## Design of Bridge Foundations using a Performance-Based Soil-Structure Interactiom Approach

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Design of Bridge Foundations using a Performance-Based Soil-Structure Interaction Approach Lance A. Roberts1, Damon Fick2, and Anil Misra3

1. Corresponding Author: Assistant Professor, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701; Phone: (605) 394-5172; Fax: (605) 394-5171; Email: Lance.Roberts@sdsmt.edu. Assistant Professor, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701; Phone: (605) 394-5381; Fax: (605) 394-5171; Email: Damon.Fick@sdsmt.edu. Professor, University of Kansas, 1530 W. 15th St., Lawrence, KS 66045; Phone: (785) 864-1750; Fax: (785) 864-5631; Email: amisra@ku.edu.

2. 3.

ABSTRACT The design of deep foundations must consider soil-structure interaction in order to properly model the side and tip resistance components. A soil-structure interaction model such as the t-z model method allows for the settlement analysis of a deep foundation over a range of applied vertical loads. The developed load-settlement curve can be analyzed using performance-based design criteria, such as a limiting tolerable settlement and a serviceability settlement. The limiting tolerable settlement can be selected to correspond to a movement that will either cause excessive stresses in the structure or render a structure inoperable while a serviceability settlement would correspond to a movement that would cause adverse performance or excessive maintenance issues with the structure. In this paper, a performance-based soilstructure interaction design approach for axial design of deep foundations under the AASHTO Strength and Service Limit States is presented. The design approach can be integrated within the Load and Resistance Factor Design (LRFD) framework to develop an efficient methodology for satisfying these limit state criteria. INTRODUCTION The axial design of deep foundations has traditionally followed an ultimate limit state approach where the ultimate capacity is determined using either static capacity predictions or field load test interpretations. A range of ultimate capacities are obtained when using either of these methods. For example, a number of interpretation techniques can be used to obtain the ultimate capacity from field load tests, such as Davisson’s method, DeBeer’s method, and Chin’s method (Fellenius 1990). The same is true for the static capacity prediction techniques, with methods such as the α-method, β-method, or O’Neill and Reese methods (Das 2007). Interestingly, none of the current design or analysis techniques for deep foundations explicitly considers the global response of the structure itself. Global structure response should include serviceability issues, such as structure function or maintenance, in addition to overstress conditions at the various strength limit states. One manner in which the design of deep foundations can be addressed with respect to structure response is the utilization of a performance-based design approach. In a performance-based approach, the design criteria for the strength and serviceability limit states are stated with respect to tolerable settlements of the

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structure, rather than the ultimate capacity of an individual deep foundation. The tolerable settlements can be selected to correspond to a movement that will either cause excessive stresses in the structure or render a structure functionally inoperable due to serviceability limits. Since the ultimate capacity of a deep foundation is typically achieved only after the foundation has settled a significant amount, the use of tolerable settlement criteria for the structure within the deep foundation design approach will ensure that the structure can functionally operate within a desired tolerance throughout its lifetime. In this paper, a performance-based design approach for axial design of deep foundations is presented. The approach utilizes a soil-structure interaction model in order to develop the load-settlement behavior of the deep foundation element. The developed load-settlement curves are analyzed at a limiting tolerable settlement and a serviceability settlement for the strength and service limit state, respectively. These settlements are based on the global response of the supporting structure. The performance-based design approach is integrated within the Load and Resistance Factor Design (LRFD) framework to rationally incorporate design uncertainty into the process. The result is an efficient deep foundation design method for satisfying the established strength and serviceability limit state criteria, while ensuring implementation of the LRFD approach. A design example, utilizing actual field load test data, is included to demonstrate the applicability of the method. LOAD-SETTLEMENT USING SOIL-STRUCTURE INTERACTION A soil-structure interaction approach called the t-z model method has been extensively utilized for the development of non-linear load-settlement curves of deep foundations in Misra and Roberts (2006), Misra et al. (2007), Roberts et al. (2008) and Roberts and Misra (2010). In the t-z model approach, the resistance of the soil along the interface of the deep foundation and at the tip is represented by a non-linear spring system as shown in Figure 1a. A differential equation describing the forcebalance for the deep foundation system subjected to a boundary condition at the head and at the tip has been solved using a finite difference approach (see Misra and Roberts 2006, Misra et al. 2007). This results in the determination of the head settlement behavior and strain distribution within the deep foundation. Due to construction processes, moisture variation, and frost consideration, the upper 1 m of the soil-structure interface is often considered to be non-interacting in the overall foundation resistance as shown in Figure 1b. As the deep foundation is loaded, the non-linear springs will deform based upon their strength and stiffness characteristics and the deep foundation will undergo settlement. In an isotropic, uniform half-space, an increase in the applied load will result in yielding of the interface springs beginning at the top of the deep foundation and progressing to the tip as shown in Figure 1b. At some load, all of the springs will yield and the foundation will fail by plunging. Thus, the use of a t-z model allows for the development of a loadsettlement curve that represents the behavior of the deep foundation over a wide range of applied loads.

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Spring Slider

Spring Slider

(a)

(b)

Figure 1. (a) Non-linear spring system along deep foundation interface and tip and (b) schematic of deep foundation element. The force-displacement behavior of the soil-structure interface springs is often assumed to be hyperbolic with an initial stiffness, Kinit, and an ultimate strength, qo, which is the product of the deep foundation perimeter and the ultimate shear strength of the soil-structure interface, τu, in drained or undrained conditions. The forcedisplacement behavior of the tip soil can be similarly represented using the initial tip soil stiffness, Kti, and the ultimate strength of the tip soil, qt, in drained or undrained conditions (Misra and Roberts 2006). The soil-structure interface strength and stiffness parameters are related to the deep foundation type, construction techniques, and properties of the soil strata. The tip soil strength and stiffness parameters are generally only related to the deep foundation type and properties of the soil at the tip and tend to have less dependency on construction method. For a homogenous and isotropic soil deposit, an ultimate strength and initial stiffness magnitude must be assigned for the soil-structure interface and the tip soil, thereby resulting in four required model parameters as described above. In most deep foundation applications, however, the site is never homogenous and isotropic, and thus the ultimate strength and initial stiffness model parameters can vary along the length of the deep foundation and from one foundation to the next. This variation in subsurface conditions, along with variable construction techniques for deep foundations, creates the rationale for utilizing a reliability-based design (RBD) procedure to efficiently handle the potential uncertainties in the foundation design. The ultimate strength and initial stiffness parameters can be determined using correlations to site investigation or laboratory test data. In addition, the model parameters can be back-computed directly from field load test data. The general procedure to back-calculate the t-z model parameters using field load test data requires matching the load-settlement behavior of the t-z model to the field generated curve (Roberts et al. 2008). In addition, the internal strains computed by the t-z model are also matched to the strain measurements in the field. Thus, the nominal spring parameters determined utilizing a t-z model back-computation process can be directly verified from field settlement performance of an installed deep foundation at

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a given site. This can be quite beneficial in the design process, as model bias will be significantly reduced in the design, thereby resulting in an improved method for limit state prediction of foundation performance. LOAD AND RESISTANCE FACTOR DESIGN (LRFD) It is well-understood by engineers that uncertainty exists in any deep foundation design. Typical sources of uncertainty are inherent variability, measurement errors, and transformation uncertainty (Phoon et al. 1995). In addition, uncertainties from construction variability and model error can have significant contributions (Roberts and Misra 2010). In the typical deep foundation design approach, nominal (i.e. average or lower bound) values for the required soil parameters are utilized in a static capacity prediction model to determine the ultimate capacity of the foundation. Design uncertainty is managed by assigning either a global factor of safety to the calculated ultimate capacity of the foundation or by assigning nominal safety factors to the individual components that make up the total design (Phoon et al. 1995). Regardless of the method used, safety factors are typically assigned based on the design engineer’s judgment and without quantification of actual design uncertainty magnitudes (Kulhawy and Phoon 2006). This can lead to foundation designs that are conservative, and thus inefficient, or designs that are unsafe. Therefore, the application of an RBD approach, such as the LRFD method, is beneficial. In an RBD procedure, the magnitude of design uncertainty can be rationally incorporated within the overall design process, thereby resulting in a safe and efficient design methodology. To that end, RBD procedures are being increasingly utilized in the design of geotechnical structures, such as deep foundations (AASHTO 2007). For deep foundation design, the LRFD procedure involves quantifying the design uncertainties, utilizing a model to predict the resistance of the foundation, and performing a probabilistic analysis utilizing both the model and the design uncertainties. The following inequality must be satisfied in the LRFD approach: γ i Qi ≤ φ R R (1)

where, γi is a load factor, Qi is a load, φR is the resistance factor and R is the nominal foundation resistance. Eq. 1 replaces the global factor of safety equation currently utilized in the allowable stress design (ASD) approach. The load factors have been extensively developed for structural design of bridges and other structures (Nowak 1995). Therefore, it is important to focus on the calibration of the resistance factor for the design of deep foundations. Following the First Order, Second Moment (FOSM) method, the resistance factor, φR, is computed as follows (Baecher and Christian 2003):

φR = λR ? ?

2 2 ? 1 + ΩQD + ΩQL +γ L ? ? 1 + ΩR2 ? E( QL ) ?

? γ D E( QD )

(2)

where, λR is the bias of the resistance, λQD and λQL are the bias of the dead load and live load, respectively, γD and γL are the load factors for the dead load and live load, respectively, ΩQD, ΩQL, ΩR, are the coefficient of variation (COV) for the dead load,

? ? E( QD ) ? λQD + λQL ? e ? ? E( QL ) ? ?

βT ln?? 1+ΩR2 ? ?1+ΩQD2 +ΩQL2 ?? ?? ?? ?? ?? ?? ??

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live load and resistance, respectively, E(QD) and E(QL) are the expected values of the dead and live load, respectively, and βT is the target reliability index. The COV and bias of the dead and live load, along with the dead load and live load factors, have been extensively investigated, with typical values given in Baecher and Christian (2003). The ratio of the expected value of the dead load to the expected value of the live load does not significantly affect the value of the resistance factor and can be assigned a magnitude based on the characteristics of the structure, with a value typically between 2 and 4 (Baecher and Christian 2003). The target reliability index, βT, relates the probability the deep foundation does not meet a selected performance level (USACE 1997). In deep foundation design, a βT of between 2.0 and 3.5 is generally utilized (Kulhawy and Phoon 2006). A βT of 3.0, for example, corresponds to a probability of unsatisfactory performance of approximately 0.1%. Therefore, after assigning magnitudes to the known variables in Eq. 2, it is observed that the only unknown parameters are the COV of the resistance, ΩR, and the bias of the resistance, λR. It is thus critical that the developed resistance factor calibration process focus on the determination of these parameters. Design uncertainties can be easily incorporated within the t-z model analysis approach. The observed uncertainties at a given site, based on either the site exploration process or field load test data, directly affect the magnitude of the t-z model parameters. Therefore, the t-z model parameters can be assumed as random variables and defined with a mean (i.e. nominal magnitude) and COV within a specified probability distribution function (PDF). The COV of the model parameters must reflect the uncertainty realized by the “within-site” variability, which is comprised of inherent variability, variability due to construction, and variances in deep foundation geometry and material strength (Zhang 2008). Once the uncertainty within the t-z model parameters is defined, a Latin Hypercube simulation can be conducted. This process allows for the random sampling of each of the model parameters for a given number of trials. The randomly selected values for each of the model parameters are substituted into the t-z model analysis and a complete loadsettlement curve is generated for that trial. The process is repeated with new random values for the model parameters for each trial, thereby resulting in a large number of load-settlement curves. This has significant implications for the design of deep foundations, as additional efficiency in the design is possible by fully understanding the effect of the load-settlement curve shape. Therefore, by quantifying the variability in the deep foundation settlement, a logical process to incorporate performance-based design criteria, such as a tolerable settlement magnitude, will allow for determination of ΩR and λR in Eq. 2 and, subsequently, the resistance factor, φR, using the randomly generated load-settlement curves. RESISTANCE FACTOR CALIBRATION The design of deep foundations has been traditionally based on determining the ultimate capacity of the foundation using any number of static capacity approaches. However, deep foundations generally do not fail catastrophically at a definite ultimate load, such as the load computed by a static capacity approach. Instead, when subjected to an increase loading, deep foundations will continue to settle until the

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settlement magnitude becomes greater than what can be tolerated by the structure. Therefore, the design of deep foundations should be conducted using a performancebased design approach, where the design criteria are defined in terms of tolerable settlements of the structure rather than an ultimate capacity (Foschi et al. 2002). To accomplish this, the analysis of the randomly generated load-settlement curves described above requires the definition of two performance-based criteria: (1) a limiting tolerable settlement, which corresponds to a settlement under the factored load that leads to overstress, and thus unsatisfactory performance or potential failure, of the structure; and (2) a serviceability settlement, which corresponds to a settlement under the service load where the functionality, durability, or maintenance of a structure may be adversely affected. Figure 2 displays the results of the random generation of a large number of loadsettlement curves based on some magnitude of variability at a site. From Figure 2, it is observed that the analysis of the load-settlement curves at a specified limiting tolerable settlement results in a series of corresponding loads. These loads are assumed to be the resistance of the deep foundation and can be used to develop a resistance PDF as shown in Figure 3. It is also observed in Figure 2 that the loadsettlement curves can be examined at the service load, which will result in a series of serviceability settlements. These settlements can be used to develop a PDF of settlements as shown in Figure 4. In order to calibrate a site specific resistance factor for the strength limit state, the statistical parameters of the PDF in Figure 3 are utilized. The COV of the PDF in Figure 3 represents the variability of the deep foundation resistance at the limiting tolerable settlement and is thus assumed to be equal to ΩR. Since the t-z model was utilized to match the load-settlement performance of the deep foundation in the field, the bias of the resistance, λR, is assumed to be equal to unity (Roberts et al. 2008, Roberts and Misra 2010). This assumption is appropriate since the t-z model load-settlement and strain behavior can directly correspond to the field load test data. Once these values for ΩR and λR are substituted into Eq. 5, along with the selected value of βf at the factored limit state, the resistance factor for the strength limit state is computed. The factored resistance of the deep foundation is computed to be the nominal resistance, R, as shown in Figure 3, multiplied by the resistance factor. The design is satisfied if the factored resistance is greater than the factored load. A statistical analysis can be conducted using the PDF of settlement in Figure 4 to satisfy the service limit state design criteria. Based on the mean and COV of the PDF in Figure 4, it is possible to compute the probability that the settlement of a deep foundation constructed in the field will exceed the serviceability settlement specified in the design criteria. This probability of exceedance is shown in Figure 4 as the shaded area under the PDF. Since the probability of exceedance is likely to be very small, it can be expressed as a reliability index, β. Based on reliability indices and performance criteria provided in USACE (1997), the design engineer can select an appropriate value for the target reliability index for the service limit state, βs, based on functionality, durability, or maintenance considerations for the structure. Thus, if the value of β, determined using the PDF of settlement shown in Figure 4, is greater than the βs value selected by the design engineer, the design of the deep foundation is satisfied at the service limit state.

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Load (kN)

0 0 1000 2000 3000 4000 5000

20

u (mm)

30

Limiting Tolerable Settlement = 40 mm

40

50

60

Figure 2. Randomly generated load-settlement curves using t-z model approach.

Figure 3. PDF of load corresponding to a limiting tolerable settlement.

Figure 4. PDF of settlement corresponding to the service load.

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Serviceability Settlement @ 1000 kN

10

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The presented design approach is fundamentally different than the LRFD methods currently utilized in the AASHTO specifications. The AASHTO specifications require the use of a single resistance factor at the strength limit state that has been calibrated utilizing a single βT (see AASHTO 2007). This single resistance factor is applicable to all sites, regardless of the inherent level of variability within the site. The presented approach, conversely, requires judgment by the design engineer in order to select an appropriate value of βT for calculation of the resistance factor, φR, and βs to evaluate the serviceability settlement. Although significant information exists in the literature that can guide the design engineer to select an appropriate value of βT for the strength limit state (Kulhawy and Phoon 2006), the selected value of βs for the service limit state can vary and is related to the importance of maintaining the functionality of the structure. However, this level of judgment is essential in the deep foundation RBD process in order to permit flexibility for the design engineer to make modifications for site and/or project specific conditions (Kulhawy and Phoon 2009). The efficiency of the design can be improved by revising the geometry of the deep foundation and regenerating the random load-settlement curves using the t-z model approach. The load-settlement curves are reanalyzed at both the strength and service displacement limits until each limit state is achieved as efficiently as desired. For example, the efficiency of the deep foundation can be improved by revising the design to: (1) reduce the ratio between the factored resistance and the factored load at the strength limit state to approach unity; or (2) reduce the ratio between the computed β and the selected βs at the serviceability limit state. Thus, the developed approach explicitly permits the probabilistic integration of design uncertainties for both limit states, thereby resulting in a safe and efficient design that is site specific. DETERMINATION OF PERFORMANCE-BASED DESIGN CRITERIA In order to apply the performance-based soil structure interaction design method, settlement criteria based on serviceability and limiting tolerable displacements must be selected. The selected serviceability settlement may be based on expansion joint performance, deck cracking, or the drivability of a bridge structure as perceived by vehicle operators. Differential and total settlements under working loads have been suggested by Thornley (1959) to be restricted to 6.25 mm and 19 mm respectively. Of the 280 bridge structures evaluated by Moulton (1985), vertical displacements of less than 25.4 mm for simply supported and continuous structures made of concrete or steel did not require costly maintenance and/or repairs. In addition to suggestions from other researchers, it is it is likely the design engineer will select serviceability settlements based on experience or observed performance with similar structures. Limiting tolerable settlements are based on costly repairs of a structure due to overstress of individual members. These stresses can be difficult to quantify because of the variation of settlements that may occur in adjacent foundations and the ability of individual piers and girders of continuous structures to redistribute forces. One of the advantages of a performance based design method is the ability to maximize efficiency of a design based on expected performance levels of the structure. Because the accuracy of the t-z model depends on the input parameters from the site, performance of the structure can be related to the level of soil

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exploration and field load test data. For example, it has been suggested in Roberts and Misra (2010) that the design of deep foundations be divided into three design levels: Level “A”, Level “B”, Level “C”. Level “A” would correspond to a design where significant load testing is planned at the site in order to reliably predict the performance and uncertainty. Level “B” would correspond to a design where one or two load tests are planned at the site to confirm nominal performance, while uncertainty would be characterized by a significant subsurface exploration program. Level “C” would correspond to a design where no load testing is planned and thus the nominal performance is based on experience (i.e. a database of model parameters), with uncertainty determined using minimal subsurface exploration. To that end, the limiting tolerable settlements could therefore be selected by multiplying the selected serviceability settlements by an amplification factor, Cd, which would be based on the aforementioned design level and also related to the βT factors and performance levels from USACE (1997). For a “Good” performance level, USACE (1997) suggests a βT value of 4, which would correspond to the amplification factor, Cd, for a Level “A” design. Performance levels “Above Average” and “Below Average” would represent Level “B” and “C” designs with amplification factors of 3 and 2.5 respectively. As more research becomes available, the Cd factors could be adjusted to include the affects of different materials, bridge structures, and construction techniques on performance. The following example illustrates the design of a bridge foundation illustrating the performance based soil structure interaction approach. DESIGN EXAMPLE FOR BRIDGE STRUCTURE A continuous span, prestressed concrete girder bridge located in the Midwest of the United States required drilled shafts to support the superstructure. The Service Limit State and Strength Limit State I loads per foundation were specified as 3900 kN and 5400 kN, respectively. Based on functionality and maintenance considerations, the serviceability settlement was specified as 6.25 mm with a βs value of 2. The design was to be completed at Level “B”, resulting in a limiting tolerable displacement of 3.0 x 6.25 mm = 19 mm. An intensive site investigation and laboratory testing program was conducted. The geology at the site consisted of approximately 8.5 m of overburden soil comprised primarily of clay, with a layer of silty sand. Below the overburden, the bedrock consisted of shale of the Fairport Chalk Member. The design included a field load test of a sacrificial test shaft using an Osterberg cell device O-Cell. In lieu of testing the entire soil-structure interface along an installed drilled shaft, only the interface resistance within the shale was tested. To that end, the test shaft was installed solely within the shale bedrock for an approximate length of 4 m. The diameter of the test shaft was 1070 mm. The O-Cell was located at the base of the test shaft with the top of concrete located near the bedrock/overburden soil interface. Upward and downward movements of the O-Cell were measured at discrete loads. The test was concluded once the maximum side friction resistance along the shale interface was achieved. The t-z model was utilized, along with the measured O-Cell test data, to back-compute the soil-structure interface and tip soil parameters for the

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shale. A plot of the upward and downward movement of the O-Cell from the load test is shown in Figure 5 as a series of points. The predicted upward and downward movement of the test shaft using the t-z model has been superimposed on the field test points in Figure 5 as solid lines. As can be observed, the t-z model parameters for the shale bedrock have been back-computed to provide a reasonable fit to the field test data, within ±5% throughout the entire series of measured data. The t-z model parameters for the shale were determined as follows for the interface and tip, respectively: τu = 530 kPa, Kinit = 1030 MPa, qt = 11 MPa, and Kti = 575 MPa.

40 30 20 10

Upward movement of O-Cell plate

u (mm)

0 -10 -20

Downward movement of O-Cell plate

-30 -40 0 1000 2000 3000 4000 5000 6000 7000

Load (kN)

Figure 5. The t-z model fit to the movement curves from O-Cell field load test. The t-z model was employed to calibrate a site specific resistance factor for design of the drilled shafts at the strength limit state, along with ensuring that the service limit state requirements were satisfied. Based on the site investigation data, the COV of the interface and tip parameters was assumed to be 20% and 10%, respectively. The difference in the COV values between the interface and tip was necessary due to construction variations for drilled shafts and the effect of these variations on the interface parameters. All data was incorporated into a Latin Hypercube sampling technique to randomly generate 1000 load-settlement curves as shown in Figure 6. The curves are intended to represent the variability in the loadsettlement behavior of drilled shafts installed at the site. In the simulations, the diameter of the drilled shaft was taken as 1070 mm with an installed length of 13 m. The randomly generated load-settlement curves were analyzed at the specified limiting tolerable settlement and service load to develop a PDF of drilled shaft resistance and settlement, respectively. The mean of the resistance PDF was taken as the nominal resistance, R, and the COV of the PDF was computed to be 18%. The COV value, along with a βT of 3.0, was substituted into Eq. 2 to calibrate the resistance factor for design. The factors related to the dead and live loads in Eq. 2 were based on values given in Baecher and Christian (2003). Using the PDF of settlement, the probability of exceedance for the specified serviceability settlement was computed, along with a corresponding value of β. The results of the RBD computations are given in Table 1.

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Load (kN)

0 0

R = Nominal Resistance

5000

10000

15000

20000

25000

5 10 15

Service Limit State Load

u (mm)

20 25 30 35 40

Limiting Tolerable Settlement for Strength Limit State

Figure 6. Randomly generated load-settlement curves for drilled shafts at site. Table 1. Strength and Service Limit State I computations.

Strength Limit State I Service Limit State I Nominal Factored Nominal COV of Probability of Resistance Resistance Settlement Pile Head φ Exceedance (kN) (kN) (mm) Settlement 14750 0.60 8850 2.03 0.10 0%

β ∞

As observed from the computations shown in Table 1, the factored resistance of the drilled shaft is greater than the factored load and thus the Strength Limit State I requirements are satisfied. For the Service Limit State I, the probability of exceeding the serviceability settlement of 6.25 mm at the service load is statistically 0%, which corresponds to an infinite value for β. Therefore, the computations demonstrate that the design of the drilled shaft is controlled by the strength limit state and that the length of the drilled shaft could be decreased in order to increase the efficiency of the design. For example, additional computations suggest that the length of the drilled shaft within the shale bedrock could potentially be reduced by more than 50% to more efficiently satisfy the strength limit state design criteria. CONCLUSIONS A proposed performance-based design methodology for axial design of deep foundations has been presented. The methodology utilizes a t-z model to randomly generate load-settlement curves for analysis using both strength and service limit state design criteria. The limit state design criteria were specified in terms settlements at the factored and service loads, respectively, rather than in terms of capacity. The methodology was integrated within the LRFD framework in order to rationally incorporate design uncertainties into the overall design process.

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The implementation of the LRFD method requires the calibration of a resistance factor that explicitly accounts for the uncertainty in the resistance of a deep foundation due to a number of sources. The paper presented the resistance factor calibration process based on the analysis of randomly generated load-settlement curves at the limiting tolerable settlement and service load. Probability distribution functions were developed which provided the necessary statistical parameters to compute a resistance factor and probability of exceedance for a site specific design. The result is an efficient and consistent design methodology for satisfying the limit state design criteria while ensuring safety within the system. A method to determine the magnitude of the serviceability settlement and limiting tolerable settlement was introduced, including the use of an amplification factor. However, more research must be conducted to develop the magnitude of serviceability settlements and amplification factors for different types of bridge structures. A demonstration of the developed performance-based design methodology was included to outline the ease of the approach. It was observed that the utilization of the developed method within the LRFD framework allows the engineer to assess the optimum deep foundation for a particular site. The use of the LRFD approach has ensured that the optimum deep foundation system will ensure safety and consistency in the design. Improved efficiency within the design can ultimately save significant time and money on large projects. REFERENCES AASHTO. (2007) LRFD Bridge Design Specifications. 4th Edition. American Association of State Highway and Transportation Officials, Washington, D.C. Baecher, G.B. and Christian, J.T. (2003) Reliability and Statistics in Geotechnical Engineering. John Wiley & Sons, West Sussex, UK. Das, B.M. (2007) Principles of Foundation Engineering. Thomson, Toronto. Fellenius, B.H. (1990) Guidelines for the Interpretation and Analysis of the Static Loading Test. Deep Foundations Institute, Hawthorne, New Jersey. Foschi, R.O., Li, H. and Zhang, J. (2002) “Reliability and performance-based design: A computational approach and applications.” Structural Safety, 24, 205-218. Kulhawy, F.H. and Phoon, K.K. (2006) “Some critical issues in Geo-RBD calibrations for foundations.” Geotechnical Engineering in the Information Technology Age, Proceedings of the GeoCongress, ASCE, Reston. Kulhawy, F.H. and Phoon, K.K. (2009) “Geo-RBD for foundations – Let’s do it right!” Contemporary Topics in In-Situ Testing, Analysis, and Reliability of Foundations, Proceedings from the International Foundation Congress and Equipment Expo, ASCE, Reston. Misra, A. and Roberts, L.A. (2006) “Probabilistic analysis of drilled shaft service limit state using the ‘t-z’ method.” Canadian Geotechnical Journal, 43(12), 13241332. Misra, A., Roberts, L.A., and Levorson, S.M. (2007) “Reliability analysis of drilled shaft behavior using finite difference method and Monte Carlo simulation.” Journal of Geotechnical and Geological Engineering, 25(1), 65-77.

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Moulton, L.K, GangaRao, H.V.S. and Halvorsen, G.T. (1985) Tolerable Movement Criteria for Highway Bridges. Publication FHWA-RD-85-107. U.S. Department of Transportation. Nowak, A.S. (1995) “Calibration of LRFD bridge code.” Journal of Structural Engineering, 121(8), 1245-1251. Phoon, K-K., Kulhawy, F.H. and Grigoriu, M.D. (1995) Reliability-Based Design of Foundations for Transmission Line Structures. Report TR-105000, Electric Power Research Institute, Palo Alto. Roberts, L.A., Misra, A. and Levorson, S.M. (2008) “Practical method for Load and Resistance Factor Design (LRFD) of deep foundations at the strength and service limit states. International Journal of Geotechnical Engineering, 2(4), 355-368. Roberts, L.A. and Misra, A. (2010) “Performance-based design of deep foundation systems within the LRFD framework.” Proceedings of the Transportation Research Board Annual Meeting, Washington, D.C. Thornley, J.H. (1959) Foundation Design and Practice. Columbia University Press, Morningside Heights, New York. USACE. (1997) Engineering and Design: Introduction to Probability and Reliability Methods for Use in Geotechnical Engineering. Engineering Technical Letter No. 1110-2-547, Department of the Army, Washington, D.C. Zhang, L.M. (2008) “Reliability verification using pile load tests.” Reliability-Based Design in Geotechnical Engineering: Computations and Applications, Edited by Kok-Kwang Phoon, Taylor & Francis, New York.

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