4.1. Definition of failure load
The ultimate axial capacities of model piles were estimated from load-relative displacement curves. The pile displacement, S (mm) is expressed in non-dimensional form in terms of pile diameter, D (mm) as percentage relative displacement ratio, S/D (%). Terzaghi [52] and Meyerhof [37] proposed that, the ultimate axial pile capacities are estimated from the load-displacement curve as the load corresponding to relative displacement (S/D) equal to 10%. Additionally, Das [12] described that, the maximum resistance at pile tip will not be mobilized until the pile tip has moved about 10–25% of the pile diameter. Due to no peak failure point specified at load-relative displacement curves is exhibited, the ultimate axial load of a single pile (Qult.) was estimated from load-relative displacement curves as the load corresponding to relative displacement (S/D) equal to 10%.
4.2. Load-displacement relationship
To study the behavior of the axial capacity of a single pile, eighty-four tests were performed using seven different cross sections of piles with pile length equals to 200 and 600 mm. From these tests, the load-displacement curves were obtained and presented in Figures (4 to 9). Figure 4a shows typical axial compression load versus relative displacement, S/D (%) for different model piles having L/D = 10 are installed in loose sand (Dr = 33%) using non-displacement technique. It is observed that, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 20% then afterwards it is linear. It is also indicated that, the loading rate for open-ended pipe and square open-ended piles increased in the phases of the axial loading until the maximum (Qaxial) values approximately equal to 37.4N and 59.7N respectively corresponding to relative displacement of about 23.35% and 23.8% respectively. Afterwards, the loading rate is constant (more vertical settlement without additional load). The ultimate capacities (Qult.) were found to be 57N, 29N, 35.4N, 63.5N, 44.8N, 50.8N and 72.4N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Also Fig. 4b shows typical axial compression load versus normalized displacement, S/D (%) for different model piles having L/D = 30 are installed in loose sand (Dr = 33%) using non-displacement technique. It is clear that, for square open-ended, square closed-ended, open-ended pipe and rectangular piles, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 10% then afterwards it is linear. While, for closed-ended pipe, conical base pipe and tapered piles, non-linear relationship in the early stages of the loading until relative displacement of approximately 15% however afterwards it is linearly. It is indicated that, the loading rate for open-ended pile increased in the phases of the axial loading until the maximum (Qaxial) value approximately equals to 95.3N corresponding to relative displacement of about 28.85%. Afterwards, the loading rate is constant (more vertical settlement without additional load). The corresponding ultimate capacities (Qult.) were found to 125N, 62.2N, 85.95N, 115.3N, 106.9N, 95.8N and 144.7N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles. Comparing between the results presented in Fig. 4a and Fig. 4b, it is found that, model piles with L/D = 30 have more resistance than model piles with L/D = 10. This observation due to that, the shaft resistance of model piles (Qs) increases with the increase of the surface area of pile per unit length. It is observed that, the load capacity of piles is highly affected by the pile length to diameter (L/D) ratio. In addition, Fig. 5a indicates load-relative displacement curves for different model piles with L/D = 10 are installed in loose sand (Dr = 33%) using jacking technique. It is clearly that, for open-ended pipe, conical base pipe, square open-ended, and square closed-ended piles, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 20% however afterwards it is linearly. However, for tapered and closed-ended pipe piles, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 15% then afterwards it is linearly. For rectangular pile, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 10% then afterwards it is linearly. The ultimate capacities (Qult.) were found to be 91.9N, 45.6N, 55.3N, 73.1N, 64.4N, 81.4N and 108.6N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles. From the same figure, the ultimate axial capacity (Qult.) value of tapered pile was found to be increased by 11.35% compared with the (Qult.) value of square closed-ended pile. This observation due to that, the tapering degree (α) of model pile increases the internal friction angle between pile and sand (δ) that has an influence on the taper coefficient (Kt). It has been clearly observed that, for piles installed in sand via jacking method technique, the influence of tapering degree is highly affected on the axial pile capacity. On the other hand, Fig. 5b illustrations load-relative displacement curves for different model piles with L/D = 30 are installed in loose sand (Dr = 33%) using jacking technique. It is observed that, for open-ended pipe, conical base pipe, square open-ended, square closed-ended and closed-ended pipe piles, in the early phases of the loading, non-linearly relationship until relative displacement of approximately 10% then afterwards it is linearly. However, for tapered and rectangular piles, at the early phases of the loading, non-linearly relationship until relative displacement of almost 20% then afterwards it is linearly. It is also observed that, the loading rate for open-ended pipe and conical base pipe piles increased in the phases of the axial loading until the maximum (Qaxial) values about equal to 128.9N and 155.95N respectively corresponding to relative displacement of about 15% and 21.65% respectively. Afterwards, the loading rate is constant (more vertical settlement without additional load). The corresponding ultimate capacities (Qult.) were found to be 298.9N, 126.8N, 150N, 200.9N, 166.7N, 280N and 340.7N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. The same figure also indicates that; the ultimate axial capacity (Qult.) value of tapered pile was found to be increased by 39.37% compared with the (Qult.) value of square closed-ended pile. On the other hand, Fig. 6a indicates the relationship of the axial compression load versus relative displacement curves for different model piles having L/D = 10 are installed in medium dense sand (Dr = 60%) using non-displacement technique. This figure indicates that, for open-ended pipe, conical base pipe, and square closed-ended piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.35% then it is non-linearly in phases of the axial loading until relative displacement of almost 15%, afterwards it is linearly. The same figure also indicates that; at the early phases of the loading, linearly relationship for square open-ended, tapered, closed-ended pipe and rectangular piles until relative displacement of almost 0.30% then it is non-linearly relationship in phases of the axial loading until relative displacement of almost 10%, afterwards it is linearly. It is observed that, the loading rate for open-ended pipe pile increased in the stages of the axial loading up to the maximum (Qaxial) value approximately equal to 114.6N corresponding to relative displacement of about 21.90%. Afterwards, the loading rate is constant (more vertical settlement without additional load). The observed (Qult.) results were found to be 215.8N, 102.6N, 115.1N, 191.3N, 136.9N, 164N and 226.8N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Also Fig. 6b indicates load-relative displacement curves for different model piles with L/D = 30 are installed in medium dense sand (Dr = 60%) using non-displacement technique. This figure indicates that, for open-ended pipe, square open-ended, and tapered piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.25% then it is non-linearly relationship in phases of the axial loading until relative displacement of approximately 10%, afterwards it is linearly. The same figure also indicates that; at the early phases of the loading, linearly relationship for conical base pipe, closed-ended pipe, square closed-ended and rectangular piles until relative displacement of almost 0.20% then it is non-linearly relationship in phases of the axial loading until relative displacement of almost 5%, afterwards it is linearly. It is also observed that, the loading rate for open-ended pipe and conical base pipe piles increased in the phases of the axial loading until the maximum (Qaxial) values approximately equal to 141.3N and 145.95N respectively corresponding to relative displacement of about 11.15% and 11.60% respectively. Afterwards, the loading rate is constant (more vertical settlement without additional load). the corresponding capacities (Qult.) were found to be 321.1N, 140.7N, 145.5N, 341.3N, 185.1N, 280N and 434.3N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. It can be concluded that, the piles installed in medium dense sand have more resistance than piles installed in loose sand. This observation is due to that, the friction angle of sand (φ) has a great influence on the shaft resistance of pile (Qs). It has been clearly observed that, the relative sand density has a major influence on the axial pile load capacity.
Furthermore, Fig. 7a indicates load-relative displacement curves for different model piles with L/D = 10 are installed in medium dense sand (Dr = 60%) using jacking technique. It is observed that, for open-ended pipe, conical base pipe, square open-ended, closed-ended pipe and tapered piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.20% then it is non-linearly in phases of the axial loading until relative displacement of almost 10%, afterwards it is linearly. It is also indicated that, at the early phases of the loading, linearly relationship for square closed-ended and rectangular piles until relative displacement of almost 0.05% then it is non-linearly in phases of the axial loading until relative displacement of almost 5%, afterwards it is linearly. The same figure also showed that, the loading rate for open-ended pipe and conical base pipe piles increased in the phases of the axial loading until the maximum (Qaxial) values approximately equal to 385.5N and 465N respectively corresponding to relative displacement of about 11.70% and 30% respectively. Afterwards, the loading rate is constant (more vertical settlement without additional load). The observed capacities (Qult.) were found to be 553N, 384.5N, 439.1N, 518N, 492.7N, 566N and 600N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. From the same figure, analyzing the relation between axial compression load and relative displacement for square closed-ended (SCEP) and closed-ended pipe (CEPP) piles, the (Qaxial) values equal to 285.95N and 265.95N respectively at relative displacement of about 0.05%, the loading rate (Qrate) for (SCEP) pile is greater than (CEPP) pile up to relative displacement of about 1.75% corresponding to axial load equal to 425.95N, then the (Qrate) for (CEPP) pile is greater than (SCEP) pile up to relative displacement of about 21.75% corresponding to axial load approximately equal to 600N, afterwards (Qrate) (SCEP) pile is greater than (CEPP) pile. This observation due to that, square closed-ended pile has more the perimeter surface and tip cross section area than closed-ended pipe pile. Moreover, Fig. 7b indicates load-relative displacement curves for different model piles with L/D = 30 are installed in medium dense sand (Dr = 60%) using jacking technique. It is observed that, for model piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.20% then it is non-linearly in phases of the axial loading until relative displacement of almost 10%, afterwards it is linearly. It also observed that, the loading rate for open-ended pipe and conical base pipe piles increased in the phases of the axial loading until the maximum (Qaxial) values approximately equal to 457N and 489N respectively corresponding to relative displacement of about 15% and 12.40% respectively. Afterwards, the loading rate is constant (more vertical settlement without additional load). The corresponding ultimate capacities (Qult.) were found to be 678.4N, 453N, 486N, 610N, 510N, 703.5N and 777N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Comparing the results of tapered piles shown in Figures (5 and 7); it is found that, there is a large difference between the corresponding ultimate capacities (Qult.). This observation due to that, the internal friction angle between pile and sand (δ) has an influence on the taper coefficient (Kt) and friction angle of sand (φ). It has been clearly observed that, the influence of tapering degree is highly affected on axial pile capacity by increasing the relative sand density. Figure 8a illustrations load-relative displacement curves for different model piles with L/D = 10 are installed in dense sand (Dr = 80%) using non-displacement technique. It is clear that, for model piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.15% then it is non-linearly in phases of the axial loading until relative displacement of about 10%, afterwards it is linearly. At normalized displacement ratio S/D of about 10%, The corresponding ultimate capacities (Qult.) were found to be 239.6N, 172.4N, 152.7N, 219.6N, 194.1N, 210.9N and 262.2N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. The same figure also shows that; the (Qult.) value of open-ended pipe pile was found to be increased by 12.90% compared with the (Qult.) value of conical base pipe pile. In contrast, conical cross-sectional base pipe pile has more resistance than open-ended pipe pile at the same conditions in the two cases of loose and medium sand. This observation may be due to that, the effect of soil plugging within open-ended pipe pile is significant increased the inner shaft resistance (Qinner). Therefore, the total pile resistance was increased. On the other hand, Fig. 8b indicates load-relative displacement curves for different model piles with L/D = 30 are installed in dense sand (Dr = 80%) using non-displacement technique. This figure indicates that, for model piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.15% then it is non-linearly in phases of the axial loading until relative displacement of almost 10%, afterwards it is linear. The same figure also indicates that; the corresponding capacities (Qult.) were found to be 425 N, 259N, 172N, 475N, 312N, 399N and 486N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Furthermore, Fig. 9a indicates load-relative displacement curves for different model piles with L/D = 10 are installed in dense sand (Dr = 80%) using jacking technique. It is observed that, for model piles, at the early phases of the loading, linearly relationship until relative displacement of almost 0.1% then it is non-linearly in phases of the axial loading until relative displacement of almost 10%, afterwards it is linearly. The corresponding capacities (Qult.) were found to be 637N, 425N, 494N, 594N, 541.7N, 670N and 756N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Finally, Fig. 9b indicates load-relative displacement curves for different model piles with L/D = 30 are installed in dense sand (Dr = 80%) using jacking technique. It is observed that, at the early phases of the loading for open-ended pipe, square open-ended, square closed-ended and conical base pipe piles, linearly relationship until relative displacement of almost 0.15% then it is non-linearly in phases of the axial loading until relative displacement of about 10%, afterwards it is linear. It is also observed that, at the early phases of the loading for closed-ended pipe, tapered and rectangular piles, linearly relationship until relative displacement of almost 0.10% then it is non-linearly in phases of the axial loading until relative displacement of almost 5%, afterwards it is linearly. The corresponding ultimate capacities (Qult.) were found to be 1035N, 698N, 954N, 812N, 746N, 1111N and 1248N for closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. On the other hand, during the pile load test for conical base pipe pile, the vertical displacement readings of a two dial gauge were nearly identical. This observation due to the advantage of conical base that distributes the driven load evenly around the pile circumference and not causing added stresses on one section of the pile as described by Erhart [25]. In this model study, conical base pipe piles are used as a modified alternative to open-ended pipe piles to install piles into hard layer (dense sand, Dr = 80%) using jacking technique. The results showed that, conical cross-sectional base pipe pile has more resistance than open-ended pipe pile. While, more investigations described that, the load capacity of open-ended pipe piles increase with increasing the pile diameters. Therefore, it should be designed and checked to ensure that the conical cross-sectional base pipe pile does not decrease the base load capacity of the plugging soil lower than the estimated value in the design as recommended by API [3].
4.3. Influence of pile cross section
To study the influence of the pile cross section on its axial capacity, seven different piles with the same geometry properties are used as tested models. The relation between axial compression load and relative displacement, S/D (%) for the seven model piles are shown in Figures (4 to 9). These figures show that; the rectangular piles have the maximum resistance compared with the different model piles. It should be noted that; the rectangular pile is the optimization cross-sectional under the same pile geometry and soil conditions. The difference in axial pile capacities is referred to the change in the end bearing stress at the pile tip due to the different pile configurations which have different cross sectional area. And also, the radial stress around the pile perimeter due to the different pile cross sections that have a great influence in the earth pressure that highly affected on axial pile capacity. The summary of the values of ultimate axial compression capacity for different model piles in sand using non-displacement technique are presented in Tables 4. For model piles with L/D = 10 in sand using non-displacement technique, the ultimate axial capacity (Qult.) values of rectangular piles were found to be (1.27, 2.50, 2.05, 1.14, 1.62 and 1.43), (1.05, 2.21, 1.97, 1.19, 1.66 and 1.38) and (1.09, 1.52, 1.72, 1.19, 1.35 and 1.24) times of the (Qult.) values of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended and tapered piles in the cases of loose, medium dense and dense sand respectively. From the same figures, for model piles with L/D = 30 in sand using non-displacement technique, the ultimate axial capacity (Qult.) values of rectangular piles were found to be (1.16, 2.33, 1.68, 1.25, 1.35 and 1.51), (1.35, 3.09, 2.98, 1.27, 2.35 and 1.55) and (1.14, 1.88, 2.83, 1.02, 1.56 and 1.22) times of the (Qult.) values of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended and tapered piles in the cases of loose, medium dense and dense sand respectively. While, for model piles with L/D of 10 and 30 in sand using non-displacement technique, the ultimate axial capacity (Qult.) values of closed-ended pipe piles were found to be increased by (97% and 101%), (110% and 128%) and (39% and 64%) comparing with the (Qult.) values of open-ended pipe piles in the cases of loose, medium dense and dense sand respectively. Moreover, for piles with L/D ratio of 10 and 30 in sand using non-displacement technique, the ultimate axial capacity (Qult.) values of closed-ended pipe piles were found to be increased by (61% and 45%), (87% and 121%) and (57% and 147%) comparing with the (Qult.) values of conical base pipe piles in the cases of loose, medium dense and dense sand respectively. Comparing between model piles having the same diameter; it is found that, the closed-ended pipe piles have more resistance comparing with the open-ended pipe [49] and conical base pipe piles. On the other hand, for piles with L/D of 10 and 30 in loose sand using non-displacement technique, the ultimate axial capacity (Qult.) values of square closed-ended piles were found to be increased by (42% and 25%) and (8% and 20%) comparing with the (Qult.) values of square open-ended and tapered piles respectively. While, these values were found to be increased by (40% and 17%) and (84% and 22%) in the case of medium dense sand. Finally, these values were found to be increased by (13% and 4%) and (52% and 19%) in the case of dense sand. Comparing between model piles with the same width are installed in sand using non-displacement technique; it is found that, the square closed-ended pile is a highly effective and more resistance compared with the square open-ended [22] and tapered piles. This observation due to square closed-ended piles have a large cross-sectional area at the tip pile. The summary of the values of ultimate axial compression capacity for different model piles in sand using jacking technique are presented in Tables 5. On the other hand, for model piles with L/D = 10 in sand using jacking technique, the ultimate axial capacity (Qult.) values of rectangular piles were found to be (1.18, 2.38, 1.96, 1.49, 1.69 and 1.33), (1.08, 1.56, 1.37, 1.16, 1.22 and 1.06) and (1.19, 1.78, 1.53, 1.27, 1.40 and 1.13) times of the (Qult.) values of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended and tapered piles in the cases of loose, medium dense and dense sand respectively. The results indicated that, for model piles with L/D = 30 in sand using jacking technique, the ultimate axial capacity (Qult.) values of rectangular piles were found to be (1.14, 2.69, 2.27, 1.70, 2.04 and 1.22), (1.15, 1.72, 1.60, 1.27, 1.52 and 1.10) and (1.21, 1.79, 1.31, 1.54, 1.67 and 1.12) times of the (Qult.) values of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended and tapered piles in the cases of loose, medium dense and dense sand respectively. However, for model piles with L/D of 10 and 30 in sand using jacking technique, the ultimate axial capacity (Qult.) values of closed-ended pipe piles were found to be increased by (102% and 136%), (44% and 50%) and (50% and 48%) comparing with the (Qult.) values of open-ended pipe piles in the cases of loose, medium dense and dense sand respectively. From the same figures, for model piles with L/D of 10 and 30 in sand using jacking technique, the ultimate axial capacity (Qult.) values of closed-ended pipe piles were found to be increased by (66% and 99%), (26% and 40%) and (29% and 8%) comparing with the (Qult.) values of conical base pipe piles in the cases of loose, medium dense and dense sand respectively. Also, for piles with L/D of 10 and 30 in sand using jacking technique, the ultimate axial capacity (Qult.) values of conical base pipe piles were found to be increased by (21% and 18%), (14% and 7%) and (16% and 37%) comparing with the (Qult.) values of open-ended pipe piles in the cases of loose, medium dense and dense sand respectively. In trend of tapering degree effect at jacking technique, it is found that, the values of ultimate axial capacity (Qult.) for tapered piles with L/D of 10 and 30 in loose sand were found to be increased by (11% and 26%) and (39% and 68%) comparing with the (Qult.) values of square closed-ended and square open-ended piles respectively. Also, these values were found to be increased by (9% and 15%) and (15% and 38%) in the case of medium dense sand. In addition, these values were found to be increased by (13% and 24%) and (37% and 49%) in the case of dense sand. These results are confirmed that, the tapered piles installed in sand using jacking technique have more resistance compared with the square closed-ended piles as described by Wei [56] and Wei and El-Naggar [56]. This observation due to the tapering degree increases the effective radius of influenced zone around the pile shaft. The densification of sand surrounding pile walls is produced additional lateral pressures led to increase the shear stresses through the pile-soil surface as indicated by Manandhar and Yasufuku [34]. The results indicated that, the tapering degree has a beneficial influence on the axial pile capacity. It should be noted that, geometry of pile toe has a significant influence on the ultimate compression load capacity and pile vertical displacement.
Table 4
The ultimate axial compression capacities for model piles using non-displacement technique
Relative density | Ultimate axial compression load, Qult. (N) |
Pile length to diameter (L/D) ratio = 10 | Pile length to diameter (L/D) ratio = 30 |
CEPP | OEPP | CBPP | SCEP | SOEP | TP | RP | CEPP | OEPP | CBPP | SCEP | SOEP | TP | RP |
Loose sand Dr = 33% | 57 | 29 | 35.4 | 63.5 | 44.8 | 50.8 | 72.4 | 125 | 62.2 | 85.95 | 115.3 | 106.9 | 95.8 | 144.7 |
Medium dense sand Dr = 60% | 215.8 | 102.6 | 115.1 | 191.3 | 136.9 | 164 | 226.8 | 321.1 | 140.7 | 145.5 | 341.3 | 185.1 | 280 | 434.3 |
Dense sand Dr = 80% | 239.6 | 172.4 | 152.7 | 219.6 | 194.1 | 210.9 | 262.2 | 425 | 259 | 172 | 475 | 312 | 399 | 486 |
CEPP: closed-ended pipe pile; OEPP: open-ended pipe pile; CBPP: conical base pipe pile; SOEP: square open-ended pile; SCEP: square closed-ended pile; TP: tapered pile and RP: rectangular pile |
Table 5
The ultimate axial compression capacities for model piles using jacking technique
Relative density | Ultimate axial compression load, Qult. (N) |
Pile length to diameter (L/D) ratio = 10 | Pile length to diameter (L/D) ratio = 30 |
CEPP | OEPP | CBPP | SCEP | SOEP | TP | RP | CEPP | OEPP | CBPP | SCEP | SOEP | TP | RP |
Loose sand Dr = 33% | 91.9 | 45.6 | 55.3 | 73.1 | 64.4 | 81.4 | 108.6 | 298.9 | 126.8 | 150 | 200.9 | 166.7 | 280 | 340.7 |
Medium dense sand Dr = 60% | 553 | 384.5 | 439.1 | 518 | 492.7 | 566 | 600 | 678.4 | 453 | 486 | 610 | 510 | 703.5 | 777 |
Dense sand Dr = 80% | 637 | 425 | 494 | 594 | 541.7 | 670 | 756 | 1035 | 698 | 954 | 812 | 746 | 1111 | 1248 |
CEPP: closed-ended pipe pile; OEPP: open-ended pipe pile; CBPP: conical base pipe pile; SOEP: square open-ended pile; SCEP: square closed-ended pile; TP: tapered pile and RP: rectangular pile |
4.4. Influence of relative sand density
Figures (10 and 11) show the influence of relative sand density (Dr) on the ultimate axial pile load. These figures give the relation between the ultimate axial load of different model piles and different relative sand densities. There are indicated that, the ultimate axial compression load of different model piles increases with the increase of relative sand density. Figure 10 shows the relation between the ultimate axial load of different model piles and different relative sand densities using non-displacement technique. It is observed that, for piles with L/D of 10 and 30, the ultimate axial load of piles in the case of medium dense sand were found to be increased by (2.79, 2.54, 2.25, 2.01, 2.06, 2.23 and 2.13) and (1.57, 1.26, 0.69, 1.96, 0.73, 1.92 and 2.00) compared with the ultimate axial load of piles in loose sand for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. It is also observed that, for piles with L/D of 10 and 30, the ultimate axial load of piles in the case of dense sand were found to be increased by (3.20, 4.94, 3.31, 2.46, 3.33, 3.15 and 2.62) and (2.40, 3.16, 1.00, 3.12, 1.92, 3.16 and 2.36) compared with the ultimate axial load of piles in loose sand for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Furthermore, Fig. 11 shows the relation between the ultimate axial load of different model piles and different sand relative densities using jacking technique. This figure indicates that, for piles with L/D of 10 and 30, the ultimate axial load of piles in the case of medium dense sand were found to be increased by (5.02, 7.43, 6.94, 6.09, 6.65, 5.95 and 4.52) and (1.27, 2.57, 2.24, 2.04, 2.06, 1.51 and 1.28) compared with the ultimate axial load of piles in loose sand for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. This figure also indicates that, for piles with L/D of 10 and 30, the ultimate axial load of piles in the case of dense sand were found to be increased by (5.93, 8.32, 7.93, 7.13, 7.41, 7.23 and 5.96) and (2.46, 4.50, 5.36, 3.04, 3.48, 2.97 and 2.66) compared with the ultimate axial load of piles in loose sand for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. It is mentioned that, the relative sand density is the most effective factor for axial pile capacity.
4.5. Influence of (pile length/diameter) ratio
The effect of (pile length/diameter) ratio, L/D on the ultimate axial load for different model piles was studied and presented in Figures (12 and 13). These figures indicate the relation of the ultimate axial load for model piles with different (pile length/diameter) ratio. These figures are indicated that, the ultimate axial load of model pile increases with the increase of the (pile length/diameter) ratio. Figure 12 illustrations the relation between the ultimate axial load of different model piles with different (pile length/diameter) ratio using non-displacement technique. This figure indicates that, the values of the ultimate axial load of flexible piles (L/D = 30) in loose sand were found to be increased by 119%, 114%, 143%, 82% 139%, 89% and 100% compared with the values of the ultimate axial load of rigid piles (L/D = 10) for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. While, these values were found to be increased by (49%, 37%, 26%, 78%, 35%, 71% and 91%) and (77%, 50%, 13%, 116%, 61%, 89% and 85%) in the cases of medium dense and dense sand respectively. On the other hand, Fig. 13 shows the relation between the ultimate axial load of different model piles with different (pile length/diameter) ratio using jacking technique. This figure indicates that, the values of the ultimate axial load of flexible piles in loose sand were found to be increased by 225%, 178%, 171%, 175%, 159%, 244% and 214% compared with the values of the ultimate axial load of rigid piles for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. However, these percentage values were found to be increased by (23%, 18%, 11%, 18%, 4%, 24% and 30%) and (62%, 64%, 93%, 37%, 38%, 66% and 65%) in the cases of medium dense and dense sand respectively. The results are shown in Figures (12 and 13); these are indicated that, long/flexible model piles with L/D = 30 have more resistance than short/rigid model piles with L/D = 10. This observation due to that, the shaft resistance of model piles (Qs) increases with the increase of the surface area of pile per unit length. It is clearly indicated that, the compression pile load capacity is highly affected by the (pile length to diameter) ratio.
4.6. Influence of pile installation technique
So as to study the influence of pile installation technique on the ultimate axial load for model piles with different cross sections, Figures (14 and 15) are shown. These figures indicate the relation between the ultimate axial load for model piles with different cross sections and pile installation technique methods. These figures are indicated that, model piles installed in sand using jacking technique method have more resistance compared with model piles installed in sand using non-displacement technique method. Moreover, Fig. 14 indicates the relation between the ultimate axial load for model piles with different cross sections having pile length/diameter (L/D) ratio = 10 and pile installation technique methods. This figure indicates that, the ultimate axial capacities of model piles installed in loose sand using jacking method were found to be increased by 61%, 57%, 56%, 15%, 44%, 60% and 50% compared with the ultimate axial capacities of model piles installed in sand using non-displacement method for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. Whereas, these percentages were found to be increased by (156%, 275%, 281%, 171%, 260%, 245% and 165%) and (166%, 147%, 224%, 170%, 179%, 218% and 188%) in the cases of medium dense and dense sand respectively. On the other hand, Fig. 15 indicates the relation between the ultimate axial load for model piles with different cross sections having pile length/diameter (L/D) ratio = 30 and pile installation technique methods. This figure indicates that, the ultimate axial capacities of model piles installed in loose sand using jacking method were found to be increased by 139%, 104%, 75%, 74%, 56%, 192% and 135% compared with the ultimate axial capacities of model piles installed in sand using non-displacement method for the seven models of closed-ended pipe, open-ended pipe, conical base pipe, square closed-ended, square open-ended, tapered and rectangular piles respectively. However, these percentages were found to be increased by (111%, 222%, 234%, 79%, 176%, 151% and 79%) and (144%, 169%, 455%, 71%, 139%, 178% and 157%) in the cases of medium dense and dense sand respectively. From Fig. 15c (in the case of dense sand), it is found that, the ultimate axial capacity of conical base pipe pile using jacking technique method is a highly increased by 455% compared with the ultimate axial capacity in case of non-displacement technique method. This observation approved that, the conical base with sixty-degree configuration is the preferred end closure for open-ended pipe piles to install piles in heavy or hard layers as proposed by Associated Pile and Fitting Company [4].