Chapter III. Physical Model
In performing a dimensional analysis for the modeling in this project, there are seven fundamental variables that must be considered. Force (F) and length (L) are the only two basic dimensions contained in the fundamental variables as shown in Table 1.
Subtracting the number of basic dimensions from the number of fundamental variables gives the number of Pi terms, which is five. Deflection (Δ) is the non-repeating variable since it is the variable of interest and is a function of the four remaining Pi terms. This is shown by the relationship:
(Δ/D) = f [ (PD2/EI), (L/D), (H/D), (CD4/EI) ]
By equating the model Pi terms with the prototype Pi terms (ie. (L/D)m = (L/D)p ..etc), the scale factors are established. Because Pi terms are dimensionless, they have no feel for size. Therefore, small-scale (model) tests are valid. An important factor to realize in modeling considerations is that the undrained shear strength of the soil is not a function of soil stress and therefore does not need to be scaled. This allows the test soil to be directly established as the prototype soil.
Choosing a model pile diameter (D) fixes the length of the pile due to the Pi term L/D. This also fixes the height of the applied load (H) because it is linked through the Pi term H/D. Pile stiffness (EI) has not yet been set even though the pile diameter has been selected because the wall thickness, and thus the bending moment of inertia (I), has not been set. Reducing pile stiffness allows the model lateral load also to be reduced, thus making it easier to model the lateral load needed to simulate a full-scale load according to the Pi term PD2/EI.
The modulus of elasticity (E) of the model pile also may be used to control pile stiffness (EI), and thus the modeled lateral load (P). A smaller model load may be used to simulate a given full-scale load if the modulus of elasticity of the model pile is reduced. Reducing the model pile stiffness will reduce the simulated lateral load, but it must be remembered that this also will increase the likelihood of damaging the model either through yielding the model material or by buckling the model pile.
A steel pipe pile 324 mm (12.75 in.) in diameter and with a 7.94 mm (0.313 in.) wall thickness, which commonly is specified by the Utah Department of Transportation (UDOT), was selected as the prototype pile. The model pile characteristics were then selected according to dimensional analysis based on the prototype pile. Schedule 40, 6061-T6 aluminum pipe conforming to ASTM B 241 with an outside diameter of 33.4 mm (1.315 in.) and a wall thickness of 3.38 mm (0.133 in.) was chosen as the model pile material. A summary of the characteristics as they relate to prototype pile are shown in Table 2. It was necessary to select dimensions and characteristics that were consistent with the dimensional analysis while taking into consideration availabilities of possible model materials. The following relationships were established to relate the model and prototype functional parameters:
Pp = 98.6 * Pm
Δp = 9.7 * Δm
where P is the applied lateral load on the model and prototype and is the resulting deflection of the model and prototype. The relationships will not be used in the analysis in this project, but were included here for possible future reference.
A ribbed steel tank 3.05 m (10 ft.) long, 0.91 m (3 ft.) wide, and 1.22 m (4 ft.) deep was used to contain the clay soil used in lateral pile group tests. Plywood sideboards were added to the tank to increase the depth of the tank so that longer piles could be tested without introducing unwanted boundary effects. The tank was lined with multiple sheets of heavy plastic to act as a barrier in retaining water, and a geocomposite was placed inside this liner to facilitate drainage during the consolidation process.
The soil in the vessel was dredged from the gravel washing pond of a local contractor and was dumped into the tank in a slurry form. Obtaining soil in this form necessitated a consolidation period to bring the strength of the soil up to a point that would be typical for a saturated clay in the local environment. Consolidation was accomplished by mounting 10 hydraulic cylinders over the soil by means of five bolted yokes and pressurizing them to push steel plates against the soil. Figure 1 shows a schematic of the tank with the yokes in place. The consolidating pressure on the soil was maintained in increasing increments by a hydraulic accumulator with the final hydraulic pressure being 2.76 MPa (400 psi), which gave a simulated overburden stress of 80.2 kPa (1675 lb./ft2). The consolidation process took four and one-half months, after which the consolidation apparatus was disassembled and the soil was trimmed to a thickness of approximately 1.37 m (4.5 ft.). The soil was saturated during consolidation and was kept saturated for the duration of the time between consolidation and the lateral pile group tests.
Atterberg limits tests were run on samples of the soil to determine its classification. It classed as a CL type soil. Torvane, pocket penetrometer, and hydrometer analyses also were run on the soil to further determine its characteristics. Multiple tests have been run on this soil to determine its postconsolidation properties using a mini-vane shear testing device. The earliest test was in January 1995 and the most recent test was in June 1996. The average undrained shear strength values have ranged from 28.8 kPa (4.12 psi) to 34.2 kPa (4.90 psi). The results of all soil properties tests can be seen in Appendix A.
The sideboards on the test vessel were cut down prior to the pile group tests to allow better access to the piles once inserted into the soil and also to allow the loading system to be mounted without any obstruction. This also permitted much easier viewing of the actual testing activities while allowing for enough freeboard to keep the soil saturated.
Two of the five consolidation yokes were left attached to the tank while the two hydraulic cylinders bolted to each of the yokes were removed. A large plank was bolted between the yokes to fix their relative spacing and to hold them motionless. This allowed the yokes to be used as a fixed reference to which displacement measuring instruments were later attached.
For Phase 2, a substantial amount of new hardware was required. Due to the need to model a pile group, it was decided to construct six new piles that had been designed from the start as members of a group, and thus eliminate the possibility that differences between the new and old piles would introduce some compatibility problems. It also was decided that the piles should be arranged in a single row and be loaded on the linear axis of the row. This would provide the next step in complexity without introducing group effects from piles spaced laterally from each other. The new piles and the instrumentation necessary to measure loads and deflections during testing had to be designed and constructed.
The piles were made from 1 inch, Schedule 40, 6061-T6 aluminum pipe. The nominal inside diameter of this pipe is 26.645 mm (1.049 in.) with a wall thickness of 3.378 mm (0.133 in.). This pipe was purchased in 6.1m (20 ft. ) lengths and cut to the proper length of 1.524m (5 ft.) for each pile by means of a disk type cutter.
To prepare the pipes for strain gage mounting, the inside surfaces were etched with dilute phosphoric acid to remove any manufacturing residue, grease, or scale. The etching process began by plugging one end of the pipe with a rubber stopper and then pouring about 50 ml of acid into the other. A steel wool-wrapped rod was then inserted into the pipe and spun by means of an electric drill to scrub the interior. The rod was moved in and out of the pipe several times while spinning at high speed until the whole interior surface had been thoroughly etched. The pipe was rinsed with water and the operation was repeated, except that the second time an ammonia water solution was used to neutralize any remaining acid. The pipe was again rinsed and then dried with air. At the conclusion of these operations, the inside of each pipe had a polished and clean finish.
When etching was completed, a pointed steel scribing tool was used to scratch straight reference lines about 6 inches long on the outside surface at the ends of the pipes. These reference lines would be used during the gage mounting procedure to assure that the gages were being positioned properly in the piles.
Thin foil strain gages manufactured by Micro-Measurements of Raleigh, N.C., and of the type CEA-13-250UW-120 were chosen for the pile instrumentation. One hundred eighty gages were ordered along with the lead wire needed for connecting them and the epoxy for mounting them. As in the piles used in Phase 1, 28 gages were to be mounted on the inside surface of the pipes in diametrically opposed pairs spaced 95 mm (3.75 in.) apart, with the bottom most pair located 76 mm (3.0 in.) from the bottom end of the pipe, and with the upper most pair located 152 mm (6 in.) above the next closest pair. Figure 2 shows the spacing of strain gages in each pile.
Before the gages could be mounted, the lead wire had to be attached. The lead wire for the gages was a three-strand, flat type wire with red-, white-, and black-colored insulation. The length of wire required to reach each gage location in the piles, with an additional 2.13 m (7.0 ft.) for connecting purposes, was calculated. The wire was then measured out and cut. This required use of 497.1 m (1631 ft.) of wire. Half the wire was stripped of its black strand, thus leaving the red and white strands together, and the other half of the wire was stripped of its red strand, leaving the black and white strands connected. This was done to keep track of which side of the piles the gages were on, the gages connected to the red and white wires going on one side of the pile, and the gages connected to the black and white wires going on the other. The ends of the lead wires were stripped of insulation and tinned in preparation for connection to the gages.
Connecting wires to the gages was a delicate process. First, the gage was positioned on a Teflon-covered mounting board where it was held in place with a small wire spring. Rosin core solder "buttons" were then melted onto the two strain gage connecting tabs. The wire leads were trimmed to fit the tabs and then positioned and taped to the mounting board surface. The gage was brought into position. The wires then were soldered onto the gage by pressing the wire leads against the solder buttons one at a time and holding them there with the tip of the soldering iron until the buttons and leads melted together. The connection points and any length of exposed wire were then waterproofed with an acrylic sealant, which was painted on with a brush. Later, the gages and lead wires were tested with a volt meter to check for any bad connections.
All gage mounting activities took place in the CEE soils laboratory where all equipment could be left undisturbed for the work's duration. A mounting tool was specially designed and fabricated by the former CEE department technician for installing strain gages on the inside surface of the pipes. A pair of gages is mounted by first inserting the tool into the pile by means of a two-piece telescoping handle. The outer handle holds the tool in the required location and has several sliding spacers on it to keep it centered in the pile. The inner tightening handle slides inside the outer handle and is rotated to actuate the screw and wedge assembly of the tool. As the screw is turned, the wedge forces the wings apart, which press the strain gages against the inside of the pipe and hold them there while the epoxy cures. Six of the tools were used so that all of the gages at a certain location in the piles could be quickly mounted with little confusion and possible mix up. Figure 3 is a diagram of the mounting tool.
In preparation for mounting, the gages first had to be affixed to each of the tools. This was done by slipping the tool into a small vise that held it in a horizontal position and allowed it free rotation. Teflon strips covered the rubber coated wings on the tools so that the gages would not be glued to the wings during mounting. Reference lines were drawn on these Teflon surfaces to aid in gage alignment. The gages were turned upside down and lined up on the reference lines with the lead wires pointed away from or out in front of the tool. Short strips of cellophane tape were used to tack the gages in place; a strip over the wires just where they met the gage, and another strip holding the tip of the gage down. Care was taken to cover only a small amount of the gage with tape so that the surface area of the gage available for gluing was as great as possible. Two gages were attached to each tool; a red gage on the one side, and a black on the other. The lead wires for both gages were then taped to a probe that protruded from the front of the tool. The purpose of the probe was to keep the wires from getting tangled while the gages were being slid into place inside the pile. When all six of the tools had been thus prepared, a single pile was clamped into a table-top vise with its scribed orientation line aligned with a reference line on the vise. The end of a slender rod was slid through the pile and attached to a string, which was then drawn through the pile as the rod was withdrawn. To the other end of this string, the lead wires for the strain gages to be installed in this pile were taped. The wires were then pulled through the pile until enough slack remained to permit movement of the tool to which they were attached. This mounting tool, with gages, was then positioned in the end of the telescoping insertion handle and lined up preparatory to the gluing and installation procedures.
Micro Measurements M-bond AE-10 two-part epoxy was used to glue the gages to the pile walls. Mixing the epoxy was begun by placing a glass slide and small wood spatula on a scale and zeroing the readout. Next, the spatula was used to dip 0.91 grams of resin from the bottle and place it on the slide. Three drops of hardener were put on the slide with the resin and the two were then thoroughly mixed. This prepared enough epoxy to mount 12 strain gages.
The spatula was used to smear epoxy onto the two gages prepared for insertion. The mounting tool was positioned in the end of the pile while the spacers on the handle were slid into place to keep the gages from touching the inside of the pipe and wiping off the epoxy. Slight tension was held on the lead wires as the tool was slid into the pile so that the wires would not get tangled. When the gages were in the proper position and oriented correctly as shown by markings on the insertion handle, the tightening handle was turned until the tool was securely in place. The handle was gently removed from the tool and withdrawn from the pile, leaving the mounting tool and gages in place to cure for six hours.
Butyl rubber had been affixed in the top end of the pile, and into this the lead wires were pushed to keep them out of the way of further gage mounting activities. An acrylic sealant was painted on the wires and butyl rubber to hold the wires firmly in place.
This pile was moved out of the way and the process was repeated for all six of the piles. It was important to clean the insertion handle with methyl alcohol after withdrawing it each time so that any smeared epoxy would not interfere with the mounting of subsequent gages.
The working time of the epoxy dictated that gages for all six piles had to be installed in less than 30 minutes. If this was not accomplished, a new batch of epoxy had to be mixed. Two people were required to make the gage installation procedure go smoothly. This procedure was used to mount all of the gages at the 14 locations in each pile, starting with the top pair and finishing with the last pair, which was located 76.2 mm (3 in.) from the bottom.
After the six-hour curing time, the handle was pushed back into the pile until the mounting tool was engaged. The wedge actuating screw in the tool was then loosened and the wedge was forced forward from between the wings with a gentle tap to the end of the tightening handle. This allowed the wings to collapse. Gentle twisting action on the handle broke the wings loose from the gages, after which the tool was withdrawn from the pile. After the insertion tools had been removed from every pile, the strain gage circuit was checked for damage with a volt meter.
All 168 strain gages were successfully mounted without damage, but there were several anomalies noted during gage installation. One type of anomaly occurred three times, in which, upon removal of the insertion tool, one of the protective Teflon strips remained inside and attached to the wall of the pile. This was determined to be a minor problem which would not likely influence the strain reading from the affected gage. The other anomaly occurred only once and involved the Red 8 and Black 8 gages of Pile 1. During an attempt to remove the insertion tool, it was found that the gages had been mounted in a position rotated about 30 degrees off-axis from the rest of the gages. Nothing could be done to change this, but calibration factors for these gages would reflect their errant positioning.
Plugs for sealing the bottom ends of the piles were machined from solid aluminum stock. The shoulders of the plugs were sized to match the outside diameter of the piles, while the necks of the plugs fit smoothly inside. The necks were grooved to accept an O-ring that would form a tight seal when installed. Installation of the plugs was accomplished by coating the O-rings with petroleum jelly and then inserting the plugs into the piles. As an extra barrier against moisture, a metal-to-metal epoxy was smeared into the gap between the bottoms of the piles and the shoulders of the plugs, after which the plugs were pushed completely into the piles and held in place for several minutes until a primary bond could be made. Later, excess epoxy was trimmed from around the plugs.
Moisture in the piles was eliminated by purging them with nitrogen. This was done by threading a rubber hose down to the bottom of the pile and then slowly withdrawing it as nitrogen was pumped in. The nitrogen was first dried by running it through a crystal desiccant in an in-line container. A rubber stopper was then glued into the end of the pile and a seal of silicone glue was made on top of the stopper and around the wires.
Aluminum pile crowns for sealing the tops of the piles and with a provision for pinning the piles together in a linear group were designed and fabricated. Figure 4 shows the pile crowns as part of the pile cap assembly. Strain gage wires exit the crown through a side port. To assure a tight fit between crowns and piles, the inside diameter of the crowns were designed to be slightly smaller than the outside diameter of the piles. The crowns were installed by first threading all of the strain gage lead wires up through the bottom of the crown and then out through the port. Reference lines on the crowns were aligned with the lines that had earlier been scribed on the piles for the strain gage installation work. The crowns were then driven onto the piles with a heavy rubber mallet until seated.
The final step in the pile construction process was to shield lead wires from electromagnetic noise with stainless steel braided wire sheathing. Hose clamps were used to fasten sheathing to the wire ports on the pile crowns. A grounding wire was added by twisting it together with strands of the sheathing material. Enough lead wire was left exposed to allow easy connection to the data acquisition system.
Since the strain gages in the piles would be electrically excited almost continuously, there was a chance that this could cause some heating of the gages and change their resistance, thus affecting voltage output. To monitor this possible thermal drift, one of the six piles was used as a control pile. It was sunk in the soil test vessel to the same depth as the other piles. Its gages also were electrically excited in the exact manner and at the same frequency as those in the other piles, but it was not subjected to loading in any way. By comparing its initial strain gage readings with its final ones, any amount of thermal drift was accounted for and applied to the measurements taken from the other piles.
One of the points of interest in this project is the amount of lateral load that is taken up by each pile in the group. A special rod was designed in conjunction with the pile crowns not only to connect the piles in their linear group at the correct spacing, but also to measure the load transferred to each. Strain gages affixed to necked down sections between each pile connection served to function as in-line load cells. Figure 5 shows the load rod strain gage configuration.
This load rod was fabricated from 0.5 inch square 6061-T6 aluminum rod stock. The spacing of three pile diameters was set by drilling 6.35 mm (0.25 in.) holes for the pins at the proper distance intervals. Holes, 6.35 mm (0.25 in.) in diameter, for connecting the pile group to the loading mechanism also were drilled in each end. The material between the pin joints was machined down to a thickness of 4.763 mm (0.188 in.) so that strains within the range of the type CEA-13-250UW-120 strain gages to be used would be experienced.
To prepare the load rod for gage mounting, all necessary surfaces were sanded to remove any flaws or scratches left over from machining. Dilute phosphoric acid was used to etch these surfaces, which were then rinsed with water. Neutralizing was accomplished by rinsing with ammonia water. The rod was rinsed again with water and blown dry with air. The strain gages were wired and waterproofed in the same manner as those used in the piles. Four gages were first mounted to the top of the rod at the points half way between the pile pin connections. This was done by mixing a measured amount of epoxy and spreading it on each gage. The gages were placed in position on the rod and covered with small pieces of Teflon to prevent anything other than the gages from getting glued to the rod. Rubber-padded metal tabs were then placed over the gages, and spring clamps were applied to supply the holding pressure. After the requisite six-hour curing time, the other four gages were applied to the bottom of the load rod directly opposite those on the top. Butyl rubber strips then were attached to the load rod directly over and completely covering each gage to protect them from any damage. Strips of aluminum tape were wrapped around the four gage sections of the load rod, covering the gages at each location. An acrylic sealant was then painted on all of the tape seams to encapsulate the gages in waterproof environments.
Stainless steel true size pins were used to connect the load rod to the piles. Due to the precise size of these pins, very little relative movement between the load rod and the piles was possible.
Two load cells were used to measure the forces exerted on the pile group during lateral load testing, by incorporating them in the linkage between the load applying hydraulic cylinders and the pile group. Figure 6 shows the basic outline of the load cells. Aluminum 6061 T-6 strap stock 4.763 mm (0.188 in.) thick was first machined to a width of 25.4 mm (1.0 in.) and a length of 101.6 mm (4.0 in.). Connecting holes 7.938 mm (0.313 in.) in diameter were drilled in each end, and a gauge section 31.75 mm (1.25 in.) long and 12.70 mm (0.50 in.) wide was machined in the central section of each load cell. Two CEA-13-250UW-120 strain gages were mounted to this gauge section, one on each side of the cell, using the same procedure as was used for attaching strain gages to the load rod.
Measurement of the pile group displacement during testing was accomplished by using two Linear Variable Differential Transformers (LVDTs). Using two LVDTs not only allowed for measuring deflection of the pile group, but by comparing the deflections in two places, the slope of the piles could be determined. The LVDTs were purchased from RDP Electrosense Inc. of Pottstown, Penn. Since the LVDTs both were type LDC 3000C, they were identical in appearance and nearly identical in functioning characteristics. Pieces of blue and red tape were affixed to the LVDTs so they easily could be distinguished from each other. The LVDT marked with red tape was used in Phase 1 of this project. Its specification sheet gave its linear range at ± 75 mm (3.0 in.) with a sensitivity of 29.91 mV/mm (0.76 V/in.) and a linearity of 0.12 percent. The second LVDT was purchased for this phase of the project because it was necessary to have two LVDTs with the capability to measure large deflections. According to the specification sheet sent with this LVDT, it had a linear range of ± 75 mm (2.9527 in.), a sensitivity of 30.23 mV/mm (0.768 V/in.), and a linearity of 0.10 percent. Blue tape was used to mark this LVDT.
Ball and socket fittings were screwed into the stationary ends and onto the sliding ends of the LVDTs. The fittings permitted a slight amount of angular movement at each end without causing binding or bending in either the LVDTs or the testing equipment and they were the means of mounting the LVDTs to the pile group.
It was necessary to use two LVDTs during testing to record deflections that were used as boundary conditions in the data reduction process. One was mounted at the pinned load rod/pile crown connection elevation to measure group deflection, and the other was mounted 76.2 mm (3.0 in.) above the load application axis to record a second set of deflection data that was used in calculating the angle of rotation of the piles.
To connect the LVDT at the load rod-pile cap elevation, a 25.4 mm (1.0 in.), 10-24 flat head machine screw was glued onto the end of the stainless steel pin used to connect the load rod to the end pile in the group. The ball and socket end fitting on the LVDT slider was slid over the machine screw and held in place with wing nuts, which could be used to adjust the horizontal position of the LVDT.
Modifications had to be made to the pile crown on the end pile in the group in order to allow the second LVDT to be mounted in the elevated position necessary for calculating pile head slope. Figure 7 shows the mounting configuration of the LVDTs. The first step in the modification process was to drill a hole vertically down into the solid part of the pile crown, far enough away from the pin connection to not interfere with the pin. This hole was then tapped with a 10-24 thread. The head was cut off a 101.4 mm (4.0 in.) 10-24 machine screw, which was then screwed down into the hole. A nut was then screwed all the way down onto the machine screw until it tightened up against the top of the pile crown. This secured the machine screw and kept it from coming out or wiggling. The ball and socket fitting on the slider end of the LVDT was then slid down over the machine screw and held in position with wing nuts, which also were used to vertically align the LVDT.
A bracket was made from a piece of steel strap material 3.2 mm x 63.5 mm x 203.2 mm (0.125 in. x 2.5 in. x 8 in.) to which the nonmoving ends of the LVDTs were mounted by means of two 50.8 mm (2.0 in.) 10-24 machine screws. Holes were drilled in the steel strap at 12.7 mm (0.5 in.) intervals to allow the LVDTs to be spaced as conditions required. The machine screws were inserted through the holes and tightened down with nuts. Two wing nuts were used on these to allow horizontal LVDT adjustment and to fix LVDT position once they were aligned.