loading rate was set. The vertical load was applied to the model piles by means of 10 ton compression test machine. It is a displacement controlled machine with rate capability in the range 0.0001 to 59.99 mm/min.
Figure 3. Steel plate holding model piles
A 10 kN capacity load cell was used to record the applied load. The load cell was placed at the bottom of the testing machine top reaction beam. Pile head displacement was measured using a linear variable displacement transducer (LVDT) having a 25 mm range with 0.001 mm sensitivity. Data acquisition system and laptop computer were used during the test to scan, monitor and store displacement and load. Fig. 4 shows the experimental setup.
The model piles were subjected to axial compressive loads until the pile displacement reached 15 mm. For each pile group configuration, four compressive model tests were performed at constant loading rates of 0.01, 0.05, 0.1, and 1 mm/min. The width of the test tank does not permit performing the tests for 3x3 pile group with the space between the piles of 9 pile diameter. The total number of tests performed is 40 tests.
Figure 4. Schematic diagram of the experimental setup
TEST RESULTS AND DISCUSSION
Load-Displacement Response
Single Pile
The measured load-displacement curves for a single pile are shown in Fig. 5. The figure shows that the load-displacement curves have peak values from which the pile load reduces with further displacement. The pile head displacement needed to mobilize the ultimate axial capacity ranges from 2 mm to 3 mm (about 10% of pile diameter) which is in agreement with the values suggested by Vesic (1977). The pile head displacement at failure is essentially the same for the slow and the fast tests, while only the ultimate capacity changed. It indicates that the loading rate has a negligible influence on the magnitude of the pile head displacement at failure. This is in agreement with the findings of Audibert and Dover (1982) and Al-Mhaidib (2001). It is clear from Fig. 5 that the loading rate significantly affected the load-displacement response. The faster was the rate of loading the higher was the load-displacement curves and, consequently, the larger the ultimate axial capacity of the pile. A possible explanation of this behavior is that if the rate of loading is smaller, more time is allowed for the soil to creep and relax, allowing the development of larger deformations at a given load increment and smaller strength at a given deformation increment. The final result is load-displacement curve that plots lower.
Figure 5. Typical load-displacement curves for single pile
Pile Groups
Typical variations in axial pile capacity with the pile head displacement are shown in Figs. 6 to 10 for different pile group configurations. The results of other tests on other pile group configurations showed similar behavior. Similar to the results of single pile, the load-displacement responses were significantly affected by the loading rate. The axial pile capacity increases as the rate of loading increases. The pile head displacement needed to mobilize the ultimate axial capacity for all tests ranges from 2 mm to 3 mm (about 10% of pile diameter) similar to the results of the single pile. Therefore, the effect of loading rate on the pile head displacement at failure is insignificant.
Figure 6. Typical load-displacement curves for pile groups (2x1- 3d)
Figure 7. Typical load-displacement curves for pile groups (3x1- 3d)
Figure 8. Typical load-displacement curves for pile groups (2x2- 9d)
Figure 9. Typical load-displacement curves for pile groups (2x3- 9d)
Figure 10. Typical load-displacement curves for pile groups (3x3- 3d)
Effect of Loading Rate on Axial Pile Capacity
In Figs. 11 and 12 the values of the axial pile capacity are plotted versus the loading rate in a semilogarithmic format for piles with center-to-center spacing between piles of 3d and 9d, respectively. It is clear from these figures that the axial pile capacity approximately assumed a linear relationship with the logarithm of loading rate. Regardless of the pile group configuration and the spacing between the piles in a group, in all plots, the trend of increasing axial pile capacity with loading rate is evident.
The relationship between the axial pile capacity and loading rate depicted in Figs. 11 and 12 can be expressed as:
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(1) |
where q is the axial pile capacity, r is the loading rate, c a is constant, and a is the loading-rate capacity parameter measuring the increase of axial pile capacity (q) with loading rate (r). The values of the correlation coefficient, r2, are high, ranging from 0.92 to 0.99.
The parameter a represents the slope of the linear relationship between q and Log (r) and is defined as:
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(2) |
where qhigh and qlow are the axial capacity of pile group (in kN) corresponding to loading rate rhigh and rlow (in mm/min), respectively. The parameter a describes the increase of axial pile capacity for a tenfold increase of loading rate. The obtained values of a from all tests are listed in Table 2. These values reveal the following two trends. First, the values of a increase as the number of piles in a group increases as shown in Fig. 13. The second trend is that the center-to-center spacing between piles in a group has relatively little effect on the values of a (Table 2 and Fig. 14). There is a slight increase in the values of a when the center-to-center spacing between piles in a group increases from 3d to 9d.
Figure 11. Variations of axial pile capacity with loading rate for piles with 3d spacing
Figure 12. Variations of axial pile capacity with loading rate for piles with 9d spacing
Table 2. Values of loading-rate capacity parameter a
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| Pile group configuration | Spacing between piles | |
| 3d | 9d | |
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| 2x1 3x1 2x2 2x3 3x3 | 0.144 0.213 0.285 0.409 0.591 |
0.148 0.227 0.316 0.443 - |
| Single | 0.078 | |
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A normalized factor (Na) is introduced to describe the influence of the loading rate (r) on the axial pile capacity (q) in a more consistent and practical way than the parameter a. The factor Na is obtained by dividing the parameter a by the axial pile capacity at a reference loading rate (qref). In this study, the reference loading rate was taken to be the lowest rate (0.01 mm/min). The factor Na can be expressed as:
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(3) |
Figure 13. Parameter a versus number of piles in a group
Table 3. Values of normalized factor Na (%)
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| Pile group configuration | Spacing between piles | |
| 3d | 9d | |
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| 2x1 3x1 2x2 2x3 3x3 | 28.86 29.33 30.02 30.31 30.50 |
28.72 29.39 32.86 32.09 - |
| Single | 27.74 | |
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Figure 14. Parameter a versus (spacing/diameter) ratio
The normalized axial pile capacities (q/q0.01mm/min) are plotted versus the normalized loading rates (r/0.01) for all tests in Figs. 15 and 16 for piles with center-to-center spacing between piles of 3d and 9d, respectively. The data show fairly consistent linear trends and plot in a narrow range close together unlike the a lines on Figs. 11 and 12. The correlation coefficient, r2, values are high ranging from 0.93 to 0.99. The slope of the straight lines in Figs. 15 and 16 is the factor Na. The obtained values of Na from all tests are presented in Table 3. The average value of Na is equal to about 30% for all the test results. This indicates that there is a 30% increase in axial capacity of the piles when the loading rate increases from 0.01 mm/min to 1 mm/min, i.e. 100-fold increase.
Figure 15. Variations of normalized axial pile capacity with normalized loading rate for piles with 3d spacing
Figure 16. Variations of normalized axial pile capacity with normalized loading rate for piles with 9d spacing
Group Efficiency
The overall behavior of a pile group is given by the efficiency of the group, and it is estimated using the formula:
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(4) |
where h = efficiency of the pile group; Qg = axial capacity of the pile group; Qs= axial capacity of a single pile; n1 = number of rows in the pile group; and n2 = number of columns in the pile group.
The group efficiencies obtained using equation (4) are computed for all pile group configurations tested and listed in Table 4. It can be seen from this table that the effect of loading rate on the efficiency h, within a group configuration, for the different pile group configurations is insignificant. The efficiency h does not change much within a pile group configuration when the loading rate is changed. For example, the efficiency h for 3x1 pile group changed from 0.85 to 0.88 and from 0.90 to 0.94 for 3d spacing and 9d spacing, respectively. The efficiency also changed from 0.78 to 0.80 for 3d spacing for 3x3 pile group. There is a good agreement between the group efficiencies obtained in this study for piles with 3d spacing (ranging from 0.79 to 0.89 on average) and group efficiencies for pile groups in clay with 2d to 4d spacing reported by Zhang et. al (2001) ranging from 0.83 to 0.88 based on a compiled database of pile group load tests.
Table 4. Values of group efficiency h
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| Pile group configuration | Loading rate (mm/min) | Spacing between piles | |
| 3d | 9d | ||
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| 2x1 | 1 0.1 0.05 0.01 Average |
0.91 0.87 0.90 0.89 0.89 |
0.97 0.93 0.94 0.96 0.95 |
| 3x1 | 1 0.1 0.05 0.01 Average |
0.88 0.85 0.87 0.86 0.86 |
0.94 0.90 0.92 0.92 0.92 |
| 2x2 | 1 0.1 0.05 0.01 Average |
0.87 0.81 0.83 0.84 0.84 |
0.91 0.88 0.87 0.86 0.88 |
| 2x3 | 1 0.1 0.05 0.01 Average |
0.83 0.80 0.82 0.80 0.81 |
0.87 0.82 0.83 0.82 0.84 |
| 3x3 | 1 0.1 0.05 0.01 Average |
0.80 0.79 0.80 0.78 0.79 |
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The average values of group efficiency h, from Table 4, are plotted versus number of piles in a group in Fig. 17. This figure shows that, for the same center-to-center spacing between piles in a group, the efficiency h decreases with an increase in the number of piles in a group. This is in agreement of results of O'Neill (1983) for piles tested under axial loads, Gandhi and Selvam (1997) and Patra and Pise (2001) for piles tested under lateral loads. This can be attributed to the increased area of overlapping zones between piles. The average values of group efficiency h are also plotted versus spacing/diameter (s/d) ratio in Fig. 18 to show the effect of spacing on group efficiency. As seen in Fig. 18, the efficiency increases with increase in spacing between piles in a group. A possible explanation of this behavior is that as the spacing between piles in a group is increased, the overlapping area is reduced, and hence the efficiency increases.
Figure 17. Group efficiency h versus number of piles in a group
Figure 18. Group efficiency h versus (spacing/diameter) ratio
The average values of group efficiency are compared with those calculated from Convese-Labarre equation (Bolin 1941) and listed in Table 5. According to Convese-Labarre equation, which is considered as one of the most acceptable equations for calculating group efficiency in clay, the efficiency of group piles is expressed as:
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(5) |
where h = efficiency of the pile group; q = arctan d/s (in degrees); d = pile diameter; s = center-to-center spacing between piles in a group; n1 = number of rows in a pile group; and n2 = number of columns in a pile group.
There is a fairly good agreement between the values of the group efficiency computed in the present study and those calculated from Convese-Labarre equation as shown in Table 5.
Table 5. Comparison between obtained and calculated values of group efficiency
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| Pile group configuration | S p a c i n g b e t w e e n p i l e s | |||
| 3d | 9d | |||
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| This study | Converse-Labarre | This study | Converse-Labarre | |
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| 2x1 3x1 2x2 2x3 3x3 | 0.89 0.86 0.84 0.81 0.79 |
0.90 0.86 0.80 0.76 0.73 |
0.95 0.92 0.88 0.84 - |
0.96 0.95 0.93 0.92 - |
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SUMMARY AND CONCLUSIONS
In this paper, the behavior of pile groups under different loading rates was studied by conducting tests on model pile groups. The tests were conducted in a clayey soil bed prepared in a test tank. The model pile groups were subjected to axial compressive loads at four loading rates of 0.01 mm/min, 0.05 mm/min, 0.1 mm/min and 1 mm/min. At each loading rate, five different pile group configurations (from line pile groups to square and rectangular pile groups) were tested. The center-to-center spacing of piles in a group was three or nine times the pile diameter. Along with the pile groups, a single pile was also tested. The total number of tests performed in this study was forty tests.
The magnitude of loading rate effect on axial pile capacity is measured in this study with two quantities. The first quantity is the loading-rate capacity parameter a representing the slope of capacity-log(loading rate) trend line. The parameter a describes the increase of capacity for tenfold increase of loading rate. The second quantity is the capacity-loading rate factor Na, which is a normalized quantity, that is more suitable for the assessment of the effect of the loading rate on the pile capacity than the parameter a.
Based on the results of present experimental investigation, the following conclusions are drawn, which of course apply to the range of loading rates considered in this study:
Loading rate has a significant influence on the load-displacement response, where the faster loading resulted in a stronger soil response. Increasing the loading rate resulted in higher load-displacement curves. Loading rate has a negligible influence on the magnitude of the pile head displacement at failure, which was found to be in the range of 2 mm to 3 mm, about 10% of pile diameter.
The axial pile capacity was profoundly influenced by the loading rate. The axial compressive capacity of pile group in clay increases as the loading rate increases. The variations in the axial pile capacity with the logarithm of loading rate plot approximately along a straight line. The slope of this line, the parameter a, ranged from 0.078 to 0.591 depending on the pile group configuration and center-to-center spacing of piles in a group. The value of a increased as the number of piles in a group increased. The center-to-center spacing between piles in a group had relatively little effect on the values of a. The average value of the normalized factor Na equal to about 30% for all the test results, which indicated that there was a 30% increase in axial capacity of the piles when the loading rate increased from 0.01 mm/min to 1 mm/min, i.e. 100-fold increase.
The effect of loading rate on the efficiency of pile group, within a group configuration, for the different pile group configurations is insignificant. For the same center-to-center spacing between piles in a group, the group efficiency decreases with an increase in the number of piles in a group. The efficiency increases with increase in spacing between piles in a group. The efficiency values obtained in this study are in good agreement with those reported in the literature and with those calculated from Convese-Labarre equation.
The results obtained from this type of model testing have to be cautiously used when applying to field situations. Because the size of piles used in model testing is small, it is quite possible that some of the observed results can not directly applied to the prototype piles installed in the field. Model tests help with understanding the fundamental aspects of load transfer mechanisms; however, it cannot duplicate the total behavior of piles because the actual stress states in the soil cannot be modeled entirely, especially the stresses induced during pile installation. Gravity stresses in deep soil deposits could be modeled by conducting laboratory tests in centrifuges. However, the availability of centrifuges for pile testing is very limited.
Further experimental work that covers wide variations in loading rate, pile characteristics, and soil properties is needed to achieve definite conclusions about the effects of loading rate on axial capacity of pile groups. The results of this study is hoped to simulate further research in this direction.
ACKNOWLEDGEMENT
The author would like to acknowledge the research grant No. 6/425 provided by the Deanship of Scientific Research at King Saud University, through Research Center at College of Engineering, Riyadh, Saudi Arabia.
REFERENCES
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