Behavior of Fiber-Reinforced Polymer Composite Piles Under Vertical Loads

508 COMPLIANCE CAPTIONS

Figure 1. Photo.Marine borers parenthesis Limnoria end parenthesis attacking untreated timber piles that support many of New York 's highways and harbor piers. This figure is a color photograph of deteriorating piles in a water environment. The tubular piles appear to be highly deteriorated wood supporting beams below a road, bridge, or pier. Some of the piles are so highly deteriorated that they no longer are in contact with the beam that they are intended to support.

Figure 2. Photo. Complete corrosion of steel H piles supporting a harbor pier parenthesis recently installed retrofit channels are already corroding end parenthesis. This figure is a color photograph of corroding piles in a water environment. The rectangular steel piles that are supporting pier beams show rust and corrosion near the surface of the piles in contact with the water. The figure also shows corrosion of the more recent retrofitted channel bars installed adjacent to the H pilings.

Figure 3. Photo. Fender piles in U.S. Naval Submarine Base, San Diego, California. This figure is a color photograph of a set of fender piles around the outside of an installation at the San Diego, California, U.S. Naval Submarine Base. The fender piles depict an example of one experimental use of fiber-reinforced polymer composite piles.

Figure 4. Photo. Fendering system in U.S. Navy Pier 10, San Diego, California. This figure is a color photograph of a large number of fender piles lining the outside of a very long pier. The fender piles are regularly spaced along the perimeter of the Navy pier. The fender piles depict an example of one experimental use of fiber-reinforced polymer composite piles.

Figure 5. Photo. Fendering system, Nashville Avenue Marine Terminal, Port of New Orleans, Louisiana. This figure is a color photograph of a large number of fender piles lining the outside of a very long pier. The fender piles are regularly spaced along one outer side of the pier. The fender piles depict an example of one experimental use of fiber-reinforced polymer composite piles.

Figure 6. Photo. Floating dock project. This figure is a color photograph of a floating dock consisting of piles. The dock is supported by a large number of tubular fiber-reinforced polymer piles. The pile-supported dock demonstrates one experimental use of fiber-reinforced polymer composite piles.

Figure 7. Photo. Port of Elizabeth demonstration site. This figure is a color photograph of the location of the experimental tests conducted to address research and development needs, and to assess the feasibility of using fiber-reinforced polymer composite piles as vertical load-bearing piles. The demonstration site is located at the Port of Elizabeth in New Jersey, a facility provided by the Port Authority of New York and New Jersey. The photograph shows composite piles in the foreground and testing equipment in the background.

Figure 8. Illustration. Locations of the pile manufacturers. This figure is an outline map of the United States showing the locations of five fiber-reinforced polymer pile manufacturers. Plastic Piling, Incorporated, is located in southern California; U.S. Plastic Lumber is located in Illinois; Seaward International, Incorporated., is located in Virginia; Lancaster Composite is located in Pennsylvania; and American Ecoboard is located in New York State.

Figure 9. Photo. SEAPILE composite marine piles. This figure is a colored photograph of the SEAPILE fiber-reinforced polymer composite pile in cross section. The photograph identifies and labels the components of the composite pile. The pile consists of a smooth rust-colored outer polyethylene skin, a blue-grey inner core made of recycled plastic, and blue-grey foam between the inner core and the skin. The foam is made of recycled plastic and contains 16 longitudinally oriented fiberglass rebars.

Figure 10. Graph. Stress-strain relationship of 4.4-centimeter parenthesis 1.75-inch end parenthesis fiberglass bars. This figure presents the results of the axial compression tests conducted on two fiberglass bars used to reinforce the fiber-reinforced polymer pile. The graph shows a plot of the stress-strain relationship of the fiberglass bars. The X axis is strain in units of meters per meter parenthesis zero to 0.05 end parenthesis and the Y axis is stress in kilopascals parenthesis zero to 400,000 end parenthesis. The stress-strain curve for both fiberglass bars begins at zero and increases in a directly proportional relationship to a maximum stress of 360,000 kilopascals at a strain of 0.025. Failure of the fiberglass bars occurs at 360,000 kilopascals. The lines depicting the stress-strain relationship of bars 1 and 2 decrease rapidly to about 175,000 kilopascals at a strain of about 0.032 for bar number 1 and to about 75,000 kilopascals at a strain of about 0.043 for bar number 2. For purposes of conversion, one meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 11. Photo. Fiberglass bar before axial compression test and disintegrated fiberglass parts. This figure is a color photograph of the 4.4-centimeter- parenthesis 1.75-inch- end parenthesis diameter fiberglass bar before and after completion of the axial compression test. The left side of the photograph shows the intact fiberglass bundle before the test. The right side of the photograph shows the bundle broken into three strands. As the photograph depicts, disintegration resulted from a break in the outer binding that holds together the fiberglass bundle. A ballpoint pen is included in the photograph for scale. The broken fiberglass bundles are two to three times the thickness of the pen.

Figure 12. Graph. Stress-vertical strain relationship of SEAPILE pile recycled plastic. This figure presents the results of the axial compression test conducted on the recycled plastic foam material that surrounds the fiberglass bars in the SEAPILE composite pile. The graph shows a plot of the stress-strain relationship of the foam at two different strain rates. The X axis is vertical strain in units of meters per meter parenthesis zero to 0.2 end parenthesis, and the Y axis is stress in kilopascals parenthesis zero to 14,000 end parenthesis. The stress-strain curves for the recycled plastic foam are logarithmic in shape. At a strain rate of 0.33 percent per minute, the curve begins at zero and increases logarithmically to a maximum of about 11,800 kilopascals at a vertical strain of 0.14. For a reduced strain rate of 0.083 percent per minute, the curve begins at zero and increases logarithmically to a maximum of about 8,000 kilopascals at a vertical strain of 0.12. The nonlinear nature of the curve suggests that the response to axial loading is dependent on the vertical strain rate. For purposes of conversion, 1 meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 13. Graph. Stress-radial strain relationship of SEAPILE pile recycled plastic; rate 0.33 percent per minute. This figure presents the results of the axial compression test conducted on the recycled plastic foam material that surrounds the fiberglass bars in the SEAPILE composite pile. The graph shows a plot of the stress-strain relationship of the foam at a strain rate of 0.33 percent per minute. The X axis is radial strain in units of meters per meter parenthesis zero to 0.025 end parenthesis, and the Y axis is stress in kilopascals parenthesis zero to 12,000 end parenthesis. The stress-strain curve for the recycled plastic foam is logarithmic in shape. The curve begins at zero and increases logarithmically to a maximum of about 10,000 kilopascals at a radial strain of approximately 0.023. The graph indicates that an applied stress of about 5,000 kilopascals results in a radial strain of 0.005, and an applied stress of about 7,500 kilopascals results in a radial strain of 0.01. For purposes of conversion, 1 meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 14. Graph. Force-vertical strain relationship of SEAPILE pile sample. This figure presents the results of the axial compression test conducted on an 81-centimeter- parenthesis 32-inch- end parenthesis long and 40.6-centimeter- parenthesis 16-inch- end parenthesis diameter SEAPILE composite pile sample with 16 fiberglass rebar. The graph shows a plot of the force-vertical strain relationship of the composite sample and the 16 reinforcing bars. The X axis is vertical strain in units of meters per meter parenthesis zero to 0.035 end parenthesis, and the Y axis is force in kilonewtons parenthesis zero to 10,000 end parenthesis. The force-strain curve for the composite pile is a linear relationship, which shows that the vertical strain measured is nearly directly proportional to the force applied. The line begins at zero and reaches a maximum force near 9,000 kilonewtons, at which point the composite sample reaches a brittle failure. The failure corresponds to a vertical strain of approximately 0.019. At an applied force of about 4,700 kilonewtons, the vertical strain on the composite sample corresponds to 0.01. The force-vertical strain relationship is also shown for the 16 fiberglass rebars. This relationship is linear, but not exactly directly proportional. The line begins at zero and reaches a maximum force near 9,000 kilonewtons at a strain of approximately 0.026, at which point the line turns downward to a point where the force is about 4,500 kilonewtons and the strain on the rebars is about 0.032. The graph indicates that, for the same applied force, the strain is higher on the fiberglass bars than on the composite pile sample. The graph also contains a dotted straight diagonal line that rises from left to right. The line's significance is not described on the graph or in the text. For purposes of conversion, 1 meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 15. Photo. SEAPILE pile sample after axial compression test. This figure is a color photograph of the SEAPILE composite pile sample taken after the completion of the compression test. The figure consists of a main photograph of the two longitudinal halves of the pile sample and two small insets. The longitudinal sections of the composite pile reveal that the inner core and the fiberglass rods are not damaged, and that the damage resulting from the compression test on the pile is restricted to the upper section of the recycled plastic foam. One inset photograph in the upper-left corner is a front view of the pile sample standing upright. This photograph shows the damage to the recycled foam material surrounding the core and in which are embedded the 16 fiberglass rods. The outer material has visible vertical cracks around the upper circumference. The second inset photograph in the upper-right corner is a cross section of the SEAPILE composite pile showing the undamaged core, 16 undamaged fiberglass rebar, and the recycled plastic foam surrounding the rebar. The cross section does not reveal any damage. The photograph is dated July 2, 2002.

Figure 16. Equation. Applied load F. The applied load, F, equals the product of the stress of the total section of the sample, sigma subscript c, times the cross-sectional area of the sample, A subscript c. This product, in turn, equals the sum of the product of the number of bars in the composite section, n, times the stress of the fiberglass bar, sigma subscript b, times the section area of the fiberglass bar, A subscript b, plus the product of the stress of the plastic, sigma subscript p, times the section area of the plastic, A subscript p.

Figure 17. Equation. Young's modulus E. Young's modulus, E, equals the quotient of sigma subscript b divided by Young's modulus of the bar, E subscript b. This quotient, in turn, equals two other quotients. The first is sigma subscript p divided by Young's modulus of the plastic, E subscript p. The second is sigma subscript c divided by Young's modulus of the total section of the sample, E subscript c.

Figure 18. Equation. Sigma subscript c divided by sigma subscript b. Sigma subscript c divided by sigma subscript b equals the quotient of E subscript c divided by E subscript b. This quotient, in turn, equals the sum of two terms. The first term is the product of n times the quotient of A subscript b divided by A. The second term is the product of the quotient of E subscript p divided by E subscript b times the sum of 1 minus the quotient of n times A subscript b divided by A.

Figure 19. Equation. E subscript c divided by E subscript b. E subscript c divided by E subscript b equals the sum of alpha, which is the quotient of n times A subscript b divided by A and is defined as the replacement factor, plus the product of beta, which is E subscript p divided by E subscript b, and is defined as the relative axial stiffness coefficient, times the sum of 1 minus alpha.

Figure 20. Equation. G subscript c. The equivalent shear modulus, G subscript c, equals the quotient of E subscript c divided by the product of 2 times the sum of 1 plus the Poisson's ratio value of the composite material, upsilon subscript c.

Figure 21. Equation. R subscript c divided by R subscript b. The equivalent compression strength of the composite material, R subscript c, divided by the compression strength of the recycled plastic mobilized at the failure strain of the fiberglass bar, R subscript b, equals the sum of alpha plus the product of eta, which is the compression strength ratio of the component materials, times the sum of 1 minus alpha.

Figure 22. Equation. F L F. The failure load factor, F L F, equals the quotient of F subscript c divided by the product of n, which is number of bars in the composite material, times F subscript b. FLF also equals the quotient of the product of E subscript c times A subscript c divided by the product of E subscript b times n times A subscript b. FLF also equals the sum of 1 plus the product of beta times the sum of the quotient of 1 divided by alpha minus 1.

Figure 23. Equation. Bending moment M. Bending moment, M, divided by the second derivative of the displacement variation with depth, y double prime, equals the product of E subscript c times I subscript c. That product in turn equals the sum of the product of E subscript p times I subscript p plus the product of E subscript b times the summation of I subscript b times the sum of 1 minus the quotient of E subscript p divided by E subscript b.

Figure 24. Equation. Moment of inertia I subscript c parenthesis 1 end parenthesis. I subscript c equals the product of the quotient of E subscript b divided by E subscript c times the sum of the following: the product of the quotient of E subscript p divided by E subscript b times I subscript p, plus the product of the summation of I subscript b times the sum of 1 minus the quotient of E subscript p divided by E subscript b.

Figure 25. Equation. Moment of inertia I subscript c parenthesis 2 end parenthesis. I subscript c equals the product of the quotient of E subscript b divided by E subscript c times the sum of the following: the product of beta times I subscript p plus the product of the summation of I subscript b times the sum of 1 minus beta.

Figure 26. Equation. Relative inertia moment coefficient lambda. The relative inertia moment coefficient lambda equals I subscript p divided by the summation of I subscript b.

Figure 27. Equation. I subscript c divided by the summation of I subscript b. I subscript c divided by the summation of I subscript b equals the quotient of the sum of 1 plus the product of beta times the sum of lambda minus 1, divided by the sum of alpha plus the product of beta times the sum of 1 minus alpha.

Figure 28. Equation. Critical buckling force P subscript c r. The critical buckling force, P subscript c r, equals the quotient of the product of pie squared times Young's modulus, E, times the moment of inertia, I, divided by the square of the length of the bar, l.

Figure 29. Equation. P subscript c c of axially loaded bar. P subscript c r equals the equivalent critical buckling load calculated for the composite material according to Euler's equation, P subscript c r superscript o, divided by the sum of 1 plus the quotient of P subscript c r superscript o divided by the product of G subscript c times A.

Figure 30. Equation. Equivalent critical buckling load for composite material. P subscript c r superscript o equals the quotient of the product of pie squared times E subscript c times I subscript c, divided by the square of the length of the bar, l.

Figure 31. Equation. Critical buckling load factor B L F. The critical buckling load factor, B L F, equals the quotient of P subscript c r superscript c divided by the summation of P subscript c r superscript b. That quotient, in turn, equals the product of three quotients. The first quotient is E subscript c divided by E subscript b. The second quotient is I subscript c divided by the product of n times I subscript b. The third quotient is 1 divided by the sum of 1 plus the quotient of P subscript c r superscript o divided by the product of G subscript c times A.

Figure 32. Equation. Critical buckling load decomposed. P subscript c r superscript c divided by the sum of P subscript c r superscript b equals the product of lambda subscript o and two terms. The first term is the sum of alpha plus the product of beta times the sum of 1 minus alpha. The second term is 1 divided by the sum of 1 plus the quotient of P subscript c r superscript o divided by the product of G subscript c times A.

Figure 33. Graph. Buckling force versus length for SEAPILE pile sample and 16 fiberglass bars. This figure presents the relationship between the critical buckling load and the lengths of the SEAPILE composite pile sample, and the group of 16 fiberglass rebar. The X axis is length in centimeters parenthesis zero to 350 end parenthesis and the Y axis is force in kilonewtons parenthesis zero to 200,000 end parenthesis. This graph shows that the critical bucking load varies with the length of the composite sample and with the length of the fiberglass rods. For the 16 fiberglass rods, the buckling load-length relationship is shown as a descending curve. The line descends sharply to approximately 25 centimeters at approximately18,000 kilonewtons, at which point it flattens, reaching approximately 0.0 kilonewtons at 50 centimeters. The force-length curve for the composite material is also an inverse relationship, but its descent is more gradual. At approximately 108,000 kilonewtons, the X axis reading is approximately 25 centimeters. The chart also shows a line for the compressive strength, which is uniform and depicted as a straight line, parallel to the X axis, at about 10,000 kilonewtons. The plastic effect is also labeled on the chart as the difference between the buckling force-length relationship curves for the 16 fiberglass bars and the composite material. For purposes of conversion, one centimeter equals 0.39 inch, and 1 kilonewton equals 224.7 poundsforce.

Figure 34. Photo. Plastic Piling, Incorporated, pile. This figure is a color photograph showing a cross section of a recycled plastic pile manufactured by Plastic Piling, Incorporated. The cross section of the pile, 38.7 centimeters parenthesis 15.25 inches end parenthesis in diameter, shows 16 steel reinforcing rods, each 2.54 centimeters parenthesis 1.0 inch end parenthesis in diameter, embedded in a circular arrangement near the circumference of the recycled plastic pile.

Figure 35. Graph. Plastic Piling, Incorporated, pile-stress-strain relationship. This figure presents the results of the axial compression test conducted on the steel-reinforced Plastic Piling, Incorporated, recycled plastic pile. The graph shows a curve of the stress-strain relationship of the pile. The X axis is strain in units of meters per meter parenthesis zero to 0.05 end parenthesis, and the Y axis is stress in kilopascals parenthesis zero to 50,000 end parenthesis. The stress-strain curve for the recycled plastic pile has three distinct components. Initially, the curve is steep, reaching 30,000 kilopascals before the strain reaches 0.005. Between 30,000 and 45,000 kilopascals, the stress-strain curve is less steep and corresponds to a wide strain range between 0.005 and 0.035. A peak occurs at 45,000 kilopascals, and the third part of the curve is a decline to about 32,000 kilopascals. For purposes of conversion, 1 meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 36. Photo. Trimax pile. This figure is a color photograph showing three lengths of Trimax structural plastic lumber material resting on wood pallets. The cylindrical piles are solid recycled plastic with no visible reinforcing bars or rods.

Figure 37. Graph. Trimax pile-vertical stress-strain curves at different rates. This figure presents the results of vertical compression tests conducted on the Trimax recycled plastic pile. The graph shows plots of the stress-strain relationships of the material at five different strain rates. The X axis is vertical strain in units of meters per meter parenthesis zero to 0.2 end parenthesis, and the Y axis is stress in kilopascals parenthesis zero to 9,000 end parenthesis. The stress-strain curves for the recycled material are all logarithmic in shape. Curves are shown for the following five strain rates: 0.036 percent per minute, 0.083 percent per minute, 0.167 percent per minute, 0.33 percent per minute, and 1.66 percent per minute. At the lowest strain rate, the curve levels off near 6,000 kilopascals, with a corresponding strain of about 0.1. At the highest strain rate, the curve reaches a maximum of about 8,500 kilopascals, with a corresponding strain of about 0.11. The vertical stress-strain curves suggest that the response of the Trimax recycled plastic material to axial loading is dependent on the strain rate. One kilopascal equals 0.145 poundforce per square inch.

Figure 38. Graph. Trimax pile-vertical stress-lateral strain curve; strain rate 0.33 percent per minute. This figure presents the results of the axial compression test conducted on the Trimax recycled plastic pile. The graph shows a plot of the stress-strain relationship of the plastic at a strain rate of 0.33 percent per minute. The X axis is radial strain in units of meters per meter parenthesis zero to 0.14 end parenthesis, and the Y axis is stress in kilopascals parenthesis zero to 8,000 end parenthesis. The stress-strain curve for the recycled plastic is logarithmic in shape. The curve begins at zero and increases logarithmically to a maximum of about 7,000 kilopascals, which corresponds to a radial strain of approximately 0.125. The graph indicates that an applied stress of about 4,000 kilopascals results in a radial strain of 0.015 and an applied stress of about 6,000 kilopascals results in a radial strain of 0.06. For purposes of conversion, 1 meter equals 1.09 yards, and 1 kilopascal equals 0.145 poundforce per square inch.

Figure 39. Photo. Port of Elizabeth demonstration site. This figure is a color photograph of the location where the full-scale loading tests were conducted to evaluate the behavior of fiber-reinforced polymer composite piles under vertical loads. The demonstration site is located at the Port of Elizabeth in New Jersey, a facility provided by the Port Authority of New York and New Jersey. The photograph shows 10 composite pile samples in the foreground and testing equipment in the background.

Figure 40. Photo. Equipment used in the in-load tests. Companion to figure 41. This figure is a color photograph of the laboratory setup used to conduct load tests to evaluate the behavior of the composite pile materials under vertical loads. The photograph shows many of the components identified in the figure 41 schematic, including the test frame and, from top to bottom, the dead load, steel beam, load cell, hydraulic jack, and steel frame connected to the test pile.

Figure 41. Illustration. Schematic of the equipment used in the in-load tests. Companion to figure 40. This figure is a line drawing that illustrates the components of the laboratory setup used to conduct load tests to evaluate the behavior of the composite pile materials under vertical loads. The illustration shows two horizontal steel beams with the dead load at the top. Below the steel beam and above the swivel plate are the loading plate and the load cell. This assembly is followed by a hydraulic jack, another steel plate, and the upper section of the test pile. Further down the test pile is a steel frame connected to the pile. On either side of the test pile, horizontally in line with the steel frame connected to the pile, is a reference beam. Above the reference beams, on opposites sides of the test pile, are two linear variable differential transformers. Below the steel frame, the pile extends into the ground.

Figure 42. Illustration. Data acquisition system. This figure is a schematic line drawing of the test pile fitted with monitoring gauges and of the system used to collect data for online monitoring during the tests. About 90 percent of the pile is shown below the ground surface. The water table is identified at 1.7 meters parenthesis 5.5 feet end parenthesis below the surface. The general soil profile is identified as 4.6 meters parenthesis 15 feet end parenthesis of fill material, followed by 2.1 meters parenthesis 6.9 feet end parenthesis of soft clay, followed by 5.5 meters parenthesis 18 feet end parenthesis of sand; below the sand, the soil is labeled "clay." The data acquisition system shown in the schematic consists of a variety of components. Attached to the test pile are three pairs of strain gauges. Two gauges are located at a depth near the water table, two gauges are located in the middle of the sand layer, and two gauges are located near the bottom of the pile in the clay layer. The signal from the strain gauges travels up to the Model 8032 Multiplexer and is transferred to the Model 8020 Datalogger. From there, the data go to a laptop computer. Power is provided by a 110-volt power supply. At the top of the test pile are four linear variable differential transformers. A plus or minus 15-volt power supply is connected to the linear variable differential transformers. Signals from the linear variable differential transformers are routed to two terminal block Multiplexers parenthesis 777687-22 end parenthesis, then to two Multiplexer cards parenthesis 776570-22 end parenthesis, then to the slot chassis box parenthesis 776570-01 end parenthesis, then to the D A Q Card parenthesis 777231-01 end parenthesis, and finally to the laptop computer.

Figure 43. Photo. Strain gauges installation in pile of Lancaster Composite, Incorporated. This figure is a color photograph of two vibrating wire strain gauges that were installed in the test piles. The gauges consist of wired tubes the length of the test pile, and steel spacer assemblies attached to the top of the gauges. Three inset photographs show the steps involved before the strain gauges are enclosed in the test pile. They show the strain gauge wires being inserted into hollow fiberglass tubing, the assembled gauges and tubed wires, and the assembled gauges and tubed wires in the test pile tubular shell before casting.

Figure 44. Photo. Vibrating and foil strain gauges attached to steel cage in Plastic Piling, Incorporated, pile. This figure is a color photograph of the tubular steel cage assembly, consisting of 16 reinforcing steel bars welded to a spiral reinforcing cage, before the polymer is added. Also shown in the photograph is the steel mold pipe for casting the plastic pile. Two inset photographs show a longitudinal view of the steel cage assembly with the attached strain gauges and a cross-sectional view of the steel mold pipe containing the steel bar cage assembly.

Figure 45. Photo. Vibrating and foil strain gauges attached to SEAPILE composite marine pile. This figure is a colored photograph of the SEAPILE fiber-reinforced polymer composite pile showing the end of the pile as well as its length. The photograph shows the blue-grey recycled plastic core and the 16 longitudinally oriented fiberglass rebar. A vibrating wire strain gauge is shown attached to the shell of the pile. An inset photograph shows the attachment of a strain gauge to one of the exposed fiberglass rebar.

Figure 46. Illustration. Schematic drawing of Port Elizabeth site. This figure is a schematic grid of the layout of test piles at the Port Elizabeth testing site. The grid shows the locations of 12 test piles and 2 soil borings. Horizontally from the top left of the plot is the location of pile number 11. Six meters parenthesis 19.7 feet end parenthesis to the right of pile number 11 is a set of four piles, numbers 8, 5, 2, and 1, each 3 meters parenthesis 9.8 feet end parenthesis apart. All of the piles in this top row, except for pile number 1, contain no instrumentation. Pile number 1 is a steel pipe pile. In the second row from the top of the plot, 2 meters parenthesis 6.6 feet end parenthesis down from the first row of piles, are four piles and soil boring number 1. Pile number 12, containing no instrumentation, is vertically aligned with the center of pile number 11. Six meters parenthesis 19.7 feet end parenthesis to the right of pile number 12 is a set of three piles, numbers 9, 6, and 3, each located 3 meters parenthesis 9.8 feet end parenthesis apart and their centers vertically aligned with piles 8, 5, and 2 in the row above. Pile numbers 9 and 6 contain several strain gauge instruments at several depths. Pile number 3 contains two strain gauge instruments at one depth. To the far right of the second row, vertically aligned with the center of pile number 1 above, is soil boring number 1. In the third row from the top, 2 meters parenthesis 6.6 feet end parenthesis down from the second row of piles, is a soil boring and a set of three piles. Soil boring number 2 is vertically aligned with the center of pile number 12 above. Six meters parenthesis 19.7 feet end parenthesis to the right of soil boring number 2 is a set of three piles, numbers 10, 7, and 4, each located 3 meters parenthesis 9.8 feet end parenthesis apart and their centers vertically aligned with piles 9, 6, and 3 in the above row. Pile numbers 10, 7, and 4 each contain two strain gauge instruments at one depth.

Figure 47. Graph. Lancaster pile-settlement-time relationship. This figure is a graph presenting data relating settlement of the Lancaster pile over time. The X axis is time in minutes parenthesis zero to 1,200 end parenthesis, and the Y axis is settlement in centimeters, descending from zero to 2 parenthesis zero to 0.79 inch end parenthesis. The plot for the Lancaster pile has two distinct components that correspond to the loading cycles. The overall trend shown on the chart is a generally linear relationship of increasing settlement with increasing time; increasing settlement means the plot is generally descending from left to right. The plot consists of a series of small steps, each representing loading increments of 10 metric tons. Between zero and 200 minutes, the pile settlement is 0.2 centimeter parenthesis 0.08 inch end parenthesis. At approximately 500 minutes, the settlement is approximately 0.8 centimeter parenthesis 0.31 inch end parenthesis, which corresponds to a total cumulative load of 100 metric metric tons. At this point, the plot rises, meaning the settlement decreases, in four small steps, representing the unloading of the pile in 25-ton increments. The second loading cycle is similar to the first, but the steps are less defined. At the end of the second cycle at approximately 960 minutes, with a load of 128 metric tons, the total cumulative settlement is about 1.7 centimeters parenthesis 0.67 inch end parenthesis.

Figure 48. Graph. Plastic Piling, Incorporated, pile-settlement-time relationship. This figure is a graph presenting data relating settlement of the Plastic Piling, Incorporated, pile over time. The X axis is time in minutes parenthesis zero to 800 end parenthesis and the Y axis is settlement in centimeters, descending from zero to 3.5 parenthesis or zero to 1.4 inches end parenthesis. The plot for the Plastic Piling, Incorporated, pile has two distinct components that correspond to the loading cycles. The overall trend shown on the chart is increasing settlement with an increase in time; increasing settlement means the plot is generally descending from left to right. The plot consists of a series of small steps, each representing loading increments of 10 metric tons. Between zero and 200 minutes, the pile settlement is 0.5 centimeter parenthesis 0.2 inch end parenthesis. At approximately 275 minutes, the settlement is approximately 0.75 centimeter parenthesis 0.29 inch end parenthesis, which corresponds to a total cumulative load of 100 metric tons. At this point, the plot rises, meaning the settlement decreases, in four steps, representing the unloading of the pile in 25-ton increments. The second loading cycle is similar to the first, but the 10-ton-increment steps are less defined. At the end of the second cycle at approximately 610 minutes, with a load of 115 metric tons, the total cumulative settlement is about 1.6 centimeters parenthesis 0.63 inch end parenthesis.

Figure 49. Graph. SEAPILE pile-settlement-time relationship. This figure is a graph presenting data relating settlement of the SEAPILE pile over time. The X axis is time in minutes parenthesis zero to 450 end parenthesis, and the Y axis is settlement in centimeters, descending from zero to 3.5 parenthesis zero to 1.4 inches end parenthesis. The plot for the SEAPILE pile indicates one loading cycle. The overall trend shown on the chart is an increase in settlement with an increase in time; increasing settlement means the plot is generally descending from left to right. The plot consists of a series of small steps, each representing loading increments of 10 metric tons. Between zero and 125 minutes, the pile settlement is 0.5 centimeter parenthesis 0.2 inch end parenthesis. At approximately 275 minutes, the settlement is approximately 1.2 centimeters parenthesis 0.47 inch end parenthesis, which corresponds to a total cumulative load of 90 metric tons. At this point, the plot falls rapidly, which is an increase in settlement, to 3 centimeters parenthesis 1.2 inches end parenthesis at approximately 310 minutes. This is followed by stepwise decreases in settlement, or a rising plot, representing unloading of the pile in 25-ton increments.

Figure 50. Graph. American Ecoboard pile-settlement-time relationship. This figure is a graph presenting data relating settlement of the American Ecoboard pile over time. The X axis is time in minutes parenthesis zero to 1000 end parenthesis and the Y axis is settlement in centimeters, descending from zero to 10 parenthesis zero to 3.9 inches end parenthesis. The plot for the Ecoboard pile indicates one loading cycle. The overall trend shown on the chart is an increase in settlement with an increase in time; increasing settlement means that the plot is generally descending from left to right. The plot consists of a series of small steps, each representing loading increments of 10 metric tons. Between zero and about 210 minutes, the pile settlement is 2 centimeters parenthesis 0.79 inch end parenthesis. At approximately 680 minutes, the settlement is approximately 9.3 centimeters parenthesis 3.7 inches end parenthesis. At this point, the plot rises, showing a stepwise decrease in settlement apparently due to unloading, reaching approximately 3.6 centimeters parenthesis 1.4 inches end parenthesis at approximately 750 minutes.

Figure 51. Equation. Settlement, S. Settlement, S, equals the sum of three terms. The first is 0.004 meters. The second is the quotient of the pile diameter, D, in meters, divided by 120. The third is the settlement due to the elastic compression of a free-standing pile column, S subscript e l.

Figure 52. Graph. Lancaster Composite pile-Davisson criteria and measured load-settlement curve. This figure presents measured and calculated plots for load versus pile settlement for the Lancaster Composite pile. The measured data are from static load tests. The X axis is load parenthesis zero to 140 metric tons force parenthesis zero to 308 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 2 centimeters parenthesis zero to 0.79 inch end parenthesis. Plots are presented for two loading cycles, for the Davisson criteria and for the Davisson unloading-reloading slope. The plot for cycle 1 descends almost linearly and shows that the settlement increases with the increasing load to the pile. Under a load of 20 metric tons force parenthesis 44 kips end parenthesis, the pile settlement is about 0.05 centimeter parenthesis 0.02 inch end parenthesis. With a load of 50 metric tons force parenthesis 110 kips end parenthesis, the settlement increases to 0.2 centimeter parenthesis 0.08 inch end parenthesis. At the maximum load of 100 metric tons force parenthesis 220 kips end parenthesis, the pile settlement is approximately 0.75 centimeters parenthesis 0.29 inch end parenthesis. As the load is reduced, the plot rises to the left, reaching a settlement of 0.4 centimeters parenthesis 0.16 inch end parenthesis at zero metric tons force parenthesis zero kips end parenthesis. Cycle 2 begins at this point. When the plot for cycle 2 reaches a load of about 75 metric tons force parenthesis 165 kips end parenthesis, the settlement is approximately 0.7 centimeters parenthesis 0.28 inch end parenthesis. At 100 metric tons force parenthesis 220 kips end parenthesis and 0.8 centimeter parenthesis 0.32 inch end parenthesis, the cycle 2 plot begins descending more sharply. At the maximum load during cycle 2 of about 130 metric tons force parenthesis 286 kips end parenthesis, settlement of the Lancaster pile is 1.75 centimeters parenthesis 0.69 inch end parenthesis. As the cycle 2 load is reduced, the plot rises to the left, reaching a settlement of 1.2 centimeters parenthesis 0.47 inch end parenthesis at zero metric tons force parenthesis zero kips end parenthesis. The Davisson criteria plot is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to 1.38 centimeters parenthesis 0.54 inch end parenthesis at a load of 130 metric tons force parenthesis 286 kips end parenthesis. The plot of the Davisson unloading-reloading slope is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to 1.25 centimeters parenthesis 0.49 inch end parenthesis at a load of 130 metric tons force parenthesis 286 kips end parenthesis. The Davisson unloading-reloading plot intersects the cycle 2 curve at a load of 119 metric tons force parenthesis 262 kips end parenthesis and a settlement of approximately 1.25 centimeters parenthesis 0.49 inch end parenthesis. The Davisson criteria plot intersects the cycle 2 curve at a load of 122 metric tons force parenthesis 268 kips end parenthesis and a settlement of approximately 1.3 centimeters parenthesis 0.51 inch end parenthesis.

Figure 53. Graph. Plastic Piling, Incorporated, pile-Davisson criteria and measured load-settlement curve. This figure presents measured and calculated plots for load versus pile settlement curves for the Plastic Piling, Incorporated, pile. The measured data are from static load tests. The X axis is load parenthesis zero to 140 metric tons parenthesis zero to 308 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 4 centimeters parenthesis zero to 1.6 inches end parenthesis. Plots are presented for two loading cycles, for the Davisson criteria and for the Davisson unloading-reloading slope. The plot for cycle 1 descends almost linearly and shows that the settlement increases with the increasing load to the pile. Under a load of 30 metric tons force parenthesis 66 kips end parenthesis, the pile settlement is approximately 0.2 centimeter parenthesis 0.08 inch end parenthesis. With a load of 60 metric tons force parenthesis 132 kips end parenthesis, the settlement increases to 0.45 centimeter parenthesis 0.18 inch end parenthesis. At a load of 100 metric tons force parenthesis 220 kips end parenthesis, the pile settlement is approximately 0.75 centimeter parenthesis 0.29 inch end parenthesis. At 110 metric tons force parenthesis 242 kips end parenthesis and 0.9 centimeter parenthesis 0.35 inch end parenthesis, the cycle 1 plot begins descending more sharply. At the maximum load during cycle 1 of 120 metric tons force parenthesis 264 kips end parenthesis, the settlement of the pile is 3 centimeters parenthesis 1.17 inches end parenthesis. As the cycle 1 load is reduced, the plot rises to the left, reaching a settlement of 2.25 centimeters parenthesis 0.88 inch end parenthesis at zero metric tons force parenthesis zero kips end parenthesis. For cycle 2 with no load, the curve begins at zero centimeters parenthesis zero inches end parenthesis. Under a load of 40 metric tons force parenthesis 88 kips end parenthesis, the settlement is approximately 0.2 centimeter parenthesis 0.08 inch end parenthesis, and with a maximum load of 100 metric tons force parenthesis 220 kips end parenthesis, settlement is approximately 0.75 centimeter parenthesis 0.29 inch end parenthesis. As the cycle 2 load is reduced, the plot rises to the left, reaching 0.1 centimeter parenthesis 0.39 inch end parenthesis. The Davisson criteria plot is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to 3.4 centimeters parenthesis 1.3 inches end parenthesis at a load of 120 metric tons force parenthesis 264 kips end parenthesis. The plot of the Davisson unloading-reloading slope is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to 1.5 centimeters parenthesis 0.59 inch end parenthesis at a load of 120 metric tons force parenthesis 264 kips end parenthesis. The Davisson unloading-reloading slope intersects the cycle 1 plot at a load of 114 metric tons force parenthesis 251 kips end parenthesis and a settlement of approximately 1.5 centimeters parenthesis 0.59 inch end parenthesis, and the Davisson criteria plot intersects the cycle 2 plot at a load of 100 metric tons force parenthesis 220 kips end parenthesis and a settlement of approximately 2.9 centimeters parenthesis 1.13 inches end parenthesis.

Figure 54. Graph. SEAPILE pile-Davisson criteria and measured load-settlement curve. This figure presents measured and calculated plots for load versus pile settlement for the SEAPILE pile. The measured data are from static load tests. The X axis is load parenthesis zero to 120 metric tons force parenthesis zero to 264 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 6 centimeters parenthesis zero to 2.4 inches end parenthesis. Plots are presented for the static load test, for the Davisson criteria, and for the Davisson unloading-reloading slope. The plot for the static load test is nearly linear and shows that the settlement increases with the increasing load to the pile. Under a load of 50 metric tons force parenthesis 110 kips end parenthesis, the pile settlement is about 0.5 centimeter parenthesis 0.2 inch end parenthesis. With a load of 80 metric tons force parenthesis 176 kips end parenthesis, the settlement is approximately 1 centimeter parenthesis 0.39 inch end parenthesis. At this point, the plot begins to descend more sharply, reaching 3.0 centimeters parenthesis 1.17 inches end parenthesis in settlement under a load of approximately 90 metric tons force parenthesis 198 kips end parenthesis. As the load is reduced, the plot rises to the left, reaching a settlement of approximately 2.1 centimeters parenthesis 0.82 inch end parenthesis at a load of zero. The Davisson criteria plot is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to 5 centimeters parenthesis 2 inches end parenthesis under a load of 100 metric tons force parenthesis 220 kips end parenthesis. The plot of the Davisson unloading-reloading slope is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis at a load of zero to approximately 1.8 centimeters parenthesis 0.71 inch end parenthesis under a load of 90 metric tons force parenthesis 198 kips end parenthesis. The Davisson unloading-reloading slope intersects the static load test plot at a load of 85 metric tons force parenthesis 187 kips end parenthesis and a settlement of approximately 1.75 centimeters parenthesis 0.68 inch end parenthesis. The Davisson criteria plot intersects the static load test curve at a load of approximately 50 metric tons force parenthesis 110 kips end parenthesis and a settlement of approximately 2.8 centimeters parenthesis 1.1 inches end parenthesis.

Figure 55. Graph. American Ecoboard pile-Davisson criteria and measured load-settlement curve. This figure presents measured and calculated plots for load versus pile settlement for the American Ecoboard pile. The measured data are from static load tests. The X axis is load parenthesis zero to 70 metric tons force parenthesis zero to 154 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 12 centimeters parenthesis zero to 4.7 inches end parenthesis. Plots are presented for the static load test, for the Davisson criteria, and for the Davisson unloading-reloading slope. The plot for the static load test is nearly linear and shows that the settlement increases with the increasing load to the pile. Under a load of 20 metric tons force parenthesis 44 kips end parenthesis, the pile settlement is about 1.2 centimeters parenthesis 0.47 inch end parenthesis. With a load of 40 metric tons force parenthesis 88 kips end parenthesis, the settlement is approximately 4.2 centimeters parenthesis 1.6 inches end parenthesis. With a load of 60 metric tons force parenthesis 132 kips end parenthesis, the settlement is approximately 9.4 centimeters parenthesis 3.7 inches end parenthesis. At this point, the load is reduced and the plot rises to the left, reaching a settlement of approximately 2.9 centimeters parenthesis 1.13 inches end parenthesis at a load of zero. The Davisson criteria plot is linear, descending from 0.75 centimeter parenthesis 0.29 inch end parenthesis under zero load to approximately 7.5 centimeters parenthesis 2.9 inches end parenthesis under a load of 55 metric tons force parenthesis 121 kips end parenthesis. The plot of the unloading-reloading slope is linear, descending from approximately 3.5 centimeters parenthesis 1.4 inches end parenthesis under zero load to approximately 10 centimeters parenthesis 3.9 inches end parenthesis under a load of 55 metric tons force parenthesis 121 kips end parenthesis. The unloading-reloading slope intersects the static load test curve at a load of 50 metric tons force parenthesis 110 kips end parenthesis and a settlement of approximately 9.4 centimeters parenthesis 3.7 inches end parenthesis. The Davisson criteria plot intersects the static load test curve at a load of 50 metric tons force parenthesis 110 kips end parenthesis and a settlement of approximately 6.7 centimeters parenthesis 2.6 inches end parenthesis.

Figure 56. DeBeer criterion plotted for fiber-reinforced polymer piles. This figure presents the load-settlement curves for the fiber-reinforced polymer piles plotted on a log-log scale. The purpose of the plots is to determine the DeBeer ultimate, or yield, loads. The X axis is load from 1 to 1000 metric tons force parenthesis 2.2 to 2,200 kips end parenthesis on a log scale. The Y axis is pile settlement descending from 0.01 to 10 centimeters parenthesis 0.004 to 3.9 inches end parenthesis on a log scale. The plots for all four fiber-reinforced polymer pile types are roughly similar in shape. The Lancaster pile is the uppermost plot, a diagonal line from the upper left to the lower right of the chart. Below the plot for the Lancaster pile are the plots for the Plastic Piling, Incorporated, pile, the SEAPILE pile, and the American Ecoboard pile. The load that corresponds to the point on each plot where the slope changes is the DeBeer ultimate, or yield, load. For the Lancaster pile and the Plastic Piling, Incorporated, pile, this point is 110 metric tons force parenthesis 242 kips end parenthesis. For the SEAPILE pile, the ultimate, or yield, load is 80 metric tons force parenthesis 176 kips end parenthesis. The ultimate, or yield, load for the American Ecoboard pile cannot be determined because the slope does not change.

Figure 57. Graph. Chin-Kondner method plotted for fiber-reinforced polymer piles. This figure presents plots of the relationship between the settlement and the pile top settlement divided by the load for the Lancaster, SEAPILE, and Plastic Piling, Incorporated, piles. The purpose is to determine the ultimate loads for three fiber-reinforced polymer piles. The X axis is the settlement from zero to 3.5 centimeters parenthesis zero to 1.4 inches end parenthesis, and the Y axis is the settlement divided by the load descending from zero to 0.035 centimeters per metric ton force parenthesis zero to 0.0063 inch per kip end parenthesis. The plots for the three piles are nearly straight lines. The plot for the Lancaster pile is the uppermost, diagonal line from the upper left to the lower right. The plot begins at approximately 0.1 centimeter parenthesis 0.004 inch end parenthesis, corresponding to a settlement-over-load value of approximately 0.0025 centimeter per metric ton force parenthesis 0.00045 inch per kip end parenthesis, and ends at approximately 1.75 centimeters parenthesis 0.69 inch end parenthesis, corresponding to a settlement-over-load value of approximately 0.013 centimeter per metric ton force parenthesis 0.0023 inch per kip end parenthesis. Below and nearly parallel to the plot of the Lancaster pile is the plot of the Plastic Piling, Incorporated, pile. The plot begins at approximately 0.1 centimeter parenthesis 0.004 inch end parenthesis, corresponding to a settlement-over-load value of approximately 0.005 centimeter per metric ton force parenthesis 0.0009 inch per kip end parenthesis, and ends at 3 centimeters parenthesis 1.2 inches end parenthesis, corresponding to a settlement-over-load value of approximately 0.025 centimeter per metric ton force parenthesis 0.0045 inch per kip end parenthesis. Below the Plastic Piling, Incorporated, plot and nearly parallel to it, the plot for the SEAPILE pile begins at approximately 0.05 centimeter parenthesis 0.02 inch end parenthesis, corresponding to a settlement-over-load value of approximately 0.007 centimeter per metric ton force parenthesis 0.0013 inch per kip end parenthesis, and ends at 3 centimeters parenthesis 1.2 inches end parenthesis, corresponding to a settlement-over-load value of approximately 0.034 centimeter per metric ton force parenthesis 0.0061 inch per kip end parenthesis.

Figure 58. Graph. Chin-Kondner method plotted for American Ecoboard pile. This figure presents the plot of the relationship between the settlement and the pile top settlement divided by the load for the American Ecoboard pile. The X axis is the settlement from zero to 10 centimeters parenthesis zero to 3.9 inches end parenthesis, and the Y axis is the settlement divided by the load descending from zero to 0.18 centimeter per metric ton force parenthesis zero to 0.032 inch per kip end parenthesis. The plot for the Ecoboard pile is, roughly, a falling exponential function. The first five data points occur between settlement values of zero and 0.5 centimeter parenthesis zero and 0.2 inch end parenthesis, corresponding to settlement-over-load values between 0.02 and 0.055 centimeter per metric ton force parenthesis 0.0036 and 0.0099 inch per kip end parenthesis. At this point, the slope flattens, eventually reaching a settlement value of 9.5 centimeters parenthesis 3.7 inches end parenthesis and a settlement-over-load value of 0.158 centimeter per metric ton force parenthesis 0.028 inch per kip end parenthesis.

Figure 59. Equation. Ultimate load capacity P subscript u c. The ultimate load capacity, P subscript u c, equals the sum of three terms. The first is the summation of the product of the ultimate shaft friction resistance in compression parenthesis over the entire embedded length of the pile shaft end parenthesis, f subscript s, times the pile perimeter, C, times the length of the pile in a specific soil layer or sublayer, d z. The second term is the product of the ultimate base pressure in compression, f subscript b, times the cross-sectional area of the pile base, A subscript b. The third term is the negative value of the weight of the pile, W subscript p.

Figure 60. Equation. Ultimate shaft friction in compression f subscript s. The ultimate shaft friction in compression, f subscript s, equals the product of the adhesion factor, alpha, times the undrained shear strength, s subscript u.

Figure 61. Equation. Ultimate end bearing resistance f subscript b. The ultimate end bearing resistance, f subscript b, equals the product of the bearing capacity factor, N subscript c, times s subscript u.

Figure 62. Equation. Relationship between f subscript s and in situ stresses. The ultimate shaft friction in compression, f subscript s, equals the product of the lateral stress coefficient, K subscript s, times the effective vertical stress at the level of point under consideration, sigma prime subscript v, times the tangent of delta, the pile-soil friction angle.

Figure 63. Equation. Empirical correlations for shaft friction. The shaft friction, f subscript s, equals the sum of the empirical coefficient A subscript N plus the product of the empirical coefficient B subscript N times N.

Figure 64. Equation. Empirical correlation for end bearing resistance. The end bearing resistance, f subscript b, equals the product of the empirical factor C subscript N times the average standard penetration test blow count within the effective depth of influence below the pile base, N subscript b.

Figure 65. Graph. Plastic Piling, Incorporated, pile, measured loads versus depth. For the Plastic Piling, Incorporated, pile, this figure is a graph of the relationship between the measured load and depth. The X axis is load in metric tons force and ranges from zero to 140 parenthesis zero to 308 kips end parenthesis. The Y axis is depth in meters and descends from zero to 20 parenthesis zero to 65.6 feet end parenthesis. Fifteen lines are plotted on the graph. Twelve are blue and indicate pile loading. Three are red and indicate pile unloading. The 15 plots are logarithmic in shape, the left-most plot being just barely logarithmic and the right-most plot being the most logarithmic. The left, or bottom, termination point for each of the 15 plots is at a load of zero metric tons force and a depth of approximately 19.5 meters parenthesis 64.0 feet end parenthesis. The left-most plot rises, just barely logarithmically, to a depth of zero meters and a load of approximately 14 metric tons force parenthesis 30.8 kips end parenthesis. The right-most plot rises, in a more pronounced logarithmic fashion, to a depth of zero meters and a load of approximately 115 metric tons force parenthesis 253 kips end parenthesis.

Figure 66. Graph. SEAPILE pile, measured loads versus depth. For the SEAPILE pile, this figure is a graph of the relationship between the measured load and depth. The X axis is load in metric tons force and ranges from zero to 100 parenthesis zero to 220 kips end parenthesis. The Y axis is depth in meters and descends from zero to 20 parenthesis zero to 65.6 feet end parenthesis. Eleven lines are plotted on the graph. Eight are blue and indicate pile loading. Three are red and indicate pile unloading. The 11 plots are logarithmic in shape, the left-most plot being just barely logarithmic and the right-most plot being the most logarithmic. The left, or bottom, termination point for each of the 11 plots is at a load of zero metric tons force and a depth of approximately 19 meters parenthesis 62 feet end parenthesis. The left-most plot rises, just barely logarithmically, to a depth of zero meters and a load of approximately 15 metric tons force parenthesis 33 kips end parenthesis. The right-most plot rises, in a more pronounced logarithmic fashion, to a depth of zero meters and a load of approximately 90 metric tons force parenthesis 198 kips end parenthesis.

Figure 67. Graph. Lancaster Composite, Incorporated, pile, measured loads versus depth. For the Lancaster Composite, Incorporated, pile, this figure is a graph of the relationship between the measured load and depth. The X axis is load in metric tons force and ranges from zero to 140 parenthesis zero to 308 kips end parenthesis. The Y axis is depth in meters and descends from zero to 20 parenthesis zero to 65.6 feet end parenthesis. Seventeen lines are plotted on the graph. Thirteen are blue and indicate pile loading. Four are red and indicate pile unloading. The 17 plots depict linear, or straight-line, relationships. The left, or bottom, termination point for each of the 17 plots is at a depth of approximately 19.5 meters parenthesis 64.0 feet end parenthesis and within a load range from zero to approximately 13 metric tons force parenthesis zero to 28.6 kips end parenthesis. The left-most plot rises to a depth of zero meters and a load of approximately 5 metric tons force parenthesis 11 kips end parenthesis. The right-most plot rises to a depth of zero meters and a load of approximately 130 metric tons force parenthesis 286 kips end parenthesis.

Figure 68. Photo. Plastic Piling, Incorporated, pile. This figure consists of two color photographs of the Plastic Piling, Incorporated, pile: parenthesis a end parenthesis before and parenthesis b end parenthesis after driving. The first photograph, on the left, is a cross section of the recycled plastic pile manufactured by Plastic Piling, Incorporated The cross section of the pile shows 16 steel reinforcing rods embedded in a circular arrangement near the circumference of the recycled plastic pile. The second photograph, on the right, shows the condition of the top of the Plastic Piling, Incorporated, pile after driving during the installation. The top of this pile reveals degradation of the plastic material containing the steel rebar.

Figure 69. Photo. SEAPILE pile. This figure consists of two color photographs of the SEAPILE pile: parenthesis a end parenthesis before and parenthesis b end parenthesis after driving. The first photograph, on the left, is a cross section of the recycled plastic pile manufactured by SEAPILE. The cross section of the pile shows 16 fiberglass reinforcing rods embedded in a circular arrangement within the material between the inner core and the skin of the composite pile. The second photograph, on the right, shows the condition of the top of the SEAPILE pile after driving during the installation. The top of this pile reveals minor damage to the top from the driving, but no visible degradation of the recycled plastic or the fiberglass rods.

Figure 70. Photo. Lancaster Composite, Incorporated, pile. This figure consists of two color photographs of the Lancaster Composite pile: parenthesis a end parenthesis before and parenthesis b end parenthesis after driving. The first photograph, on the left, shows cross sections of three fiber-reinforced polymer composite piles manufactured by Lancaster Composite, Incorporated. The second photograph, on the right, shows the condition of the top of the Lancaster Composite pile after driving during the installation. Any degradation the top of the pile might have sustained is difficult to discern from the photograph.

Figure 71. Photo. American Ecoboard pile. This figure consists of two color photographs of the American Ecoboard pile: parenthesis a end parenthesis before and parenthesis b end parenthesis after driving. The first photograph, on the left, shows two lengths of pile in a horizontal position on the ground. The ends of each pile are only marginally visible. The second photograph, on the right, shows the condition of the top of the American Ecoboard pile after driving during the installation. Some scaring of the top of the pile is discernable.

Figure 72. Equation. Dynamic modulus E. The dynamic modulus E equals the square root of the quotient of the wave speed, c, divided by the material density, rho.

Figure 73. Equation. Pile particle speed v. The pile particle speed calculated from the acceleration record, v, equals the product of the material wave speed, c, times the measured strain, epsilon.

Figure 74. Graph. American Ecoboard pile-blows per foot versus elastic modulus. This figure presents the results of a parametric study and shows the effect of the number of blows per foot on the elastic modulus of the Ecoboard pile. The X axis is the elastic modulus parenthesis 200 to 400 kips per square inch end parenthesis, and the Y axis is number of blows per foot parenthesis 29 to 37 end parenthesis. The plot shows a generally linear relationship with the elastic modulus increasing as the number of blows per foot decreases. A blow count of 36 per foot corresponds to an elastic modulus of about 220 kips per square inch. A blow count of 33 per foot corresponds to an elastic modulus of about 270 kips per square inch. A blow count of 30 per foot relates to an elastic modulus of approximately 385 kips per square inch. The results show that the effect of the elastic modulus on the blow count is relatively small. For conversion purposes, 1 kip per square inch equals 6,894 kilopascals, and 1 foot equals 0.305 meters.

Figure 75. Graph. Plastic Piling, Incorporated, pile-blows per foot versus elastic modulus. This figure presents the results of a parametric study and shows the effect of the number of blows per foot on the elastic modulus of the Plastic Piling, Incorporated, pile. The X axis is the elastic modulus parenthesis 1,000 to 1,800 kips per square inch end parenthesis and the Y axis is number of blows per foot parenthesis zero to 1,600 end parenthesis. The plot is a roughly negative exponential curve showing the elastic modulus increasing as the number of blows per foot decreases. A blow count of 1,500 per foot corresponds to an elastic modulus of approximately 1,300 kips per square inch. A blow count of 550 per foot corresponds to an elastic modulus of approximately 1,450 kips per square inch, and a blow count of 275 per foot relates to an elastic modulus of approximately 1,720 kips per square inch. For conversion purposes, 1 kip per square inch equals 6,894 kilopascals, and 1 foot equals 0.305 meters.

Figure 76. Graph. SEAPILE pile-blows per foot versus elastic modulus. This figure presents the results of a parametric study and shows the effect of the number of blows per foot on the elastic modulus of the SEAPILE pile. The X axis is the elastic modulus parenthesis 700 to 1,200 kips per square inch end parenthesis and the Y axis is number of blows per foot parenthesis zero to 1,400 end parenthesis. The plot is a roughly negative exponential curve showing the elastic modulus increasing as the number of blows per foot decreases. A blow count of 1,275 per foot corresponds to an elastic modulus of 800 kips per square inch. A blow count of about 300 per foot corresponds to an elastic modulus of about 940 kips per square inch, and a blow count of 175 per foot relates to an elastic modulus of approximately 1,160 kips per square inch. For conversion purposes, 1 kip per square inch equals 6,894 kilopascals, and 1 foot equals 0.305 meters.

Figure 77. Equation. S_elastic. The settlement due to the elastic compression, S subscript elastic, equals the quotient of the maximum applied or ultimate load, P subscript max, divided by the product of the elastic modulus of the pile, E, times the pile section area, A, all times the quotient of the pile length, L, divided by 2.

Figure 78. Graph. Static load test and Case Pile Wave Analysis Program analysis- Lancaster Composite, Incorporated, pile. For the Lancaster Composite pile, this figure compares two load-settlement plots from the static load test with a load-settlement plot predicted by the Case Pile Wave Analysis Program. The X axis is load parenthesis zero to 140 metric tons force parenthesis zero to 308 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 2 centimeters parenthesis zero to 0.79 inch end parenthesis. The plot for cycle 1 is nearly linear and begins with a load of zero at a settlement of zero. Under a load of 50 metric tons force parenthesis 110 kips end parenthesis, the settlement is 0.2 centimeters parenthesis 0.08 inch end parenthesis. At the maximum load of 100 metric tons force parenthesis 220 kips end parenthesis, the pile settlement is approximately 0.75 centimeters parenthesis 0.29 inch end parenthesis. At this point, the cycle 1 plot begins ascending to the left, eventually reaching a load of zero at a settlement of 0.4 centimeters parenthesis 0.16 inch end parenthesis, where cycle 2 begins. In cycle 2, the plot gently descends linearly to a load of approximately 103 metric tons force parenthesis 227 kips end parenthesis at a settlement of approximately 0.85 centimeters parenthesis 0.33 inch end parenthesis.The plot then descends much more sharply, reaching a load of about 130 metric tons force parenthesis 286 kips end parenthesis at a settlement of approximately1.75 centimeters parenthesis 0.69 inch end parenthesis. The cycle 2 plot then begins ascending to the left, reaching a load of zero at a settlement of approximately 1.24 centimeters parenthesis 0.48 inch end parenthesis.The Case Pile Wave Analysis Program plot begins at a load of zero and a settlement of zero and descends almost linearly to the right, reaching a load of 100 metric tons force parenthesis 220 kips end parenthesis at a settlement of 0.6 centimeters parenthesis 0.23 inch end parenthesis. At this point, the Case Pile Wave Analysis Program plot begins ascending to the left, reaching a load of zero at a settlement of approximately 0.17 centimeter parenthesis 0.07 inch end parenthesis.

Figure 79. Graph. Static load test and Case Pile Wave Analysis Program analysis-Plastic Piling, Incorporated, pile. For the Plastic Piling, Incorporated, pile, this figure compares two load-settlement plots from the static load test with a load-settlement plot predicted by the Case Pile Wave Analysis Program. The X axis is load parenthesis zero to 140 metric tons force parenthesis zero to 308 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 3.5 centimeters parenthesis zero to 1.4 inches end parenthesis. The plot for cycle 1 is nearly linear and begins with a load of zero at a settlement of zero. Under a load of 50 metric tons force parenthesis 110 kips end parenthesis, the settlement is approximately 0.25 centimeter parenthesis 0.10 inch end parenthesis. At the maximum load of 100 metric tons force parenthesis 220 kips end parenthesis, the pile settlement is approximately 0.75 centimeter parenthesis 0.29 inch end parenthesis. At this point, the cycle 1 plot begins ascending to the left, eventually reaching a load of zero at a settlement of approximately 0.1 centimeter parenthesis 0.04 inch end parenthesis. Cycle 2 begins just a little above this point. In cycle 2, the plot gently descends linearly to a load of approximately 105 metric tons force parenthesis 231 kips end parenthesis at a settlement of approximately 0.8 centimeter parenthesis 0.31 inch end parenthesis.The plot then descends much more sharply, reaching a load of approximately 120 metric tons force parenthesis 264 kips end parenthesis at a settlement of approximately 3.0 centimeters parenthesis 1.2 inches end parenthesis. The cycle 2 plot then begins ascending to the left, reaching a load of zero at a settlement of approximately 2.25 centimeters parenthesis 0.88 inch end parenthesis.The Case Pile Wave Analysis Program plot begins at a load of zero and a settlement of zero and descends almost linearly to the right, reaching a load of 100 metric tons force parenthesis 220 kips end parenthesis at a settlement of approximately 0.6 centimeter parenthesis 0.23 inch end parenthesis. At this point, the Case Pile Wave Analysis Program plot begins ascending to the left, reaching a load of zero at a settlement of approximately 0.1 centimeter parenthesis 0.04 inch end parenthesis.

Figure 80. Graph. Static load test and Case Pile Wave Analysis Program analysis-SEAPILE pile. For the SEAPILE pile, this figure compares the load-settlement plot from the static load test with the load-settlement plot predicted by the Case Pile Wave Analysis Program. The X axis is load parenthesis zero to 100 metric tons force parenthesis zero to 220 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 3.5 centimeters parenthesis zero to 1.4 inches end parenthesis. The static load test plot is nearly linear and begins with a load of zero at a settlement of zero. Under a load of 50 metric tons force parenthesis 110 kips end parenthesis, the settlement is approximately 0.5 centimeter parenthesis 0.2 inch end parenthesis. At 75 metric tons force parenthesis 165 kips end parenthesis, the pile settlement is approximately 0.8 centimeter parenthesis 0.31 inch end parenthesis. At this point, the static load test plot descends much more sharply, reaching a load of approximately 90 metric tons force parenthesis 198 kips end parenthesis at a settlement of approximately 3.15 centimeters parenthesis 1.23 inches end parenthesis. The static load test plot then begins ascending to the left, reaching a load of zero at a settlement of approximately 2.15 centimeters parenthesis 0.84 inch end parenthesis.The Case Pile Wave Analysis Program plot begins at a load of zero and a settlement of zero and descends almost linearly to the right, reaching a load of approximately 92 metric tons force parenthesis 202 kips end parenthesis at a settlement of approximately 1.6 centimeters parenthesis 0.62 inch end parenthesis. At this point, the Case Pile Wave Analysis Program plot begins ascending to the left, reaching a load of zero at a settlement of approximately 0.2 centimeter parenthesis 0.08 inch end parenthesis.

Figure 81. Graph. Static load test and Case Pile Wave Analysis Program analysis-American Ecoboard pile. For the American Ecoboard pile, this figure compares the load-settlement plot from the static load test with the load-settlement plot predicted by the Case Pile Wave Analysis Program. The X axis is load parenthesis zero to 70 metric tons force parenthesis zero to 154 kips end parenthesis end parenthesis, and the Y axis is settlement descending from zero to 10 centimeters parenthesis zero to 3.9 inches end parenthesis. The static load test plot is approximately linear and begins with a load of zero at a settlement of zero. Under a load of 35 metric tons force parenthesis 77 kips end parenthesis, the settlement is approximately 3.5 centimeters parenthesis 1.4 inches end parenthesis. At 60 metric tons force parenthesis 132 kips end parenthesis, the pile settlement is approximately 9.4 centimeters parenthesis 3.7 inches end parenthesis. At this point, the static load test plot begins ascending to the left, reaching a load of zero at a settlement of approximately 2.75 centimeters parenthesis 1.07 inches end parenthesis.The Case Pile Wave Analysis Program plot begins at a load of zero and a settlement of zero and descends almost linearly to the right, reaching a load of approximately 38 metric tons force parenthesis 84 kips end parenthesis at a settlement of approximately 3 centimeters parenthesis 1.2 inches end parenthesis. At this point, the Case Pile Wave Analysis Program plot begins ascending to the left, reaching a load of approximately 6 metric tons force parenthesis 13 kips end parenthesis at a settlement of approximately 1.3 centimeters parenthesis 0.51 inch end parenthesis.

Figure 82. Equation. Applied axial force F. The applied axial force, F, equals the product of the total pile cross section area, A superscript t, times the equivalent axial stress, tension, or compression acting on the pile section, sigma superscript t, all of which in turn equals the sum of the product of the allowable axial stress, tension, or compression acting in the pile reinforcements, sigma superscript r subscript allowable, times the total cross section area of the reinforcement, A superscript r, plus the product of the allowable axial stress, tension, or compression acting in the plastic material or the concrete for the Lancaster Composite, Incorporated, pile, sigma superscript p subscript allowable, times the total cross section area of the plastic or concrete materials, A superscript p.

Figure 83. Equation. Equivalent axial stress sigma superscript t. Sigma superscript t equals the sum of two terms. The first term is the product of sigma superscript r subscript allowable times the quotient of A superscript r divided by A superscript t. The second term is the product of sigma superscript p subscript allowable times the quotient of A superscript p divided by A superscript t.

Figure 84. Graph. Stress versus penetration depth for Lancaster Composite, Incorporated, static load test pile. This figure presents the pile stresses versus penetration depth for the Lancaster Composite pile. The upper X axis is the maximum measured compressive stress, and ranges from zero to 4 kips per square inch parenthesis zero to 27,576 kilopascals end parenthesis. The lower X axis is the tension stress maximum and ranges from zero to 1 kip per square inch parenthesis zero to 6,894 kilopascals end parenthesis. The Y axis is the penetration depth and ranges from zero to 60 feet parenthesis zero to 18.3 meters end parenthesis. The maximum measured compressive stress plot is an irregular line that gradually moves to the right as the penetration depth increases. The maximum measured compressive stress plot begins at a stress of approximately 0.8 kip per square inch parenthesis 5,515 kilopascals end parenthesis and a penetration depth of approximately 3 feet parenthesis 0.92 meter end parenthesis. The plot's greatest stress is approximately 2.6 kips per square inch parenthesis 17,924 kilopascals end parenthesis, which occurs at a penetration depth of approximately 53 feet parenthesis 16.2 meters end parenthesis. The tension stress maximum plot is an irregular line. Between penetration depths of zero and approximately 46 feet parenthesis zero and 14.0 meters end parenthesis, the stress is within the range of 0.25 to 0.50 kip per square inch parenthesis 1,724 to 3,447 kilopascals end parenthesis. Between approximately 46 and 56 feet parenthesis 14.0 and 17.1 meters end parenthesis, the stress ranges between 0.50 and 0.75 kip per square inch parenthesis 3,447 and 5,171 kilopascals end parenthesis.

Figure 85. Graph. Stress versus penetration depth for Plastic Piling, Incorporated, static load test pile. This figure presents the pile stresses versus penetration depth for the Plastic Piling, Incorporated, pile. The upper X axis is the maximum measured compressive stress, and ranges from zero to 2 kips per square inch parenthesis zero to 13,788 kilopascals end parenthesis. The lower X axis is the tension stress maximum and ranges from zero to 1 kip per square inch parenthesis zero to 6,894 kilopascals end parenthesis. The Y axis is the penetration depth and ranges from zero to 75 feet parenthesis zero to 22.9 meters end parenthesis. The maximum measured compressive stress plot is an irregular line. Between penetration depths of zero and approximately 28 feet parenthesis zero and 8.5 meters end parenthesis, the stress is within the range of 0.25 to 0.50 kip per square inch parenthesis 1,724 to 3,447 kilopascals end parenthesis. Between approximately 28 and 61 feet parenthesis 8.5 and 18.6 meters end parenthesis, the stress ranges between 0.50 and 0.75 kip per square inch parenthesis 3,447 and 5,171 kilopascals end parenthesis. The tension stress maximum plot is an irregular line. Between penetration depths of zero and approximately 22 feet parenthesis zero and 6.7 meters end parenthesis, the stress is within the range of 0.125 to 0.25 kip per square inch parenthesis 862 to 1,724 kilopascals end parenthesis. Between approximately 22 and 61 feet parenthesis 6.7 and 18.6 meters end parenthesis, the stress ranges from zero to 0.125 kip per square inch parenthesis zero to 862 kilopascals end parenthesis.

Figure 86. Graph. Stress versus penetration depth for SEAPILE static load test pile. This figure presents the pile stresses versus penetration depth for the SEAPILE pile. The upper X axis is the maximum measured compressive stress, and ranges from zero to 2 kips per square inch parenthesis zero to 13,788 kilopascals end parenthesis. The lower X axis is the tension stress maximum and ranges from zero to 1 kip per square inch parenthesis zero to 6,894 kilopascals end parenthesis. The Y axis is the penetration depth and ranges from zero to 75 feet parenthesis zero to 22.9 meters end parenthesis. The maximum measured compressive stress plot is an irregular line. Between penetration depths of zero and approximately 26 feet parenthesis zero and 7.9 meters end parenthesis, the stress is within the range of 0.4 to 0.6 kip per square inch parenthesis 2,758 to 4,136 kilopascals end parenthesis. Between approximately 26 and 32 feet parenthesis 7.9 and 9.8 meters end parenthesis, the stress increases from approximately 0.6 to 1.0 kip per square inch parenthesis 4,136 to 6,894 kilopascals end parenthesis. Between approximately 32 and 62 feet parenthesis 9.8 and 18.9 meters end parenthesis, the stress ranges, with the exception of 3 outliers, from approximately 0.8 to 1.0 kip per square inch parenthesis 5,515 to 6,894 kilopascals end parenthesis. The most pronounced outlier is a stress of approximately 0.4 kip per square inch parenthesis 2,785 kilopascals end parenthesis at a depth of approximately 37 feet parenthesis 11.3 meters end parenthesis. The tension stress maximum plot is an irregular line. For the entire penetration range parenthesis zero to 62 feet parenthesis zero to 18.9 meters end parenthesis end parenthesis, the stress is within the range of zero to 0.25 kip per square inch parenthesis zero to 1,724 kilopascals end parenthesis.

Figure 87. Graph. Stress versus penetration depth for American Ecoboard splice static load test pile. This figure presents the pile stresses versus penetration depth for the American Ecoboard pile. The upper X axis is the maximum measured compressive stress and ranges from zero to 1 kip per square inch parenthesis zero to 6,894 kilopascals end parenthesis. The lower X axis is the tension stress maximum and ranges from zero to 0.4 kip per square inch parenthesis zero to 2,758 kilopascals end parenthesis. The Y axis is the penetration depth and ranges from zero to 30 feet parenthesis zero to 9.2 meters end parenthesis. The maximum measured compressive stress plot is an irregular line. Between penetration depths of approximately 12 to 17 feet parenthesis 3.7 to 5.2 meters end parenthesis, the stress increases from approximately 0.3 to 0.6 kip per square inch parenthesis 2,068 to 4,136 kilopascals end parenthesis. Between approximately 17 and 29 feet parenthesis 3.7 and 8.8 meters end parenthesis, the stress ranges from 0.6 to 0.7 kip per square inch parenthesis 4,136 to 4,826 kilopascals end parenthesis. The tension stress maximum plot is an irregular line. For the entire penetration range parenthesis 12 to 29 feet parenthesis 3.7 to 8.8 meters end parenthesis end parenthesis, the stress is within the range of zero to 0.1 kip per square inch parenthesis zero to 689 kilopascals end parenthesis.