Lateral Resistance of Short Rock Sockets in Weak Rock: a Case History Text word count: Number of figures and tables: 1 Robert L. Parsons PhD, P.E (Corresponding Author) Associate Professor Department of Civil, Environmental and Architectural Engineering W 1 th St., Room University of Kansas Lawrence, KS 0 rparsons@ku.edu () - Matthew C. Pierson Assistant Professor, Cooperative Engineering Program Kemper Hall, Room Missouri State University 01 S. National Ave. Springfield, MO matthewp@ku.edu -- Isaac Willems Graduate Student Department of Civil, Environmental and Architectural Engineering W 1 th St., Room University of Kansas Lawrence, KS 0 iwillems@ku.edu (0) - Jie Han PhD, P.E Associate Professor Department of Civil, Environmental and Architectural Engineering W 1 th St., Room University of Kansas Lawrence, KS 0 jiehan@ku.edu () -1 James J. Brennan Assistant Geotechnical Engineer Kansas Department of Transportation 00 Van Buren Topeka, KS - brennan@ksdot.org () -00 TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 Lateral Capacity of Short Rock Sockets in Weak Rock: a Case History ABSTRACT The results from full-scale cyclic and repeated lateral load testing of two short rock sockets in weak rock and the recommendations developed for p-y analysis using those results are presented. Two drilled shafts were constructed in rock sockets inches in diameter to depths of approximately seven feet in limestone in Wyandotte County, Kansas. The shafts were loaded laterally during three separate test events. The shafts were tested under cyclic loading (load reversal) for loads up to 00 kips, repeated loading in one direction up to 0 kips, and to failure near 1,000 kips. Test data showed that socket behavior was essentially elastic during cyclic loading for loads of 00 kips (0% of nominal resistance) and lower. The shafts experienced permanent, accumulating deformations during repeated loading to and 0 kips. Modeling of the results showed the lateral load behavior could be effectively modeled in LPILE using the Reese weak rock model included with LPILE software. Recommendations for use in modeling are presented. 1 TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 INTRODUCTION This paper contains the results from a full-scale lateral load test of two drilled shafts constructed in short rock sockets in weak limestone, and the development of recommendations for p-y analysis using those results. Lateral nominal resistance of drilled shafts is of particular interest with regard to bridge foundations because of the significant loading conditions they experience, particularly during scour events. Lateral nominal resistance may be estimated during the design process by several methods, with one of the most common being a p-y analysis. P-y curves vary among soil types and rock formations, although general curves have been developed and are available for use in widely available software packages such as COM (public domain) and LPILE (proprietary software, Ensoft). The purpose of this research was to test the lateral capacity and develop p-y curves for short rock sockets in weak rock. Two shafts inches in diameter were constructed to depths of six and seven feet in limestone in Wyandotte County, Kansas. All overburden material was removed prior to construction. The shafts were loaded laterally during three separate test events. During the first event, the shafts were loaded in a cyclic manner (load reversal) at multiple increments up to 00 kips. The cyclic loading was of interest because of the potential for lateral loading in alternating directions on shafts supporting integral abutments. The shafts were then loaded in one direction to 0 kips. The equipment was then reconfigured and the shafts were loaded to 0 kips with repeated loading-unloading cycles at and 0 kips. The loading frame was then reinforced and the shafts were loaded to failure, which occurred near 1,000 kips. A description of the testing, analysis, and p-y curve recommendations is presented in Parsons et al. (1). Analysis of the data showed that commonly used p-y curves included within the LPILE software could be used to develop an accurate model of the static behavior of the shafts. Cyclic loading of the shafts had little effect on shaft resistance at lower loads; however permanent deformation began to accumulate at loading levels between 0 and 0 percent of nominal resistance. 0 1 THEORETICAL BACKGROUND This section contains an abridged discussion of the p-y curve method. For a more detailed discussion of the p-y curve method the reader is referred to Reese et al. (). For the p-y method the pile-soil interaction is modeled as a series of nonlinear springs, where p represents lateral load per unit length on a spring and y represents displacement of TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 0 1 the spring. The non-linear relationship is captured by the secant modulus E r, which decreases according to some function, such as a hyperbolic function, as displacement increases. The p-y method was extended to the analysis of single rock-socketed drilled shafts under lateral loading by Reese (). Reese s criteria, which he considered interim criteria pending the availability of more test data, include consideration of the secondary structures of rock masses using a rock strength reduction factor determined from the Rock Quality Designation (RQD). Other criteria used for generating p-y curves have subsequently been developed (, ). Reese s criteria have been incorporated into LPILE v.0 Plus (), and were used for the analysis described in this paper. For this method, the ultimate reaction P u (units of force per length) of rock is given by: 1 1. for 0. b for Where: q ur = uniaxial compressive strength of intact rock; α r = strength reduction factor, used to account for fracturing of rock mass, it is assumed to be 1/ for RQD of 0% and it increases linearly to 1 at a RQD of zero; b = diameter of the drilled shaft, and; x r = depth below rock surface. The slope of initial portion of p-y curves is given by: Where: K ir k ir *E ir K ir = initial tangent to p-y curve; E ir = initial modulus of the rock k ir = dimensionless constant The expressions for k ir, derived by correlation with experimental data, are as follows: 0 00 for 0 00 for The p-y curves developed from these relationships follow the shape shown in Figure 1. This figure shows a p-y curve with three segments; from the origin to y A, from y A to y m, and from y rm to failure. TRB 0 Annual Meeting
1 1 1 1 1 1 1 p ur y A y rm Figure 1. Sketch of p-y curve for weak rock (adapted from Reese []) The equations relating p and y for the curve in Figure 1 are as follows: K ir for y y A. for y > y A, p <p ur y 1 0 1 0 for y > 1y rm and = where k rm = a constant between 0.000 and 0.0000 that controls the overall stiffness of the p-y curves, and;.. TRB 0 Annual Meeting
1 1 1 1 FIELD TESTING Site Investigation The shafts were constructed in the fall of 00 in the northeast quadrant of the intersection of I- 0 and I- in Wyandotte County, Kansas. The sockets were in the Plattsburg Limestone. Two borings were made and cores were recovered at the site in the vicinity of the rock sockets. The site geology consisted of minimal to no soil overburden, 1.-. feet of weathered to unweathered sandstone over weak limestone. The overburden and sandstone were removed so the sockets were entirely in limestone. More detailed information is available in Parsons et al. (1). Seven unconfined compression tests of the limestone were conducted on samples from elevations considered relevant to this study. The results of those tests are reported in Table 1. Depths in Table 1 are with respect to the original ground level. RQD values of 1% and % were determined for the depth of interest from the two borings. An average of 0% was used for the site. TABLE 1 Rock Core Test Data Used for Analysis Unconfined Elastic Dry Moisture Sample No. Depth Compression Modulus Density Percent (ft) q u (psi) E (ksi) d (pcf) w % Upper Layer 1 1. 1.. 1 1. 01 1.. 1 1.0.. Lower Layer 1.0 1 1..1 1 1.0 1 1.. 1.0 0 1.0.1 1. 0 1.. Values used upper layer 0 Values used lower layer 0 0 E/q u upper layer E/q u lower layer 0 effective unt wt (all layers) 1 lb/ft RQD 0% 1 Note: E was determined from unconfined compression testing TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 0 1 This rock core data was considered to represent two layers; an upper, more weathered layer and a lower more competent layer. Representative values for unconfined compressive strength (q u ) and initial intact rock modulus (E) were adjusted from the averages somewhat to account for spatial relationships among sampling points. The E/q u ratios are slightly above 00, which is consistent with published values (). Concrete cylinders were taken when the shafts were constructed and the -day curing strength was determined to be,00 psi. Given the additional strength gain that should have occurred prior to actual testing of the shafts and based on the strength gain from cylinders from a concurrent study (), a concrete strength of,00 psi was used for modeling purposes. Shaft Details The test shafts were inches in diameter and spaced 1 inches apart center to center. They were cast in sockets approximately six feet deep for the north shaft and seven feet deep for the south shaft. Shaft reinforcement consisted of 1 # longitudinal bars and hoops made of # bars on a one foot spacing within the socket and a spacing of approximately six inches above ground at the point of load application. The load was applied approximately one foot above ground level. The concrete met KDOT standard specifications for drilled shafts. Testing Lateral load testing was conducted as part of three separate tests in 00. The first test consisted of cyclic (load reversal) testing up to 00 kips for a series of primary load increments, where 00 kips was the maximum load that could be achieved in both directions with the equipment configuration used. The equipment was configured such that two separate load systems could load the shafts in opposite directions. One set of equipment with three 0 kip hydraulic cylinders was used to jack the shafts apart, and a second set with two 0 kip cylinders was used to pull the shafts together (Figure ). Cycles of loading were applied to the shafts by alternating loading between these sets of equipment. Five or cycles were applied at each primary load increment. During each cycle the load was held at the target value until deformation stabilized for approximately 1 minute. Additional measurements were taken at intermediate increments. Load was measured using two separate systems, load cells and hydraulic pressure. The hydraulic pressure was monitored by gauge and by pressure transducer. The load cells were limited to a capacity of 00 kips and served as a backup to the pressure transducer and gauge. Deformations were determined from inclinometer measurements in each shaft and at two locations on each shaft with string pots fixed to reference beams. Pressure transducer, string pot, and load cell data was recorded automatically on a laptop computer. Photogrammetry was used as a backup system. Pressure transducer and string pot information was recorded by a laptop TRB 0 Annual Meeting
and data acquisition system. Inclinometer data was recorded by KDOT personnel with a data logger prior to each test and after each set of load cycles. string pots Inclinometer casing hemispherical ball string pots cylinders push shafts together load rods ( on each side) load cells 1 1 1 1 1 1 1 1 0 Figure. Test 1 setup For the second test the equipment was reconfigured so that all five cylinders could be used together to load the shafts as shown in Figure. Repeated loads, which consisted of loading to the target value and then reducing the load to zero, were applied at and 0 kip load levels with cycles at each load step. As loading continued for Test above 0 kips, one of the loading beams began to yield, forcing the test to be stopped. The yielding beam was reinforced and the test was restarted as Test. Loading proceeded to failure at approximately 1,000 kips for both shafts. Field Data reference beam cylinders push shafts apart Figures and show the deformations that occurred during each test event as measured by the top string pots, which were approximately. ft above ground level. Data for individual cycles are not shown in these graphs. These figures show increasing rates of deflection with increasing load to failure, which occurred at approximately 1,000 kips for both shafts. Data for the lower string pots on each shaft were similar. reference beam TRB 0 Annual Meeting
1 1 1 1 1 1 1 Figure. Loading configuration for Tests and These figures served as the primary physical test information used to calibrate the LPILE models. The string pot deformation data was checked against inclinometer data, which was used as an absolute reference when combining information from Tests 1,, and. The data plotted for Tests and were offset based on the difference in inclinometer readings taken at the end of the previous test and the beginning of the test for which the data was plotted. Additional observations can be made in addition to the general trend of the data. Little to no permanent accumulation of deformation was observed for cyclic loading of the shafts at 00 kips or lower. Accumulation of deformation was significantly greater at the 0 kip loading increment than for the kip loading increment. The south shaft deformed significantly more than the north shaft under the same loading, reaching a deformation of nearly 0. inches after cycling at 0 kips while the north shaft had a deformation of approximately 0. inches at the same point. This was likely due to natural material variability; however there was a road cut that was present approximately 0 feet behind the south shaft in the direction of loading which could have made it possible for sliding along a weak plane to have occurred in that direction. TRB 0 Annual Meeting
0 00 Accumulated deformation during repeated loading 00 Load (kips) 00 00 00 Test 1 Test Test 1 0 0 0.1 0. 0. 0. 0. 0. Deflection (inches) Figure. Deflection with loading of the north shaft. ft above ground (upper string pot) 0 00 Accumulated deformation during repeated loading 00 Load (kips) 00 00 Test 1 Test Test 00 0 Deflections are negative because the direction of movement is opposite of movement for the south shaft -1. -1.1-1 -0. -0. -0. -0. -0. -0. -0. -0. -0.1 0 Deflection (inches) Figure. Deflection with loading of the south shaft. ft above ground (upper string pot) TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 0 1 For the north shaft there was no permanent deformation between Tests 1 and, and there may have been a small rebound between testing events. However, during Test the shaft behaved as if it had a lower modulus in the early stages than it had during Test 1, but then stiffened when loading exceeded 00 kips. For the south shaft this behavior was reversed. The shaft experienced a small permanent deformation as a result of Test 1 and had a higher modulus during reloading up to kips. The behavior of the south shaft is consistent with the loading of many geomaterials, where it would be expected that some permanent deformation would be made to the material during the initial loading, and during repeated loadings the geomaterial would have elastic behavior with a higher modulus in that loading range. The mechanics behind the behavior of the north shaft are not well understood, but it may have gradually rebounded to its original position under small lateral earth pressures; then quickly moved past its maximum deformation level from Test 1 (0 kips) under loading of only 00 kips in Test. Behavior during Cycling Cyclic loading (load reversal) was applied at loads of 0, 00 and 00 kips for five cycles each during Test 1. Ten cycles were applied for a load of 00 kips. For Test the load frame was reconfigured for repeated loading where loads were applied and released in the same direction for cycles at loads of and 0 kips. This data is presented for the top string pot on the south shaft in Figure, except for two cycles at 00 kips which were not recorded. Similar accumulating deformations for high loads were also observed for the north shaft. Figure shows more detail for the deformations for the cyclic loading of the north shaft. For this figure the deformation was reset to zero at the beginning of each set of cycles. The nearly constant amplitude for each set of cycles shows there was no significant increase in movement of the shaft during cycling for loads up to 00 kips. Deformations with Depth Shaft deflections were monitored with depth using inclinometer measurements. The inclinometer casings were installed inline with the loading direction and show that while the shafts were relatively rigid for early loading, they experienced more significant bending at higher loads. The inclinometer readings from Test are shown in Figure. TRB 0 Annual Meeting
Load (kips) 00 00 00 00 00 00 00 00 0 accumulated deformation during repeated loading tight grouping of points shows elastic behavior during cycling cycle 1 cycle cycle cycle cycle cycle cycle cycle cycle cycle 1 0-0. -0. -0. -0. -0. -0. -0. -0.1 0 Deflection (inches) Figure. South shaft accumulated deformation with cyclic and repeated loading. ft above ground (upper string pot) Deformation from Cycle Starting Point 0.0 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0 kips 00 kips 00 kips 00 kips 0 00 00 00 00 00 Data Counter Figure. North shaft elastic behavior with cyclic loading at lower loads. ft above ground (upper string pot) TRB 0 Annual Meeting
- Deflection (inches) 0 0. 0. 0. 0. Deflection (inches) -0.0 0 0.0 0.1 0.1 0. 0. - - - -1-1 1 Depth below ground level (ft) 0 1 Ground End Test 1-0 load Test - 0 load 0 1 kip kip 0 kip 0 kip End Test - 0 load Ground End Test 1-0 load Test - 0 load kip kip 0 kip 0 kip End Test - 0 load Figure Inclinometer deflection with depth for test (south shaft left, north shaft right) 1 TRB 0 Annual Meeting
LPILE MODELING Modeling Parameters The rock-socket test data was modeled using the commercial program LPILE for the purpose of identifying the appropriate Reese p-y modeling parameters for limestone. The weak rock model contained within LPILE combined with a Type analysis, which considers non-linear bending, was used for the analysis. Properties used in the modeling are presented in TABLE. TABLE LPILE Modeling Parameters Shaft Properties Shaft diameter Shaft length below ground (north shaft) Shaft length below ground (north shaft) Height of load application above ground Concrete strength longitudinal reinforcement Distance from pile top (point of loading) to ground surface Yield stress of steel Steel modulus inches feet feet 1 foot 00 psi 1 - # bars 1 inches 0,000 psi,000,000 psi Rock Properties Upper Layer Lower Layer Intact rock strength psi 0 psi Intact rock modulus 0 ksi 0 ksi k rm 0.000 0.000 1 1 1 Once the geometry and reinforcement of the shaft are determined, there are only two remaining parameters that must be selected by the modeler. The value of k rm is adjustable; and the value of 0.000 that was used is within the recommended range (). There also may be some justification for reducing the rock modulus because the interim Reese criteria may not fully 1 TRB 0 Annual Meeting
1 1 1 1 1 account for the lower modulus of the rock mass as compared with the modulus of the intact rock samples as described in the next section. Discussion of Modeling When fitting the load-deformation curves generated within LPILE to the load test data, an adjustment was required to account for the accumulated deformation that occurred during repeated loading. This was addressed by shifting the LPILE curves by the amount of the accumulated deformation. These LPILE curves are plotted with the field test data in Figures and. These figures show that a relatively good fit is obtained between the weak rock LPILE model and the field test data with regard to the nominal resistance and ultimate pile head deformations, with the nominal model resistance being within about % of the observed ultimate load for both shafts. A selection of actual p-y curves generated within LPILE is presented in Figure. These p-y curves apply to both shafts. The model results predict the shafts reaching maximum moment and failing near 00 kips with nearly all bending above a depth of three feet. Lengthening the shafts has minimal impact on model resistance or pile head deflections. 0 00 Adjustments of model for permanent deformations from repeated loading load (kips) 00 00 00 00 LPILE with permanent deformations north shaft 1 1 1 0 0 0. 0. 0. 0. 1 deflection (inches) Figure. LPILE model and load test data for the north shaft. ft above ground (upper string pot) 1 TRB 0 Annual Meeting
0 00 Adjustments of model for permanent deformations from repeated loading 00 load (kips) 00 00 00 LPILE with permanent deformations south shaft 1 0-1. -1-0. -0. -0. -0. 0 deflection (inches) Figure. LPILE model and load test data for the south shaft. ft above ground (upper string pot) Depth Figure. p-y curves using the intact rock modulus, produced using LPILE () 1 TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 0 1 The model did predict somewhat less deformation than was observed in the working load range, particularly for the south shaft (Figure ). It also predicted that nearly all rock movement and shaft bending would occur in the top three feet of the socket, while inclinometer measurements show some movement all the way to the bottom of the sockets. This may have occurred because the model used does not fully account for a reduction in the modulus of the rock mass compared with the intact rock modulus; and to a degrading of the modulus and accumulation of deformation from the cyclic and repeated loading. Reducing the rock modulus used in the model by a factor between one and two orders of magnitude for the north shaft and slightly more for the south shaft improved the match in the working range, did not affect the nominal model resistance significantly, and eliminated the need to include offsets for the accumulating deformations from cyclic and repeated loading. CONCLUSIONS AND RECOMMENDATIONS Two -inch diameter drilled shafts constructed in short rock sockets in weak rock were laterally loaded to failure. Cyclic and repeated loading steps were conducted for a series of load steps prior to failure. The following conclusions were drawn from the field data. The nominal resistance of both rock sockets was approximately 1,000 kips. The nominal resistance was reached at approximately 0. inches of lateral movement for the north shaft and 0. inches for the south shaft. Both of these deformation values include deformation that accumulated during periods of repeated loading. Maximum deformations for static load test conditions would likely have been less. Deformations for the south shaft were likely due to material variability, but may have been affected (increased) by the presence of a road cut approximately 0 feet behind the shaft. The shafts behaved in an elastic manner for five cycles of loading at 0, 00 and 00 kips (0% of ultimate load) and cycles at 00 kips. The shafts experienced permanent, accumulating deformations for repeated loading at kips (approximately 0% of nominal capacity), and even greater deformations at 0 kips. The resulting field data was modeled using the interim Reese weak rock model included within the commercial software LPILE. The following conclusions were developed based on the modeling. The nominal resistance and ground line deformations of the rock sockets could be modeled reasonably well using the weak rock model contained within LPILE. Predicted 1 TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 0 1 nominal resistance was within percent of field measurements and the slope of the load-deformation curve (modulus) was consistent with field data when accumulated deformations were accounted for. For this model, most of the data to be entered is driven by the material properties and geometry, which makes construction of the model very straightforward. The authors used a value of 0.000 for k rm, which is the upper end of the recommended range. Based on these conclusions, the following preliminary recommendations are made for modeling of limestones. They are considered preliminary because they are based on a single test program and should be updated as more data becomes available. Use of the weak rock model included within LPILE for modeling short rock sockets is supported by the observations from this research. Within this model it is recommended that a value of 0.000 be used for k rm if no other information is available. It is also recommended that for cyclic or repeated loading design where the number of cycles is expected to be relatively small (i.e. extreme events), the limestone can be considered elastic for loads of less than 0% of the nominal resistance. If the intact rock modulus is the basis for selecting the rock modulus value used in LPILE, use of a reduced value may be warranted to more accurately model shaft bending and deformations in the working range. ACKNOWLEDGEMENTS The authors wish to thank the people of the Kansas Department of Transportation for their financial and logistical support that made this research possible. We particularly want to thank the people of the KDOT Geotechnical Unit and KDOT Maintenance for their help in bringing this project to fruition. We also wish to thank Mr. Jim Weaver of the University of Kansas (KU) for his help in designing and fabricating the equipment and Mr. Justin Clay of KU for his help in fabrication of the equipment for Test 1 and with some of the theoretical background presented in this paper. We also wish to thank Mr. Paul Axtell and Dan Brown of Dan Brown and Associates, who helped with the testing and interpretation of data. The help of all who participated is greatly appreciated. 1 TRB 0 Annual Meeting
1 1 1 1 1 1 1 1 0 1 REFERENCES 1. Parsons, R.L., I. Willems, M.C. Pierson, and J. Han. (0). Lateral Capacity of Rock Sockets in Limestone under Cyclic and Repeated Loading. Kansas Department of Transportation. p.. Reese, L.C., S.T. Wang, W.M. Isenhower, and J.A. Arrellaga (00). LPILE Plus.0 for Windows, A Program for the Analysis of Piles and Shafts Under Lateral Loads. Technical Manual. Ensoft, Inc. Austin TX.. Reese, L.C. (1). Analysis of Laterally Loaded Piles in Weak Rock. Journal of Geotechnical and Geoenvironmental Engineering. ASCE. Reston, Virginia. v1 n. -1.. Cho, K.H., S.C. Clark, B.D. Keany, M.A. Gabr, and R.H. Borden. (001). Laterally Loaded Drilled Shafts Embedded in Soft Rock. Soil Mechanics. Transportation Research Record. Journal of the Transportation Research Board. n1. Transportation Research Board. Washington D.C. -.. Gabr, M.A., R.H. Borden, K.H. Cho, S. Clark, and J.B. Nixon. (00). P-y Curves for Laterally Loaded Drilled Shafts Embedded in Weathered Rock. North Carolina Department of Transportation. FHWA/NC/00-00. p.. Goodman, R.E. (1). Introduction to Rock Mechanics, nd ed. John Wiley and Sons. New York. p.. Pierson, M.C., R.L. Parsons, J. Han, D. A. Brown, and W.R. Thompson. (00). Capacity of Laterally Loaded Shafts Constructed Behind the Face of a Mechanically Stabilized Earth Block Wall. Kansas Department of Transportation. Report KU-0-. p. 1 TRB 0 Annual Meeting