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PAGE 1 Analysis of Statnamic Load Test Data Using a Load Shed Distribution Model by Sonia L. Lowry A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: A. Gray Mullins, Ph.D. Rajan Sen, Ph. D. Abla Zayed, Ph. D. Date of Approval: June 28, 2005 Keywords: unloading point, drilled shaft, capacity, side shear, deep foundation Copyright 2005 Sonia Lowry PAGE 2 Acknowledgments I would like to thank Applied Foundation Testing Incorporated (AFT, Inc.) for their support of this project. AFT, Inc. both funded my work and allowed use of their testing program for the case study presented. I would also like to thank Dr. Gray Mullins for allowing me to work with him on this project and continually answering my questions. It has been a wonderful experience to learn from and work with him. And finally, I would like to thank my husband, Dayv Lowry, for all of his love and support while I have been working on both an undergraduate and graduate degree at USF and pursuing a career as a professional engineer. PAGE 3 i Table of Contents List of Tables..........................................................iii List of Figures.........................................................iv Abstract.............................................................vii 1.0 Introduction .........................................................1 1.1 Origin of Thesis ................................................1 1.2 Organization of Thesis ...........................................5 2.0 Background .........................................................7 2.1 Deep Foundations ..............................................7 2.1.1 Design ................................................7 2.1.2 Load Testing ...........................................9 2.2 Approved Load Tests ...........................................11 2.2.1 Static Load Test .......................................11 2.2.2 Dynamic Load Test .....................................12 2.2.3 Rapid Load Test .......................................12 2.3 Statnamic Device ..............................................13 2.4 Regression Methods ............................................14 2.4.1 Unloading Point Method (UPM) ..........................15 2.4.2 Signal Matching .......................................16 2.4.3 Modified Unloading Point Method (MUP) ..................17 2.4.4 Segmental Unloading Point Method (SUP) ..................17 2.5 Applicability of Statnamic Regression Methods ......................18 2.6 Limitations to the Above Methods ................................19 3.0 Approach ..........................................................22 3.1 General ......................................................22 3.2 Side Resistance ...............................................23 3.3 Tip Resistance ................................................25 3.4 Weighted Unloading Point Method (WUPM) ........................25 3.4.1 Preliminary Steps ......................................26 3.4.2 Side Shear Prediction ...................................27 3.4.3 Toe Segment ..........................................29 3.4.4 Final Steps ............................................29 PAGE 4 ii 4.0 Case Study .........................................................32 4.1 Load Test Site ................................................32 4.2 Test Shaft Construction .........................................33 4.3 Statnamic Test and SUP Analysis .................................33 4.5 Determination of Characteristic Side Shear Equations .................34 5.0 Results ............................................................39 5.1 Input Parameters ..............................................39 5.2 Forward Model and Weighted Unloading Point (WUP) ................40 5.2 Comparison to the Segmental Unloading Point Results ................41 5.3 Determination of Accurate Ultimate Static Capacity ..................42 5.4 Forward Model and WUP Using Design Values ......................43 5.4.1 Ultimate Capacity and Segment Distribution Factors ..........43 5.4.2 Initial Results .........................................44 5.4.3 Modifications to Improve Results ..........................45 5.5 Affects of Variation in Distribution Factors .........................45 6.0 Conclusions and Recommendations .....................................59 6.1 Conclusions ..................................................59 6.1.1 Advantages of the Forward ModelWeighted Unloading Point Method.............................................59 6.1.2 Disadvantages of WUPM ................................61 6.2 Recommendations .............................................61 References............................................................63 Appendices............................................................65 Appendix A Development of SSM for a Hyperbolic CapacityDisplacement Curve....................................................66 Appendix B Derivation of VelocityDependant Damping Forces............70 Appendix C Test Site Information....................................72 Appendix D Varying Distribution Factor Demonstration..................75 PAGE 5 iii List of Tables Table 21 Methods to Determine Side Resistance for Drilled Shafts (AASHTO, 2003) ................................................................8 Table 22 Methods to Determine Tip Resistance for Drilled Shafts (AASHTO, 2003)..8 Table 23 Allowable Resistance Factors (FDOT, 2005) .........................10 Table 24 Data Input Compared to Ou tput for Statnamic Regression Methods .......19 Table 51 Maximum static capacity values from each regression method ...........41 PAGE 6 iv List of Figures Figure 11 Data Regression Results Compared to Instrumentation at the Time of Load Testing..........................................................6 Figure 21 Discretization of a Deep Foundation into Two Segments ...............21 Figure 31 Flowchart for Proposed Forward Model and Weighted Unloading Point ...31 Figure 42 Load Transfer Curve Generated by SUPERSAW....................36 Figure 41 Segmental Side Shear Contributions Generated by SUPERSAW........36 Figure 43 Actual and Predicted Side Shear for Segment 1......................37 Figure 44 Actual and Predicted Side Shear for Segment 2......................37 Figure 45 Actual and Predicted Side Shear for Segment 3......................38 Figure 51Load Transfer Curve Showing Segmental Contributions to Capacity......47 Figure 52 Static Capacity and Statnamic Force from FMWUP..................47 Figure 53 Segment and Weighted Accelerations Using Forward Model ............48 Figure 54 Static Capacity Determin ed from Different Regression Methods .........48 Figure 56 Forces Transferred Through the Cervantes Test Shaft .................49 Figure 55 Static Capacity at Various Elevations of the Cervantes Test Shaft........49 Figure 57 Displacement at the Top of Segment 2 .............................50 Figure 58 Displacement at the Top of Segment 3 .............................50 Figure 59 Displacement at the Toe of the Shaft ..............................51 Figure 510 Displacement Distribution for a Predicted Capacity of 8900 kN ........51 PAGE 7 v Figure 511 Displacement for Predicted capacity of 17800 kN (200%) .............52 Figure 512 Displacement for Predicted Capacity of 11125 kN (125%) ............52 Figure 514 Displacement for Predicted Capacity of 4450 kN (50%) ..............53 Figure 513 Displacement for Predicted Capacity of 2225 kN (25%) ..............53 Figure 515 Segmental Capacity Contributions from Shaft123...................54 Figure 516 Displacement Distribution Using Load Shed Model ..................54 Figure 517 Forces Transferred Through the Test Shaft Using Load Shed Model .....55 Figure 518 Acceleration Using Load Shed Model .............................55 Figure 519 Total Capacity Predicted Using Load Shed Model and SAW...........56 Figure 520 Increasing Predicted Static Capacity to Match SAW Results...........56 Figure 521 Affects of Varying the Top Segment Distribution Fraction............57 Figure 522 Affects of Varying the End Bearing Distribution Fraction.............57 Figure 523 Affects of Varying the Toe Segment Distribution Fraction.............58 Figure 524 Affects of Varying the Intermediate Segment Distribution Fraction......58 Figure A1 %D Versus SSM from SUPERSAW Results for Segment 2............68 Figure A2 Linear Portion of %D Versus %D/SSM, Showing Equation............68 Figure A3 SSM from SUPERSAW Results and Fitted Curve ....................69 Figure B1 Static Force Multiplier, a, Used to Determine the Damping Forces .......71 Figure C1 Boring Log for the Cervantes Bridge Test Shaft......................72 Figure C2 Part 1 of the Cervantes Test Shaft Drilling Log ......................73 Figure C3 Part 2 of the Cervantes Test Shaft Drilling Log ......................74 Figure D 1 FMWUP Results for Distribution Fractions from Shaft123............77 PAGE 8 vi Figure D2 Effect of Increasing Ultimate Capacity .............................77 Figure D3 Effect of Increasing the Top Segment Distribution Fraction............78 Figure D4 Effect of Increasing End Bearing Distribution Fraction................78 Figure D5 Effect of Second Increase to Top Segment Distribution Fraction ........79 Figure D6 Effect of Decreasing the Segment 2 Distribution Fraction..............79 PAGE 9 vii Analysis of Statnamic Load Test Data Using a Load Shed Distribution Model Sonia L. Lowry ABSTRACT In the field of civil engineering, par ticularly structural foundations, lowcost options and time saving construction methods are important because both can be a burden on the public. Drilled shafts have proven to both lower cost and shorten construction time for largescale projects. However, their integrity as loadcarrying foundations has been questioned. The statnamic load test was conceived in the 1980s as an alternative method of testing these larger, deeper foundation elements. Performing a load test verifies that the load carrying capacity of a foundation is agreeable with the estimated capacity during the design phase and that no significant anomalies occurred during construction. The statnamic test, however, is cl assified as a rapid load test and requires special data regression techniques. The outcome of available regression techniques is directly related to the available instrumentation on the test shaft. Generally, the more instrumentation available, the more complete results the regression method will produce. This thesis will show that a proposed method requiring only basic instrumentation can produce more complete results using a predictive model for side shear development with displacement during the statnamic test. A driven pile or drilled shaft can be discretized into segments based on the load shed distribution model. Each segment can be analyzed as a rigid body. The total static capacity is then the summation of each segments contribution. Further, a weighted acceleration can be generated and us ed to perform an unloading point analysis. PAGE 10 1 1.0 Introduction 1.1 Origin of Thesis Design engineers in any field of engineer ing are constantly challenged to satisfy factors such as quality, safety, cost, constructibility, aesthetics, and more. There are too many factors for all of them to be considered for each project. As a result, a select few are chosen for optimization during the course of design. The optimized factors vary depending on the market for the project, including who will utilize it and who will pay for it. For example, in biomedical engineering, projects are designed to improve the quality and longevity of life. As such, cost is not always an issue but safety and quality are important. In aerospace engineering, because safety is important but can lead to unrealistic designs, material properties and quality may become more important while safety is maintained at a minimal level. Civil engineering projects, however, are often funded by taxpayer dollars, which requires cost to be a top priority. Additionally, both private and public funded civil engineering projects may become so large based on currently accepted standards that they reach ridiculous costs. Due to the potential enormity of projects, cost optimization is paramount for all civil engineering projects. As a result, methods to reduce the quantity of material used for construction but maintain acceptable loadbearing capacities are desirable. These methods often include but are not limited to: 1) newer, higher strength materials, 2) innovative geometries, and 3) reliable verificati on of a structural elements performance. PAGE 11 2 Verification of a structural elements perf ormance is highly material dependant. While steel is relatively reliable in its material properties, concrete and soil are less reliable due to difficulties with quality assurance and variability, respectively. In spite of the well understood relationships governing concrete strength and its constituent chemistry, concrete strength is periodically verified via concrete cylinder tests conducted on a representative sample of concrete (ASTM C39). This is done to note the effects of anomalies resulting from batching errors, trucking complications, adverse environmental conditions, or other potentially harmful factors. As a result of regular testing and understanding of the effect of external factors, concrete can be reliable. Soil variability and constructionrelated geotechnical effects, however, are not as well understood. Questions concerning quality assurance during construction have also arisen due to newer, faster construction methods that may potentially degrade the foundation (Tchepak, 2000). Numerous methodologies have been implemented to remove the associated uncertainties. These can be divided into two categories: preconstruction soil investigation and postconstruction performance verification in the form of load testing. Advances in the latter has lead to this thesis topic in the area of new load testing systems and associated data regression. Load testing is performed on deep foundations to verify that the expected capacity is comparable to the actual capacity after construction. A successful load test removes uncertainties associated with concretesoil interaction and demonstrates the reliability of the construction. Performing load tests allows designers to take advantage of higher resistance factors or lower safety factors because the structural performance will have PAGE 12 3 been verified. This means that more of the expected capacity is usable for design. There are three categories of deep foundation load testing: static, rapid, and dynamic. Given that deep foundations are continually increasi ng in size with the and capacity with the structures that they support, they often exceed the limitations of static and dynamic testing, bringing about the need for new testing methods. Static testing can be very expensive and timeconsuming. Dynamic testing was designed for use while driving piles and can cause significant damage to foundations; it has not been widely accepted in the foundation testing industry for drilled shaft testing (Bermingham, 2000). Statnamic load testing, a type of rapid load test, was developed by Berminghammer Foundation Equipment and The Netherlands Organization (TNO) in 1988. The statnamic test is executed by launching a reaction mass from the top of the foundation using an accelerant. The corresponding load on the foundation is equal and opposite that acting on the accelerated mass. Statnamic testing allows one of the higher resistance factors, thus it is important that the test evaluation produce adequate and reliable values for static capacity. Several methods are currently used to evaluate statnamic test data. All methods provide a way to remove the dynamic forces from the applied statnamic force to determine the static capacity. Static capacity can be given as a total resisting force or a summation of contributing resisting forces. The report of static capacity from a load test regression is directly related to the amount of data available and utilized in the analysis. In general, more types of data obtained during the test will lead to more information contained in the results, as demonstrated by Figure 11. For example, when only top of pile measurements are available, only total static capacity can be determined from current PAGE 13 4 regression methods. However, when data has been collected from embedded strain gages and/or accelerometers in conjunction with top of pile measurements, static capacity can be summarized as the load carrying contributions from various soil strata as well as end bearing. In addition to output and data collection limitations, none of the current methods for statnamic regression take advantage of available insitu soil data that is available from site tests such as the standard penetration test (SPT) or cone penetration test (CPT). Comparing the insitu conditions to the test results can demonstrate the suitability of the results, but is not part of the analysis methods. In addition to the beneficial use of higher resistance factors, load testing may be necessary when a constructed drilled shaft or driven pile is deemed questionable in its capacity to carry the required load. Load testing can be used to show whether the capacity has been compromised during construction. For example, capacity may be compromised by anomalies created during the concrete pour or possible depreciation of side shear when bentonite drilling mud is used (Tchepak, 2000). Because this decision may be based on knowledge gained during or after construction, embedding strain gages is not practical. Therefore, the data in such situations is limited to only topofpile measurements, excluding more advanced regression methods. A new method, proposed in this thesis, is designed for use when only topofpile data is available. It will consider the insitu conditions and development of side shear as it depends on soil strata. This new method will also allow for nonrigid behavior of a foundation during statnamic load testing. PAGE 14 5 1.2 Organization of Thesis The presentation of the proposed statnamic regression method will be organized into several chapters. Chapter 2 will present the statnamic load test in detail and available analysis methods. It will discuss the required instrumentation and knowledge for each type of regression as well as the caliber of results. The next chapter, Chapter 3, will discuss the proposed method conceptually and its applicability to foundation testing. Chapter 4 will focus on the load test data used to develop the proposed method. In this chapter, the test site will be described using insitu conditions and results from a segmental analysis using embedded strain gages (Winters, 2002). The results from the newest regression will be covered in Chapter 5, including a comparison to the segmental results. Finally, conclusions and recommendations will be presented in the last chapter. PAGE 15 6 Figure 11 Data Rregression Results Compared to Instrumentation at the Time of Load Testing PAGE 16 7 2.0 Background 2.1 Deep Foundations Deep foundations consist of driven piles or drilled shafts that transfer loads to soil or rock below a structure by end bearing, adhe sion or friction, or a combination of those. Typically, the Load and Resistance Factor Design (LRFD) method is used for new foundations. The LRFD method applies a resistance factor to the ultimate capacity when determining the available design capacity, as well as applying a safety factor to the design loads. To aid in cost and waste reduction, deep foundations may be tested to increase the resistance factor. Testing makes more of the ultimate capacity available to carry the design loads and can help decrease the size and/or depth of the foundation. 2.1.1 Design The basic equation accepted by AASHTO for determining ultimate capacity of a deep foundation is: Equation 2.1qqqTSP where qT is the total capacity, qS is the maximum side resistance, and qP is the maximum tip resistance. Design values for driven pile capacity are determined as a combination of soil properties and pile load tests. A drilled shafts ultimate design capacity is determined by any of several methods approved by AASHTO for calculating both side and tip resistance. A full list of these methods is shown in Table 21 for side resistance PAGE 17 8 and Table 22 for tip resistance. Methodologi cal preference is typically based on the type of soil and the experience of the designer. Table 21 Methods to Determine Side Resistance for Drilled Shafts (AASHTO, 2003)Estimating Side Resistance in Sands Touma and Reese (1974) qs = K v tanff < 2.5 TSF for which: K = 0.7 for Db 25.0 FT K = 0.6 for 25.0 FT < Db 40.0 FT K = 0.5 for Db > 40.0 FT Meyerhof (1976)qs = N/100 Quiros and Reese (1977)qs = 0.026N < 2.0 TSF Reese and Wright (1977)for N 53: qs = N/34.0 for 53 < N 100: qs = (53)/450 + 1.6 Reese and ONeill (1988) qs = v 2.0 TSF for 0.25 1.2 for which: = 1.5 0.135 zTable 22 Methods to Determine Tip Resistance for Drilled Shafts (AASHTO, 2003)Estimating Tip Resistance Touma and Reese (1974)Loose: qP(TSF) = 0.0 Medium Dense: qP(TSF) = 16/k Very Dense: qP(TSF) = 40/k!k = 1 for DP < 1.67 FT !k = 0.6 DP for DP 1.67 FT!Applicable only if DP > 10D Meyerhof (1974)qP(TSF) = (2NcorrDb)/(15DP) < (4/3)Ncorr for sand < Ncorr for nonplastic soils Reese and Wright (1977)qP(TSF) = (2/3)N for N 60 qP(TSF) = 40.0 for N > 60 Reese and ONeill (1988)qP(TSF) = 0.6N for N 75 qP(TSF) = 45.0 for N > 75Side resistance varies with the soil properties, such as SPT blowcount (N), friction angle ( ), and vertical effective stress ( v ) for drilled shafts in sands. It reaches its maximum value after a relatively small displacement, approximately 1% of the PAGE 18 9 diameter of the shaft ( Bruce, 1986). Tip resistance depends primarily on the diameter at the base and the SPT blowcount of the soil around and below the shaft. Maximum end bearing develops at displacements equal to approximately 5% of the diameter of the shaft (Reese and Wright 1977, Reese and ONeill 1988). After the ultimate capacity of a foundation element has been determined, it must be reduced by a resistance factor, as governed by AASHTO design specifications. Currently, this factor ranges from 0.45 to 0.65 without a load test, depending on the design method and soil properties (AASHTO, 2003). However, when a load test is performed and the ultimate capacity is verified, the resistance factor may be increased. 2.1.2 Load Testing Load testing of deep foundations is divided into three categories: static, rapid and dynamic. Each test is very different in how it affects the foundation element, which will be discussed in the following section. Although there are significant differences in the load test options, AASHTO allows a resistance factor of 0.80 to be used if any load test has been performed. Individual states, however, may institute their own guidelines. In Florida, the resistance factor depends on both the type of load test performed and the design method, as summarized in Table 23. PAGE 19 10 Table 23 Allowable Resistance Factors (FDOT, 2005)Drilled Shafts (Bridge Foundations) LoadingDesign Method Construction QC Method Resistance Factor, Compression For soil: FHWA alpha or beta method1Std Specifications0.60 For rock socket: McVays method2neglecting end bearing Standard Specifications 0.60 For rock socket: McVays method2including 1/3 end bearing Standard Specifications 0.55 For rock socket: McVays method2including 1/3 end bearing Statnamic Load Testing 0.70 For rock socket: McVays method2including 1/3 end bearing Static Load Testing0.75 Uplift For soil: FHWA alpha or beta method1Std SpecificationsVaries1For rock socket: McVays method2Std Specifications0.50 Lateral3FBPier4Std Specifications or Lateral Load Test51.00 Piles (All Structures) LoadingDesign Method Construction QC Method Resistance Factor, CompressionDavisson Capacity PDA (EOD)0.65 Static Load Testing0.75 Statnamic Load Testing 0.70 Uplift Skin Friction PDA0.55 Static Load Testing0.65 Lateral (Extreme Event) FBPier4Standard Specifications 1.00 Lateral Load Test51.00 1. Refer to FHWAIF99025, soils with N<15 correction suggested by ONeill. 2. Refer to FDOT Soils and Foundation Handbook 3. Extreme event. 4. Or comparable lateral analysis program. 5. When uncertain conditions are encountered. PAGE 20 11 2.2 Approved Load Tests As stated earlier, there are three categories of accepted load tests. Several factors, such as test duration and material type, determine the selection of a specific load test. One load test may also be preferable due to the resistance factor desired for determining design capacity. The three types of load test are very different and each has its benefits and limitations. 2.2.1 Static Load Test Static compressive load testing involves the placement of a large, stationary load on top of a foundation element. It is then left for a specified length of time and settlement is recorded. The static load test is administered following ASTM D114381, and these guidelines inherently create restrictions on the testable size and capacity. One major limitation of the static test is the proximity restrictions of reaction piles or anchors which is determined by the diameter of the test pile. According to the test standard, the reaction anchors should be placed no closer than five diameters of the test pile to minimize the interference in zones of influence. As a result, larger shafts would require very long clear span reaction beams. For example, a 6' diameter drilled shaft would require a 60' reaction beam (five diameters away on either side). Further, the reaction beam would need to resist even larger loads. A 1500 ton static load is a practical upper limit with extreme cases of up to 3500 tons. Supplying and placing such a beam and load combination increases the cost of the test. Such tests would require weeks of preparation, which further increases the cost. PAGE 21 12 2.2.2 Dynamic Load Test Dynamic testing is usually associated with driving piles ( ASTM D494500). When it is applied to drilled shafts, it is termed a drop hammer test. Therein, a steel mass is dropped from a prescribed distance in order to impart a sufficient force. The impact induces tensile stresses that are not well tolerated by drilled shafts constructed of reinforced concrete. This type of test is best when applied to driven piles made of steel, wood, or prestressed concrete. Concrete piles have not always used prestressed concrete, however, the reinforced concrete counterparts were heavily reinforced (~2% steel), far exceeding the reinforcement of typical drilled shafts (~1% steel). A dynamic load test has a very short duration, lasting as little as 5 milliseconds as defined by ASTM. In order to use the results, there must be a visible return of the stress wave to the surface in the recorded data (Middendorp and Van Foeken, 2000). 2.2.3 Rapid Load Test Rapid load tests do not induce tensile stresses and have minimal to no wave effects due to the duration of the load test. However, rapid tests do induce an acceleration to the entire foundation mass, which in turn requires proper evaluation techniques. The statnamic load test is a type of rapid load test based on its duration, usually lasting 100250 milliseconds (Lewis, 1999). The ASTM standard for this test is still in the drafting process; it will be similar to the test standard proposed by the Japanese Geotechnical Society (Janes et al, 2000). PAGE 22 13 2.3 Statnamic Device The statnamic test device was created by Berminghammer Foundation Equipment in cooperation with The Netherlands Organization (TNO) in the 1980s. The statnamic device consists of a piston, silencer, reaction masses, and a catch mechanism. Fuel pellets are placed into the piston and ignited within the silencer/cylinder. As pressure builds inside the combustion chamber, the piston and cylinder separate, which causes the attached reaction masses to move upward approximately three to five meters. When the masses begin to come back down, they are caught in one of several types of catching mechanisms (Stokes, 2004). The upward force on the reaction masses is an equal and opposite reaction to that on the foundation, according to Newtons second law. Due to the nature of this test, the duration is longer than that of a dynamic test and shorter than a static load test. This affects how the compression wave travels through the foundation. This is characterized by the wave number, NW, which is determined by the stress wave velocity ( c ), the load duration or period (T), and the length of the foundation (L). Equation 2.2 N cWT LHistorically, the wave number for a statnamic test ranges between 12 and 50. This is derived from a load duration of ~100 ms and pile length ranging from 8 33 m (concrete) or 20 42 m (steel). For a dynamic test, it will be less than 6; for a static test, it will be greater than 1000. If the wave number falls below the acceptable range for a statnamic test in the case of a long pile, the induced stress waves need to be accounted for in the analysis (Middendorp and Bielefeld, 1995). PAGE 23 14 Because the statnamic test differs from a dynamic and static load test, it is important to fully understand the behavior of a foundation during the test. In the late 1990s, research groups around the world began performing statnamic tests along side dynamic and static load tests and evaluating the results (Bermingham, 1998). As the behavior of the foundations under a statnamic load was described and characterized by wave number, regression methods were developed to extract the usable static capacity from test measurements under the given foundation parameters. 2.4 Regression Methods There are four current methods used to analyze statnamic test data and determine the static capacity of a drilled shaft or pile. These methods are: the unloading point method, signal matching, modified unloadi ng point, and segmental unloading point. Each regression method requires different in strumentation and produces various output. The following sections will discuss the history of each method and its use in the current statnamic testing industry. For all methods of regression, there is basic instrumentation required on the foundation during the test. This includes transducers to measure the statnamic force and record the foundation movement as time histories. The statnamic force is usually determined from a load cell containing multiple resistance type strain gages. The foundation motion may be measured by either an accelerometer or laser sensor. The laser sensor is used to quantify displacement. If acceleration is known, velocity and displacement can be found by integration. If displacement is known, velocity and acceleration can be determined through differentiation. If both acceleration and PAGE 24 15 displacement are known, one can be used to verify the other. A foundation during a statnamic test is typically modeled as a lumped mass, spring, and dashpot system because of its dynamic components. In addition to having some amount of static capacity, the foundation also has some inertial and damping resistance to the statnamic load (FSTN). The basic equation for analysis is Equation 2.3FkxSTN cvmawhere k is a spring constant, c is the damping coefficient, and m is the mass. The displacement, velocity, and acceleration are represented as x, v and a respectively. In that equation, kx represents the displacement dependent static capacity, cv is a velocity dependant damping force, and ma is the measurable inertial component. The displacement, velocity, acceleration, and mass of the foundation element can be determined from field measurements. However, k and c remain unknown and the governing equation is underspecified. Each of the following regression methods present a different approach to solve this equation. 2.4.1 Unloading Point Method (UPM) The unloading point method (UPM), was proposed in 1992 by Peter Middendorp to provide a means by which to solve the underspecified equation. He observed that foundations behaved more similarly to those under static loading than dynamic loading. During the load test, there is a point at which the velocity of the pile is zero (the point of unloading). The damping force at this instance is thus equal to zero. This reduces Equation 2.3 to: Equation 2.4FkxSTN ma PAGE 25 16 It is also assumed that the pile behaves rigidly and can be modeled as a simple spring and lumped mass system. After analyzing many Statnamic tests, Middendorp found that the ultimate static capacity was equal to the load at the time of zero velocity (Middendorp, 1992). He also determined that the damping coefficient could be determined between the time of maximum statnamic force and the unloading point. This method was widely accepted and is still used when conditions allow. A software package was developed at the University of South Florida in 1999 to automate the UPM analysis. It is a macrodriven Microsoft Excel application titled Statnamic Analysis Workbook, or SAW. This application allows the user to input statnamic test results, perform a UPM analysis, and output ultimate static capacity. SAW was developed for use when the foundation can be assumed to behave rigidly and modeled as a spring and mass system (Garbin 1999). This software is free and can be downloaded for use from http://www.eng.usf.edu/%7Egmullins/downloads 2.4.2 Signal Matching (SM) Signal matching techniques are typically used to evaluate dynamic load tests. They have also been used to analyze statnamic load tests. In the signal matching process, a foundation element is modeled with the soil behaving as a spring and dashpot. The soil is modeled as an inner and outer layer where the outer layer surrounds the inner layer and the inner layer is in contact with the foundation. The outer layer parameters, stiffness and damping, are independent of the load while the inner layer parameters vary nonlinearly with the load. A response is computed with the help of available software, such as TNOWAVE or CAPWAP, and then compared to the measured response. The PAGE 26 17 soil model parameters are then varied in an iterative manner until the computed response matches the measured response. The soil properties from the model are then used to describe the static behavior of the foundation (El Naggar and Baldinelli, 2000). This technique requires discretization of the founda tion and surrounding soil. It also requires previous knowledge of the soil conditions and its elastic or plastic behavior. For signal matching to be successful, an experienced geotechnical engineer must be available to perform the analysis and verify the results. Consequently, numerous possible solutions may be found, from which the most reasonable is selected. 2.4.3 Modified Unloading Point Method (MUP) The Modified Unloading Point Method (MUP) uses the same methodology as the unloading point method. The main difference is use of a toe accelerometer. This allows the pile to be treated as an elastically deformed lumped mass using an average acceleration, wherin the toe acceleration may be different from the top. This method is useful for relatively short piles that undergo elastic shortening during the load test. This usually occurs when drilled shafts are rocksocketed or cast in a dense bearing strata (Lewis, 1999). 2.4.4 Segmental Unloading Point Method (SUP) The Segmental Unloading Point Method was developed in 1999 to analyze statnamic tests with a wave number less than 12. Under this condition, the pile cannot be assumed to behave rigidly. It can be, however, assumed to behave rigidly in segments, or along shorter lengths of the foundation. Figure 21 illustrates the discretization of a deep foundation and the forces acting on each segment. The segments can be delineated by PAGE 27 18 strain gages placed along the length of the pile. The placement of the gages is typically based on the soil strata. This method stems from the theory that the static capacity of a foundation develops independently of the test type or duration, but is instead dependent on the stiffness of the soil strata and displacement occurring in each strata. Each segment is then analyzed independently, using strain gage data and the MUP method. The total static capacity of the pile is then equal to the summation of the contribution from each segment and end bearing at any instance in time/top displacement (Lewis, 1999). Because this method involves extensive amounts of data and calculations, an automated spreadsheet was created at the University of South Florida. This program is titled Segmental Unloading Point Enhanced Revision 4.0 Statnamic Analysis Workbook, or SUPERSAW. SUPERSAW is a macrodriven Excel workbook that uses SAW to perform the SUP method. Using Visual Basic for Applications (VBA) to make the workbook userfriendly, SUPERSAW allows the user to input several parameters, import test data, and perform multiple analyses (Winters 2002). 2.5 Applicability of Statnamic Regression Methods Each of the regression methods discussed are applicable under different conditions. The use of each method is determined by the available instrumentation, time during design or construction at which a load test is considered, and experience of the engineer or other party that will perform the analysis. Table 24 summarizes the factors that must be recorded during the test with the potential analysis results for each method. For those regressions that require only topofpile measurements (UPM and SM), a statnamic load test is an option before, during, and after construction of the foundation. PAGE 28 19 For those that require measurements at the toe or other levels (MUP and SUP), the full information obtained from a statnamic load test can only be realized if the test was planned prior to the construction phase. This is because strain gages, accelerometers, or other transducers need to be embedded, and they are not easily installed after a drilled shaft has been poured or a pile has been driven into the ground. It is recommended that an experienced engineer perform any load test analysis, however, it is especially critical when using signal matching techniques. Because there is more than one possible solution, it is important that the evaluating party has the knowledge and expertise to determine the most correct solution using available soil data. Table 24 Data Input Compared to Ou tput for Statnamic Regression MethodsRequired DataOutput Capacity InformationEmbedded Gages FSTN atopatoev toptoe FendFtotalFNYesNo UPM**SM******MUP**SUP** either displacement or acceleration is needed and can be used to calculate the other ** signal matching produces one solution, but others are possible2.6 Limitations to the Above Methods Though each of the available regression methods are effective when used as they were intended, they also have limitations. The UPM is applicable to short, rigid foundations having a typical wave number between 12 and 50. It can only produce total static capacity results. It cannot be related back to insitu conditions or separated into PAGE 29 20 side shear and end bearing components. Signal matching requires adequate soil data be collected during construction. Also, because it involves an iterative process, an experienced engineer must be present for the analysis. The MUP, similar to the UPM, requires that appropriate instrumentation can be embedded at the toe of the foundation prior to construction. It is also limited to determining total static capacity with no distinction between soil layers and end bearing. Seemingly the most useful, SUP has the ability to determine static capacity for segments in different soil strata separate from end bearing. However, it requires preconstruction preparation so that strain gages are placed in the desired locations along the length of the pile. The proposed analysis method will allow a statnamic test completed with only topofpile instrumentation to be analyzed in segments. This will allow longer foundations to be evaluated and the test can be decided upon and performed postconstruction. It will also give the user an option to determine the number and length of segments, based on the available soil data. The ultimate side shear capacity will be determined separately from end bearing, something that was not previously possible with only topofpile data available. In short, this method will allow the output benefits of running a SUP analysis without requiring em bedded strain gages or accelerometers. PAGE 30 21 Figure 21 Discretization of a Deep Foundation into Two Segments PAGE 31 22 3.0 Approach 3.1 General As discussed extensively in Chapter 2, there are several methods available for determining both design capacity based on soil properties and actual capacity based on statnamic load test regressions. The ultimate goal is that these two values are related, showing that the design procedure is valid and that material has not been wasted by constructing oversized foundation elements. Hence, the proposed method was created using the same concepts as those applied to design equations. It will consider soil properties and development of resistance as a combination of end bearing and side shear. The proposed method will also utilize ideas presented and proven by the previous methods for statnamic load test analysis. The regression will involve steps similar to those used in previous regression methods, but at the same time, it will depend on available soil data and design information, namely a load shed distribution model. This method will allow separation of the total static capacity into side resistance along desired segment lengths and tip resistance where segment lengths are defined primarily by soil strata. The governing equation to be solved for a dynamic system such as a statnamic load test is given as: Equation 3.1FkxSTN cvma PAGE 32 23 In this equation, ma and FSTN are known from field measurements. The proposed method will develop a predictive model for the static term, based on the measured displacement at the top of the foundation. The total static capacity at a given displacement for the full length of a drilled shaft can be extracted from statnamic test data as: Equation 3.2kxFSTN macvBecause FSTN and ma are known, the total static capacity can be determined if a reasonable value for cv is available. Further, if the foundation is too long or is tipped in rock, it may not behave rigidly and the induced wave behavior must be considered. This will be addressed by discretizing the foundation and analyzing each segment separately. Data for load and displacement are available for the top segment and will be used to predict those values needed for subsequent segments via assumed side shear and elastic shortening calculations. The following subsections will discuss the proposed predictive method for side shear development and the accepted method for tip resistance. Once the capacity has been predicted, it can be verified by running a UPM analysis using a weighted acceleration (produced by the new method). The weighted acceleration will be representative of the entire foundation element being tested. 3.2 Side Resistance Side resistance is equal to the frictional resistance or adhesion of the soil to the drilled shaft as it displaces. This can be affected by the soil type, soil strength, depth, time, construction method, and relative settlement (Reese & Wright, 1977). The relationship between side shear and displacement at the top of the foundation can be described by a loaddisplacement curve. It has been found that the static side resistance PAGE 33 24 develops hyperbolically with settlement or displacement caused by the total load. The slope and curvature of the loaddistribution curve for side shear is dependent on the properties of the soil strata. An empirical relationship for side shear can be found for a drilled shaft as it displaces under a statnamic load by considering the displacement relative to the diameter of the drilled shaft under given soil conditions, provided it behaves as a rigid body and the soil is the same along the length of the foundation. An empirical formula for any condition can be determined by analyzing previous statnamic test results in the same type of soil displaying a hyperbolic trend. The steps involved in this process are: 1. Represent the top displacement as percentage of the diameter (%D). 2. Represent the side shear as a fraction of ultimate side shear, referred to as the side shear multiplier (SSM). 3. Plot the linear portion of %D versus. 4. Determine the slope ( m ) and intercept ( b ) of the bestfit line. The predicted side shear can be found as a fraction of the ultimate value using (3.3). Equation 3.3 SSM %D %D mb()The SSM is the predicted side shear as a fraction of the ultimate side resistance where the actual value of ultimate side resistance is yet unknown. The method used to determine the SSM is applicable only when there is a distinct linear trend visible in Step 3. Appendix A contains an example of this procedure. %D SSM PAGE 34 25 3.3 Tip Resistance Tip resistance has been shown to develop hyperbolically with displacement, similar to side shear. However, it does not reach its maximum value until a displacement of approximately 5% of the diameter (5%D). The empirical equation for drilled shafts in sand has been previously determined to be: Equation 3.4 TCM %D %D 043 .()The TCM (tip capacity multiplier) represents the fraction of the ultimate end bearing capacity that has developed at a given displacement (Mullins and Winters, 2004). 3.4 Weighted Unloading Point (WUP) The weighted unloading point (WUP) method begins by using the known soil strata to separate the drilled shaft into segments. Each segment will be short enough to be treated as a rigid body, allowing use of topofsegment information to perform the evaluation. Each segment will also be surrounded by only one type of soil for which an empirical displacementside shear relationship is reasonably known, as well as some form of damping conditions. In addition, the toe segment will include the end bearing capacity (Equation 3.4). The analysis will then begin with the top segment and subsequent segments will follow in order until the toe segment is reached, this is the forward modeling process. The steps for the analysis are listed on the flowchart in Figure 31. Performing this analysis generates a predicted side shear and acceleration distribution along the length of the foundati on. The acceleration distribution is then lumped into a weighted acceleration which can be used for an unloading point analysis, PAGE 35 26 similar to a modified unloading point. The re sults of the unloading point analysis can be verified by comparing the total static capacity at a given displacement (~1%D). The values obtained for static capacity from the load shed distribution model and the WUP analysis should be within some acceptable proximity to each other. 3.4.1 Preliminary Steps Prior to initializing the WUP analysis, the load shed distribution model needs to be created. This will aid in determining the number of segments and their properties. The number of segments will depend on the total length of the drilled shaft and the number of soil strata surrounding it. Each segment needs to be short enough that it can be considered as a rigid body, meaning that the whole length of that segment moves at the same rate. Each segment should also be embedded in only one type of soil or contained within a permanent casing. This allows a more accurate prediction of side shear development. By using the steps listed in Section 3.2 and previous testing in similar soil, the slope and intercept to characterize side shear development can be found to begin the analysis. Properties such as length, composite Youngs modulus, diameter and area, and density are needed for each segment. Segment properties may vary due to the shaft diameter, casing, or amount of reinforcement. The analysis begins at the top because it is where the test data has been recorded. Because drilled shaft capacity develops as a function of displacement, the first step is to determine displacement from acceleration (if necessary). The equations to do this are: Equation 3.5 v aa ttvi ii iii, ,, ,()TOP TOPTOP TOP 1 112 PAGE 36 27 Equation 3.6 d vv ttdi ii iii, ,, ,()TOP TOPTOP TOP 1 112with v0,TOP being equal to zero and d0,TOP being equal to a predetermined offset. An offset should be applied to the top displacement to account for the loading that occurs during the statnamic test setup. If the top displacement is known, then acceleration and velocity should be determined for use later in the analysis using equations (3.7) and (3.8). Equation 3.7 v dd ttii iii,TOP TOPTOP 1 1 ,, Equation 3.8 a vv ttii iii,TOP TOPTOP 1 1 ,,These equations will also be used for each of the remaining segments where only displacement will be available. 3.4.2 Side Shear Prediction The process to predict side shear is the same for each segment. It will begin with force and acceleration at the top and progress to the next segment as outlined in the flow chart. The equations associated with each step follow. The subscript T indicates the top of the current segment; the subscript N indicates the bottom of the current segment and coincides with the segment number. The top of the current segment corresponds to the bottom of the previous segment and the bottom of the current segment corresponds to the top of the next segment. The first step is to represent the displacement as a percentage PAGE 37 28 of the diameter (%D). This will be used to predict side resistance as a fraction of the ultimate side shear (SSM) using (Equation 3.3). The ultimate value of side resistance for each segment will be given by the distribution fraction (DF). The distribution fraction is the fraction of the total shaft capacity (ULT) that is carried by each segment. The actual value (in units of force) for side resistance of segment n at a given displacement is then given as: Equation 3.8kxSSM*DF*ULTnn The force transferred to the remaining segments of the foundation is then determined from: Equation 3.9FFkxnn1nnn macvwhere a and v at the top of the segment are used. The amount of force absorbed through damping, cv can be determined from any of several methods. The method adopted for this study involved assigning a damping value based on the zone of influence which in turn is evaluated based on the static capacity (kx). This approach is explained further in Appendix B. Before the subsequent segments can be analyzed, the displacement at the bottom of the current segment is needed. This is found by calculating the average strain (Equations 3.10, 3.11, and 3.12) and then determining the elastic shortening in the segment (Equation 3.13). Displacement at the bottom of the segment is then determined using (Equation 3.14). All of the values obtained for the bottom of one segment are then used to repeat the side shear and elastic shortening calculations for the next segment. PAGE 38 29 Equation 3.10 T T0,TFF AE Equation 3.11 N N0,NFF AE Equation 3.12 ave NT 2 Equation 3.13 l aveNL Equation 3.14ddlNT 3.4.3 Toe Segment After the side shear has been determined down to the toe segment, the end bearing needs to be included. The relationship for end bearing with displacement is similar to side shear in sands and can be found using (Equation 3.4). The total end bearing contribution to the total capacity is then determined from: Equation 3.15FTCM*DF*ULTEND where DF is the distribution factor, or fraction of the ultimate load, that is assigned to end bearing. 3.4.4 Final Steps The total static capacity is the summation of side resistance for each segment plus end bearing. A loaddisplacement curve can be generated to show the behavior of the PAGE 39 30 foundation. The acceleration distribution can be lumped into a weighted acceleration term using Equation 3.16 a amam mweighted NN total 11...This acceleration represents the combined motion of each segment as one element, similar to the role of average acceleration in the modified unloading point method. A standard UPM, using a program such as SAW, can be performed and a new static capacity curve generated. This curve is a better representation of static capacity than using only the topofpile acceleration. The results are usable if the output capacity from SAW approximately matches the predicted static capacity for a foundation that plunges. PAGE 40 31 Figure 31 Flowchart for Proposed Forward Model and Weighted Unloading Point PAGE 41 32 4.0 Case Study To test the usability of the data regression method described in previous chapters, load test data from a previous test program was used. The information presented regarding this test site was taken from a report created by Applied Foundation Testing, Inc. for Trevi Icos South (Robertson, 2004). The test shaft was outfitted with embedded strain gages and a SUPERSAW analysis had already been performed. The new method was tested by assuming only topofpile measurements were available, and then the results were compared with those from SUPERSAW. The SUPERSAW results were also used to determine the side shear multiplier for each segment as a function of %D. 4.1 Load Test Site The test shaft was constructed December 8 th 2004 in Escambia County, Florida by Gilbert Southern. The test was funded by the Florida Department of Transportation (FDOT) and performed by Applied Foundation Testing (AFT), Inc. Subsequently, The geotechnical research group at the University of South Florida postprocessed the data using SUPERSAW. The test shaft results were to be used for construction of the Cervantes Street Bridge foundation in Pensacola, Florida. Soil investigation was performed by Ardaman &Associates using the SPT boring method. The ground elevation at the test location was 9.46 m and the boring was done to an elevation of 22 m. Approximately the t op four meters of soil consists of medium to fine sand with silt having an average blow count of less than 10. The remaining soil PAGE 42 33 layers are composed of medium to fine sand with silt having an average blow count of 38. The full boring log is shown in Appendix C. The soil conditions encountered during investigation appear to be in three distinct layers of sand. Each layer differs in color, fines content, and strength (SPT N). 4.2 Test Shaft Construction The test shaft was installed by Trevi Icos South of Tampa, Florida and inspected by Volkert Construction Services of Pensaco la, Florida. The drilling log, provided by Volkert Construction Services, is shown in Appendix C. The test shaft was constructed from ground elevation to a depth of 17.24 m for a total length of 26.7 m. The hole was drilled with a temporary casing in place at the top and bentonite drilling fluid was used for hole stabilization during drilling and concrete placement. The outer diameter of the cased segment was 1.105 m; below the casing, the shaft diameter was 1.07 m. The concrete was poured over the course of approximately two hours via tremie. The reinforcing steel cage was made up of 11, #10 bars and #4 shear hoops. Strain gages were embedded at 9 locations along the shaft to obtain sufficient data for a segmental unloading point analysis in addition to top accelerometers and a load cell. 4.3 Statnamic Test and SUP Analysis The statnamic test was performed on December 16th, 2004 by AFT, Inc. A SUP analysis was performed using the Excel software SUPERSAW by the USF Geotechnical Research group. Figure 41 shows the segmental contributions to side shear and the toe segment contribution to both side shear and end bearing. The total static capacity of this foundation was 8900 kN. As shown in the loadtransfer curve ( Figure 42), the top PAGE 43 34 segment of the shaft developed a significant portion of the capacity (~2000 kN). The toe segment (including end bearing) produced the majority of the total capacity in side shear (~5000 kN), while the intermediate segment contributed relatively little to the total capacity. 4.5 Determination of Characteri stic Side Shear Equations The equations to predict side shear used in the new analysis were found using the SUPERSAW results from the Cervantes test shaft. Comparing the load transfer curve to the boring log of the test site, the segmental side shear contributions were deemed to coincide with the three distinct soil strata. The top soil layer, having had the temporary casing and much lower average blow count, coincided with the top segment of the shaft during analysis. The side shear multiplier (SSM), having slope m = 0.9729 and intercept b = 0.1257 was fitted using the top two segments from the SUP analysis. The resulting equation for the side shear multiplier for the top segment is: Equation 4.1 SSM %D 0.97(%D)0.13 The side shear development as a fraction of the ultimate from SUPERSAW and the predicted side shear as a fraction of the ultimate using the above SSM are compared in Figure 43. The predicted model is very close to the actual values for this soil type and construction method, as evidenced by the similar curve shapes. The next segment was surrounded by the second soil strata, having an average blow count of 41. Using segments three thru five from SUPERSAW, a characteristic equation for this type of sand PAGE 44 35 and use of bentonite drilling fluid was fitted. The equation parameters, which can be substituted into Equation 4.1, are m = 1.0516 and b = 0.1267. This equation produces a sufficient predictive model for the side shear multiplier. This model is compared with the results for the corresponding segment in SUPERSAW in Figure 44. The side shear multiplier for the final segment was found using SUPERSAW segments six, eight, and nine. Figure 45 shows the comparison of the SUPERSAW results and the corresponding predictive model. The slope and intercept were determined to be m = 0.9689 and b = 0.3341, respectively, for this segment. The SSM for each segment is determined as a fraction of the ultimate resistance for that segment. It can range from 0 to greater than 1 depending on the displacement. When multiplied by the distribution fraction and total shaft capacity, it yields a value for side resistance at a given displacement for that segment. Typically, results from a SUP analysis will not be available to determine the values for m and b. Further studies using drilled shafts in sands will lead to a general equation applicable to all sands if no other information is available. PAGE 45 36 20 15 10 5 0 5 10 15 010002000300040005000600070008000900010000 Load (kN)Shaft Elevation (m) Figure 42 Load Transfer Curve Generated by SUPERSAW 40 35 30 25 20 15 10 5 0 200 180 160 140 120 100 80 60 40 20 0 Side Shear (kPa)Displacement (mm) Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 Seg 8 Seg 9Figure 41 Segmental Side Shear Contributions Generated by SUPERSAW PAGE 46 37 0 0.2 0.4 0.6 0.8 1 1.2 00.511.522.533.5 %DSide Shear actual predictedFigure 43 Actual and Predicted Side Shear for Segment 1 0 0.2 0.4 0.6 0.8 1 1.2 00.511.522.533.5 %DSide Shear actual predictedFigure 44 Actual and Predicted Side Shear for Segment 2 PAGE 47 38 0 0.2 0.4 0.6 0.8 1 1.2 00.511.522.533.5 %DSide Shear actual predictedFigure 45 Actual and Predicted Side Shear for Segment 3 PAGE 48 39 5.0 Results The Cervantes load test was analyzed using the forward model and weighted unloading point method (FMWUP). The equati ons developed to model side shear were determined from SUPERSAW results to show that it was possible to develop a relationship between capacity and displacement in a given soil type. The forward model, as outlined in Figure 31, was used to determine the force transferred throughout the shaft and acceleration at the top of each segment. The acceleration distribution, generated from the displacement, was then lumped into a weighted acceleration term and used in an unloading point analysis. The results of the forward model and WUP are presented in the following sections with a thorough comparison to SUPERSAW and standard UPM results. 5.1 Input Parameters The first step in the procedure is to determine the input parameters. Under normal conditions for application of this method, the ultimate capacity, segments, and distribution factors would be determined from soil data and design values. For this analysis, however, this information was obtained from the SUPERSAW analysis. Later sections will discuss the results when the input parameters are determined using other methods. The Cervantes test shaft was separated into three segments with an ultimate capacity of 8900 kN. This was determined from the load transfer curve generated by PAGE 49 40 SUPERSAW (Figure 51). The three segments are 3.8, 11.37, and 11.63 m in length. The carrying capacity for each was 17.1%, 26.7%, and 45.0%, respectively. The remaining 11.2% of the load was carried by end bearing. Additional parameters include mass, diameter, and the composite Youngs modulus for each segment. The diameter of the top segment was 1.105 m; its mass and modulus were was 9051.2 kg and 33410 MPa, respectively. The diameter (1.07 m) and modulus (29307 MPa) for the remaining segments were the same. The second segments mass was 24783.4 kg while the mass of the third segment was 25350.1 kg. 5.2 Forward Model and Weighted Unloading Point (WUP) The above information was used to create the forward model and perform the weighted unloading point regression. The resulting output static capacity curve is shown in Figure 52. The predicted static capacity approximately matches the weighed acceleration UPM results. The weighted acceleration is compared to the top acceleration for each segment in Figure 53. The weight ed acceleration contains a contribution from each of the segments and is thus more representative of the entire foundation motion than the toponly acceleration. The UPM results for the total static capacity using weighted acceleration and toponly acceleration are compared in Figure 54. The total predicted static capacity from the model and results from a SUP analysis are also shown. The UPM results are vastly improved using a weighted acceleration. The results using toponly overpredict capacity by as much as 20%. The values for ultimate static capacity for each method are presented in Table 51. PAGE 50 41 Table 51 Maximum static capacity values from each regression methodRegression MethodDisplacement = 1% Diameter Maximum Forward Model7200 kN9100 kN WUPM8000 kN9000 kN UPM9700 kN11000 kN SUP7500 kN8900 kN5.2 Comparison to the Segmental Unloading Point Results The forward model results were compared to SUPERSAW results to show the potential of the model and weighted acceleration method. The static capacity predicted at each level has been plotted with the equivalent results from SUPERSAW in Figure 55. These values include end bearing. Deviations, such as that for the toe segment, may be caused by discrepancies in the end bearing or forward model variables. The forces transferred through the foundation are shown in Figure 56. The distribution predicted is approximately the same as that determined from SUPERSAW. The drastic difference near the end of the pulse is due to the lack of an unloading model for side shear. Other lesser deviations may be attributed to the method and value assigned to the damping force component. This will be discussed further in a later section. Also, to show the effectiveness of the displacement prediction, the displacement at each segment interface is shown in Figures 57 thru 59. Similar to the discrepancy in forces beyond the unloading point, there are discrepancies in the displacement. However, from the start of the test until that point, the shape and magnitude of the displacement curves are very similar. The trend is less reliable for lower levels, likely PAGE 51 42 due to the propagation of errors from the top segments. The results would be less erroneous if more segments, of shorter lengths, were used in the analysis. 5.3 Determination of Accurate Ultimate Static Capacity In the load test used for analysis, a good prediction for ultimate capacity was available. Under usual circumstances, this number is based on values determined using design methods accepted by AASHTO. Hence it was of interest to determine the reliability of the forward model to converge at the most accurate value for ultimate static capacity. To do this, a range of values for predicted ultimate capacity were used and the results were compared. For this particular load test, the foundation plunged during the load test. This led to very little affect on the weighted acceleration with varied capacity. The displacement, however, was more sensitive. When the correct value for ultimate capacity is input (8900 kN), the displacement along the shaft for the dura tion of the test is as would be expected. The top displaces more than subsequent elevations, which in turn displace more than the toe of the shaft (Figure 510). If too high a value is predicted, then the displacement at the toe becomes greater than at the top. This is not the observed physical behavior during a test. For this to happen, there would need to be a tensile force applied to the toe of the shaft. For example, Figure 511 shows the results when 200% of the true capacity (17800 kN) is predicted. At values close to the actual capacity, this phenomenon in the model is not as obvious. The deviation begins to appear at ~25% above the actual capacity, as demonstrated in Figure 512. PAGE 52 43 An under prediction, however, is not as easily discernible. When values as low as only 50% of the actual amount are used, there is a slightly noticeable deviation from the expected behavior. As lower values are used for ultimate, the toe shows more positive displacement. When an extremely low value, such as 2225 kN (25% of the actual) is predicted, there is a very noticeable positive di splacement at the toe of the shaft (Figure 513). When a higher value, 50% of the actual, is predicted, there is a noticeable deviation compared to the correct displacement, but it is not enough in itself to verify the capacity (Figure 514). 5.4 Forward Model and WUP Using Design Values In a typical test where this method is applicable, a load transfer curve is not available. A capacity distribution, however, may be attained from standard design methods. For this study, Shaft 123, available online at http://www.eng.usf.edu/%7Egmullins/downloads/ was used to generate a design capacity curve, or predicted capacity of different shaft lengths, using available soil data. This is the load distribution model. The forward model and weighted acceleration term were then generated and the results are presented in the following sections. 5.4.1 Ultimate Capacity and Segment Distribution Factors The design curve, Figure 515, shows comparable segment lengths to the load transfer curve from SUPERSAW. The distri bution fractions (DF), however, are slightly different. The load shed model indicates segment DF of 0.03, 0.35, and 0.45 for segments 1, 2, and 3 respectively and 0.16 for end bearing, compared to 0.171, 0.267, 0.450 and 0.112 from SUPERSAW. The ultimate value obtained from Shaft 123 is a PAGE 53 44 conservative estimate determined from the modified method (ONeill and Hassan, 1994) where the SPT blow count is less than 15 and the method (Reese and ONeill, 1988) where the SPT blow count is greater than or equal to 15. End bearing is determined using the method presented by Reese and ONeill (1988). The other input parameters, such as mass and Youngs modulus, were the same as those used in the initial analysis. 5.4.2 Initial Results The initial results from the forward model include displacement, force transfer, and acceleration distributions as well as total static capacity. As stated in previous sections, the theoretical displacement should show that the top displaced more than the toe of the shaft. Figure 516 shows that the resulting displacement, found using the DF predicted by Shaft 123, is acceptable. The force transfer and acceleration curves are shown in Figures 517 and 518, respectively. The weighted acceleration is very similar to that generated using the load transfer curve distribution factors. The force curve, however, indicates that larger forces are being transferred through each segment. The total static capacity, both predicted and generated using SAW, are shown in Figure 519. The total predicted capacity is approximately 30% lower than the results from SAW. From previous experience with this data set, it is known that the predicted design value is also significantly lower than the actual ultimate capacity of this shaft. The following sections will discuss the affects of increasing the predicted ultimate capacity and ways to verify that the distribution factors are reasonable. PAGE 54 45 5.4.3 Modifications to Improve Results When the foundation plunges, the weighted acceleration is not affected by the predicted ultimate capacity and the total static capacity generated by SAW is reliable. Therefore, when the foundation has plunged, as it did in this case, the predicted ultimate capacity and distribution factors can be adjusted until the predicted capacity resembles the SAW results. At this point, the predicted capacity and distribution is believed to be reliable as well, thereby producing a previously unavailable load shed distribution. The Cervantes test shaft showed evid ence of plunging, therefore the SAW output is valid. The following steps were taken to show that a reliable ultimate capacity and distribution can be obtained using the forward model. First, the predicted capacity was increased incrementally until the maximum value was similar to that of the SAW results. This is shown in Figure 520 for ultimate capacity predictions of 6100 kN to 11000 kN. At 8000, 9000, and 10000 kN, the resulting curves approximated the SAW results for the weighted acceleration. At 9000 kN, the ultimate capacity is only ~1% larger than the value obtained from SUPERSAW. 5.5 Effects of Variation in Distribution Factors The distribution factors used in both analyses were similar and demonstrated very little change in the shape of the predicted static capacity. Both sets of factors indicated that the majority of the capacity was carried in the middle and toe segments, with less capacity available in the top segment and end bearing. If a significantly altered set of distribution factors are used, it will show in the resulting total static capacity curve. This will prove to be a method of demonstrating reliable ranges for the loadcarrying PAGE 55 46 contribution from each segment and tip resistance. To demonstrate this, each distribution factor (DF) was lowered to 0.10 (10%) and increased incrementally to show the affects of a DF that is too low or too high. The contri bution from the top segment, shown in Figure 521, increases the stiffness of the foundation without adding significantly to the total capacity. The arrow in this figure indicates the direction of increasing contribution. Figure 522 shows the end bearing capacity contribution. As end bearing increases, overall capacity is reduced significantly and the static capacity curve approaches a diagonal line. As the toe segment contribution increases, the foundation exhibits less stiffness, but no change in total static capacity (Figure 523). The affect of increasing the intermediate segments DF, as shown in Figure 524, increases both the stiffness of the segment as well as the total static capacity. From the trends described above, a range of approximate DFs can be determined for a foundation that has plunged and the static capacity determined using the weighted unloading point method. By adjusting the distribution factors according to the above guidelines, an accurate description of segmental contributions can be obtained. A set of curves showing the steps to more closely approximate the SAW results are shown and explained in Appendix D. This serves as an example of how the user might adjust the distribution factors to improve the results. PAGE 56 47 20 15 10 5 0 5 10 15 010002000300040005000600070008000900010000 Load (kN)Shaft Elevation (m) Segment 1 L: 3.8 m Capacity: 17.1% of Total Segment 2 L: 11.37 m Capacity: 26.7% of Total Segment 3 L: 11.63 m Capacity: 45.0% of Total End Bearing Capacity: 11.2% of TotalFigure 51 Load Transfer Curve Showing Segmental Contributions to Capacity 40 35 30 25 20 15 10 5 0 14000 12000 10000 8000 6000 4000 2000 0 Load (kN)Displacment (mm) F_STN F_STATIC F_SAWFigure 52 Static Capacity and Statnamic Force from FMWUP PAGE 57 48 40 35 30 25 20 15 10 5 0 12000 10000 8000 6000 4000 2000 0 Static Capacity (kN)Displacement (mm) Predicted SUP WUPM SAW, top onlyFigure 54 Static Capacity Determined from Different Regression Methods 100 80 60 40 20 0 20 40 60 80 100 0.00000.05000.10000.15000.20000.2500 Time (s)Acc (m/s2) Segment 1 Segment 2 Segment 3 WeightedFigure 53 Segment and Weighted Accelerations Using Forward Model PAGE 58 49 15000 10000 5000 0 5000 10000 00.050.10.150.20.25 Time (sec)Load (kN) F_statnamic F_1, Predicted F_1, SUP F_2, Predicted F_2, SUP F_3, Predicted F_3, SUPFigure 56 Forces Transferred Through the Cervantes Test Shaft 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Static Capacity (kN)Displacement (mm) 5.87', Predicted 5.87', SUP 6', Predicted 6', SUP 9.8', Predicted 9.8', SUPFigure 55 Static Capacity at Various Elevations of the Cervantes Test Shaft PAGE 59 50 40 35 30 25 20 15 10 5 0 0.00000.05000.10000.15000.20000.2500 Time (s)Displacement (mm) Predicted SUPFigure 57 Displacement at the Top of Segment 2 40 35 30 25 20 15 10 5 0 0.00000.05000.10000.15000.20000.2500 Time (s)Displacement (mm) Predicted SUPFigure 58 Displacement at the Top of Segment 3 PAGE 60 51 40 35 30 25 20 15 10 5 0 0.00000.05000.10000.15000.20000.2500 Time (s)Displacement (mm) Predicted SUPFigure 59 Displacement at the Toe of the Shaft 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 510 Displacement Distribution for a Predicted Capacity of 8900 kN PAGE 61 52 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 511 Displacement for Predicted capacity of 17800 kN (200%) 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 512 Displacement for Predicted Capacity of 11125 kN (125%) PAGE 62 53 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 514 Displacement for Predicted Capacity of 4450 kN (50%) 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 513 Displacement for Predicted Capacity of 2225 kN (25%) PAGE 63 54 45 40 35 30 25 20 15 10 5 0 5 0.00000.05000.10000.15000.20000.25000.30000.3500 Time (s)Displacement (m) TOP Segment 2 Segment 3 ToeFigure 516 Displacement Distribution Using Load Shed Model 28 24 20 16 12 8 4 0 010002000300040005000600070008000 Capacity (kN)Depth (m) Side Resistance End Bearing Total Capacity Segment 3 L: ~11.5 m DF = 0.45 Segment 2 L: ~11.5 m DF = 0.35 Segment 1 L: ~4.0 m End Bearing DF = 0.16 Total Capacity = 6100 kNFigure 515 Segmental Capacity Contributions from Shaft123 PAGE 64 55 15000 10000 5000 0 5000 10000 0.00000.05000.10000.15000.20000.2500 Time (s)Force (kN) Fstatnamic F_1 F_2 F_3Figure 517 Forces Transferred Through the Test Shaft Using Load Shed Model 100 80 60 40 20 0 20 40 60 80 100 0.00000.05000.10000.15000.20000.2500 Time (s)Acc (m/s2) Segment 1 Segment 2 Segment 3 WeightedFigure 518 Acceleration Using Load Shed Model PAGE 65 56 40 35 30 25 20 15 10 5 0 14000 12000 10000 8000 6000 4000 2000 0 Load (kN)Displacment (mm) F_STN F_STATIC F_SAWFigure 519 Total Capacity Predicted Using Load Shed Model and SAW 40 35 30 25 20 15 10 5 0 12000 10000 8000 6000 4000 2000 0 Force (kN)Displacement (mm) Ultimate = 6100 kN Ultimate = 7000 kN Ultimate = 8000 kN Ultimate = 9000 kN Ultimate = 10000 kN Ultimate = 11000 kN F_SAWFigure 520 Increasing Predicted Static Capacity to Match SAW Results PAGE 66 57 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Static Capacity (kN)Displacement (mm) top = 10% 20% 30% 40% 50% 60% 70% 80% 90% Best Estimate Figure 521 Affects of Varying the Top Segment Distribution Fraction 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Static Capacity (kN)Displacement (mm) end bearing =10% 20% 30% 40% 50% 60% 70% 80% 90% actual Figure 522 Affects of Varying the End Bearing Distribution Fraction PAGE 67 58 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Static Capacity (kN)Displacement (mm) toe =10% 20% 30% 40% 50% 60% 70% 80% 90% actual Figure 523 Affects of Varying the Toe Segment Distribution Fraction 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Static Capacity (kN)Displacement (mm) int =10% 20% 30% 40% 50% 60% 70% 80% 90% actual Figure 524 Affects of Varying the Intermediate Segment Distribution Fraction PAGE 68 59 6.0 Conclusions and Recommendations 6.1 Conclusions This thesis presented a new method for statnamic load test regression utilizing a load shed distribution model generated from available soil data and a design curve. The forward model was then created and a weight ed unloading point analysis was performed. This was done using a test shaft that had previously been analyzed using SUPERSAW with good results. First, a method to predict side shear was presented and shown to accurately determine ultimate side shear. Then, it was shown that by assuming a reasonable damping force curve, the displacement at various locations along the foundation can be predicted. From this, an acceleration at various locations can be calculated. Finally, the acceleration distribution can be lumped into a weighted acceleration and static capacity can be found using SAW or other acceptable UPM software. There are several advantages to this method as well as recommendations for future improvements. 6.1.1 Advantages of the Forward ModelWeighted Unloading Point Method The proposed FMWUPM is advantageous under certain testing conditions. When a test is called for after construction, it is not practical to install the gages required for SUP or MUP regression methods. FMWUPM does not require any embedded gages; it uses only topofpile measurements. The weighted acceleration produced has been shown to produce an improved UPM static capacity over using topofpile acceleration. PAGE 69 60 FMWUPM also utilizes available soil data and design criteria to analyze the foundation. The segments determined for analysis are based on the type and condition of the surrounding soil. The ultimate capacity prediction can be increased or decreased incrementally to determine the most correct value. In addition to producing an improved ultimate static capacity, the weighted method can verify segmental capacity and end bearing. This was not possible using the standard unloading point method. The user is able to modify the distribution factors using the following guidelines (for a plunging foundation) to determine the correct distribution of capacity. 1.Increase the top segment DF to increase the initial stiffness of the foundation. 2.Increase the end bearing DF to decrease the curvature, decrease initial stiffness, and more closely approximate a 45 line. For the particular shaft analyzed in this study, the modifications to the second and third segments had the following effect: 3.Increase the toe (third) segment DF to decrease the initial stiffness of the foundation. 4.Increase the second segment DF to increase initial stiffness as well as total static capacity. The resulting trend and degree of change associated with modifying intermediate segment DFs will vary with the length of each segment, the surrounding soil strata, and the location of that segment in proximity to the top or toe of the foundation. PAGE 70 61 6.1.2 Disadvantages of WUPM Despite the numerous advantages, there are a few disadvantages associated with this method. To be used effectively, prior knowledge of concretesoil interaction under loading in similar site conditions is required. This method is not applicable under other conditions. This method also requires that the user be familiar with the various methods available to predict damping forces. The appropriate method and values for the given conditions needs to be determined. Until further studies have been completed, these factors will limit the use of the FMWUP method. 6.2 Recommendations There are several recommendations for future use of the forward model weighted unloading point method. Many of thes e stem from the amount of available data at the time of its inception and questions that arose during the initial analysis. Most of the following recommendations can be accomplished by analyzing further case studies. The analysis presented in prior chapters was based on only one test drilled shaft placed in sands. The side shear equations developed are suitable only under similar conditions. Additional test shafts with embedded gages in other materials will be needed to generate additional empirical relationships. Additionally, further analysis of foundations in sand may lead to an improved equation for sands. Also, the statnamic load applied to Cervantes test shaft exceeded the shafts capacity and caused the foundation to plunge. This rendered the WUP analysis insensitive to changes in the model parameters, namely ultimate capacity and segment distribution factors. It is recommended that nonplunging foundations be analyzed to PAGE 71 62 improve the applicability of this method. It may prove more useful when the acceleration distribution is more sensitive to adjustments of the input values, as it may be when the shaft or pile does not plunge. Further evaluation of the effect of the method chosen to determine the damping force is also recommended. In more sensitive cases, this may drastically alter the results. There are many options for estimating the damping force and research is in progress for estimating the damping coefficient. This would enable use of the velocity term, upon which damping is dependant. An Excel workbook to automate this method is in the works, but it is not yet ready for an enduser. Further work to automate this process is recommended due to the large amount of data and repeated calculations. An automated workbook would also allow the user to input desired parameters and immediately see the results of modifying these parameters. Because the WUP uses original design values and soil information, a link from the WUP workbook to Shaft 123, or other similar software, would be beneficial. It would allow the user to compare the design load distribution with the results from the analysis. A link to SAW or another UPM workbook would also improve the usability of this method. PAGE 72 63 References AASHTO, 2003. AASHTO LRFD Bridge Design Specifications, 2003 Interim U.S. Units, Second Edition, American Association of State Highway and Transportation Officials, Washington D.C. ASTM C39/C39M04a, Standard Test Met hod for Compressive Strength of Cylindrical Concrete Specimens. American Society fo r Testing and Materials, Philadelphia, PA. ASTM D114381(1994)e1, Standard Test Method for Piles Under Static Axial Compressive Load. American Society for Testing and Materials, Philadelphia, PA. ASTM D494500, Standard Test Method for Hi ghStrain Dynamic Testing of Piles. American Society for Testing and Materials, Philadelphia, PA. Bermingham, P.D., 2000. STATNAMIC: The first ten years. Proceedings of the Second International Statnamic Seminar, Tokyo, Japan, October 2830, 1998, pp 457464. Bruce, D.A., 1986. Enhancing the performance of large diameter piles by grouting. Parts 1 and 2, Ground Engineering May and July, respectively. El Naggar, M.H. and Baldinelli, M. J.V., 2000. Interpretation of axial Statnamic load test using an automatic signal matching technique. Canadian Geotechnical Journal Vol. 37, pp 927942. FDOT, 2005. Structures Manual Florida Department of Transportation Structures Design Office, online http://www.dot.state.fl.us/Structures/Struct uresManual/CurrentRelease/FDOTBridgeMan ual.htm accessed May, 2005. Garbin, E.J., 1999. Data Interpretation for Axial Statnamic Testing and the Development of the Statnamic Analysis Workbook. Masters Thesis, University of South Florida, Tampa, FL. PAGE 73 64 Janes, M.C., Justason, M.D., and Brown, D.A., 2000. Proposed ASTM Standard test for piles under rapid axial compressive load with its draft paper Long period dynamic load testing ASTM standard draft presented to the seminar for technical discussion. Proceedings of the Second International Statnamic Seminar, Tokyo, Japan, October 2830, 1998, pp 199218. Lewis, C., 1999. Analysis of Axial Statnamic Testing Using The Segmental Unloading Point Method. Masters Thesis, University of South Florida, Tampa, Florida. Middendorp, P. et al., 1992. Statnamic load testing of foundation piles. Proceedings of the Fourth International Conference on App lication of Stress Wave Theory to Piles. The Hague, Holland, 1992, pp 581588. Middendorp, P. and Bielefeld, M.W., 1995. Statnamic load testing and the influence of stress wave phenomena. Proceedings of the First International Statnamic Seminar, Vancouver, British Columbia, September 2730, 1995. Middendorp, P. and van Foeken, R.J., 2000. When to apply dynamic load testing and STATNAMIC load testing. Proceedings of the Second International Statnamic Seminar, Tokyo, Japan, October 2830, 1998, pp 253261. Mullins, A.G. and Winters, D., 2004. Post Grouting Drilled Shaft Tips Phase II. Final Report to the Florida Department of Transportation, Tampa, Florida. Reese, L.C. and ONeill, M.W., 1988. Drilled Shafts: Construction and Design. FHWA Publication No. HI 88042. Reese, L.C. and Wright, S.J., 1977. Construction of drilled shafts and design for axial loading. Drilled shaft design and construction guidelines manual. Department of Transportation, Federal Highway Associ ation, and Offices of Research and Development, Washington D.C., pp 1747. Robertson, D.T., 2004. Final Report of Statnamic Load Testing to Trevi Icos South. Applied Foundation Testing, Inc., Green Cove Springs, FL. Stokes, M.J., 2004. Laboratory Statnamic Testing. Masters Thesis, University of South Florida, Tampa, FL. Tchepak, S., 2000. The need for pile testing. Proceedings of the Second International Statnamic Seminar, Tokyo, Japan, October 2830, 1998, pp 243252. Winters, D., 2002. SUPERSAW Statnamic An alysis Software. Masters Thesis, University of South Florida, Tampa, FL. PAGE 74 66 Appendix A Development of SSM for a Hyperbolic CapacityDisplacement Curve The side shear multiplier (SSM) is the derived from the capacitydisplacement curve of a foundation segment generated during a SUP analysis. The side shear capacity of a deep foundation develops hyperbolically as displacement increases. In order to derive the general relationship for foundation behavior during a statnamic load test, the displacement was represented as a fraction of the foundation diameter (%D) and the side shear as a fraction of the ultimate side shear for that segment (SSM). Following is the steps to the analysis completed for segment 2 of this study (segments 3, 4, and 5 from SUPERSAW). For a hyperbolic curve, y ( x ), there is a linear relationship between x and x / y ( x ) having a slope, m, and intercept, b. The SUP results for %D and SSM were then plotted as x and y ( x ), respectively. This is shown in Figure A1. The %D divided by SSM, x / y ( x ), was then plotted against %D. Because this comes from actual data that does not follow a perfect hyperbola, only a portion of the curve is actually linear, which is shown in Figure A2. The linear portion for %D less than approximately 3% was used to find the slope and intercept using the linear trendline function in Excel, as noted on the figure. This slope and intercept can then be used in a general equation for side shear development of that segment: Equation A1 SSM %D %D mb() PAGE 75 67 Appendix A (continued) Side shear (or resistance) can now be modeled for any length of segment or total static capacity prediction under the same soil conditions using Equation 3.8 and a predetermined distribution fraction. The resulting SSM compared to the actual side shear as a function of %D in Figure A3. This process can be repeated for additional segments from the same test shaft, or using results from other load test shafts and their data. PAGE 76 68 Appendix A (continued) y = 1.0516x + 0.1267 R2 = 0.990 0.5 1 1.5 2 2.5 3 3.5 4 00.511.522.533.5 %D%D/SSM Segment 2 Linear (Segment 2)Figure A2 Linear Portion of %D Versus %D/SSM, Showing Equation 0 0.2 0.4 0.6 0.8 1 1.2 00.511.522.533.5 %DSSMFigure A1 %D Versus SSM from SUPERSAW Results for Segment 2 PAGE 77 69 Appendix A (continued) 0 0.2 0.4 0.6 0.8 1 1.2 00.511.522.533.5 %DSSM actual predictedFigure A3 SSM from SUPERSAW Results and Fitted Curve PAGE 78 70 Appendix B Derivation of VelocityDependant Damping Forces The damping force term in the general equation for a dynamic system is given as cv indicating that it is velocity dependant. To improve the predictive capability of the FMWUP method, it was necessary to derive a relationship between the damping coefficient, c the velocity, v and the static force, kx. Because the damping force is believed to be related to the static force, the following equation was used: Equation B1cvv kxIn this equation, is a multiplier that was determined from the SUPERSAW analysis. SUPERSAW using the segmental unloading point method to determine the damping coefficient for each segment. This was used along with the segmental static force over time to solve for Because velocity cancels from both sides, the timedependant solution for is: Equation B2 ckxThe resulting values for for plotted for each segment with time in Figure B1. The values for segments 4 thru 10 are all in close agreement and follow a linear trend. For the FMWUP analysis presented, a value of 0.2 for the damping coefficient was used. The top three segments were disregarded for this study as they appear to be outliers for currently unknown reasons. PAGE 79 71 Appendix B (continued) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.110.120.130.140.150.160.17 Time (s) (s/m) seg 1 seg 2 seg 3 seg 4 seg 5 seg 6 seg 7 seg 8 seg 9 seg 10Figure B1 Static Force Multiplier, Used to Determine the Damping Forces (s/m) PAGE 80 72 Appendix C Test Site Information Figure C1 Boring Log for the Cervantes Bridge Test Shaft PAGE 81 73 Appendix C (continued) Figure C2 Part 1 of the Cervantes Test Shaft Drilling Log PAGE 82 74 Appendix C (continued) Figure C3 Part 2 of the Cervantes Test Shaft Drilling Log PAGE 83 75 Appendix D Varying Distribution Factor Demonstration For a plunging foundation, the total static capacity curve generated using the weighted acceleration unloading point is representative of the actual static capacity. The predicted static capacity can be adjusted until the ultimate values are close and the distribution factors for each segment and end bearing can be varied until the shape of the curve is correct. Matching the two curves is a way of verifying the distribution of capacity in the foundation. The distribution factors should always add to 1.0 (100%). The following guidelines can be used to modify the shape of the curve: 1.Increasing end bearing leads to less curvature and decrease in total capacity 2.Increasing top segment will increase the stiffness 3.Increasing toe segment will decrease stiffness 4.Increasing intermediate segments increases stiffness and total capacity For the case study used in this thesis, the actual distribution of capacity was known from a SUPERSAW analysis. The soil investigation, however, led to a slightly different distribution. Following is a demonstration of how varying the initial guess at distribution can approximate a more accurate distribution. A figure showing the results of each step is shown and numbered according to the appropriate step with the previous result shown for comparison. PAGE 84 76 Appendix D (continued) 1.Input distribution factors and ultimate capacity predictions from the load shed model created from Shaft 123: 6100 kN ultimate capacity with DF = 0.03, 0.36, 0.45, 0.16 for the three segments and end bearing, respectively. 2.Increase the ultimate capacity to 9000 kN. 3.Increase the top segment DF to 0.10, decrease end bearing DF to 0.09 4.Decrease the intermediate segment DF to 0.30 and increase end bearing to 0.15 5.Increase the top segment DF to 0.12 and decrease end bearing to 0.13 6.Decrease the intermediate segment DF to 0.25 and increase top segment to 0.17 After step 6, there is very little change in the curvature of the static capacity. This shows that the top segment contribution is in the range of 10 17% and the intermediate segment is 25 30%. The end bearing contribution is 13 15%. The toe segment accounts for approximately 45% and no adjustments were needed. These results are similar to those from the load transfer curve. The DF from the load transfer curve were 0.171, 0.267, 0.45, and 0.112 for the three segments and end bearing, respectively. PAGE 85 77 Appendix D (continued) 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAWFigure D1 FMWUP Results for Distribution Fractions from Shaft123 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAW (Previous)Figure D2 Effect of Increasing Ultimate Capacity PAGE 86 78 Appendix D (continued) 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAW (Previous)Figure D3 Effect of Increasing the Top Segment Distribution Fraction 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAW (Previous)Figure D4 Effect of Increasing End Bearing Distribution Fraction PAGE 87 79 Appendix D (continued) 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAW (Previous)Figure D5 Effect of Second Increase to Top Segment Distribution Fraction 40 35 30 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Load (kN)Displacment (mm) F_STATIC F_SAW (Previous)Figure D6 Effect of Decreasing the Segment 2 Distribution Fraction xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001670370 003 fts 005 20051216093327.0 006 med 007 cr mnuuuuuu 008 051118s2005 flu sbm s000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0001238 035 (OCoLC)62303168 SFE0001238 040 FHM c FHM 049 FHMM 090 2005 1 100 Lowry, Sonia L. 0 245 Analysis of statnamic load test data using a load shed distribution model h [electronic resource] / by Sonia L. Lowry. 260 [Tampa, Fla.] : b University of South Florida, 2005. 502 Thesis (M.S.C.E.)University of South Florida, 2005. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 87 pages. 3 520 ABSTRACT: In the field of civil engineering, particularly structural foundations, lowcost options and time saving construction methods are important because both can be a burden on the public. Drilled shafts have proven to both lower cost and shorten construction time for largescale projects. However, their integrity as loadcarrying foundations has been questioned. The statnamic load test was conceived in the 1980s as an alternative method of testing these larger, deeper foundation elements. Performing a load test verifies that the load carrying capacity of a foundation is agreeable with the estimated capacity during the design phase and that no significant anomalies occurred during construction. The statnamic test, however, is classified as a rapid load test and requires special data regression techniques. 590 Adviser: A. Gray Mullins. 653 Unloading point. Drilled shaft. Capacity. Side shear. Deep foundation. 690 Dissertations, Academic z USF x Civil Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.1238 