Proposed Specifications for LRFD Soil-Nailing Design and Construction (2011) / Chapter Skim
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3: Findings and Applications
3: Findings and Applications
Pages 6-62
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From page 6... ...
Subsequently, the chapter provides discussions of LRFD limit states in the design of SNWs and a synthesis of approaches used to calibrate resistance and load factors. Finally, calibrations of resistant factors are presented.
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This approach is used in the current AASHTO LRFD Bridge Design Specifications. In the LRFD method, two parameters account for uncertainty: load factor for load uncertainty and resistance factor for material uncertainty.
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For each strength limit state, a design equation can be generically expressed as: Where Rn = the nominal resistance of a given structural component for the strength limit state being considered; φ = a non-dimensional resistance factor related to Rn; Qi = the i-th load type that participates in this limit state; γi = a non-dimensional load factor associated with Qi; ηi = a load-modification factor; and N = the number of load types considered in the limit state. These quantities are described in the following paragraphs.
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expected to occur under normal conditions; and STOLERABLE = the maximum value of S the structure can sustain before its functionality is affected. The load factors for different load combinations to be considered in service limit states are contained in Table 3.4.1-1 of AASHTO (2007)
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Design values of resistance are obtained by reducing nominal resistances with a resistance factor, φ, that is usually ≤ 1.0. Conversely, design values of loads are obtained by increasing nominal load values using a load factor, γ, that is usually ≥ 1.0 (Figure 3-1)
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An advantage of this method is that it can provide approximate, closedform approximations for resistance factors. If the random variables Q and R are normally distributed and statistically independent, the resistance factor can be estimated as (Withiam et al., 1998)
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: If Qi involves permanent and live loads, the resistance factor can be calculated as: The Level I calibration is computationally simple and the relative contribution of each variable to the load and resistance factors can be readily identified. Occasionally, this calibration φ λ λ γ = + + + + ⎛⎝ ⎞⎠R DC DC LL LL DC LL R Q Q COV COV COV 1 1 2 2 2 λ λ βDC DC LL LL T R DC Q Q COV COV+ + + + ⎛⎝ ⎞⎠ ( )
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Select an acceptable probability of failure, Pf, and a corresponding target reliability index, βT; 4. Fix load factors in the limit state using statistics or other means; 5.
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(2001) adopted βT = 2.33 for the calibration of pullout resistance factors in MSE walls.
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3.3.2 Basic Description of Soil Nail Walls SNWs are earth-retaining structures constructed using passive reinforcing elements, referred to as soil nails. The term "passive" is used because soil nails are typically not posttensioned.
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From page 16... ...
In some cases, however, the upper rows of soil nails are post-tensioned as a means to control and limit the outward movement of the wall. Other elements commonly used in connection with the soil nail bars are centralizers and bar couplers (not shown in Figure 3-4, see additional descriptions in Appendix B)
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Typical cross section of a soil nail wall in common U.S. practice.
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However, because the load factors for basal heave are also 1.0, basal heave is considered a service limit state in this document, in order to be consistent with the current LRFD Bridge Design Specifications (AASHTO, 2007) approach.
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Limit states in soil nail walls: overall stability: (a) slip surface not intersecting nails and (b)
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. If the slip surface intersects some or all nails, the nail pullout resistance mobilized in the soil nails behind the slip surface also contributes to stability.
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3 28 γLL = load factor for live loads. As overall stability is treated as a service limit state (AASHTO, 2007)
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All load factors considered are then γ = 1.0. In this limit state, the following requirement must be satisfied: where φBH = resistance factor for basal heave (AASHTO, 2007)
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In the procedure presented below, loads caused by lateral earth pressures acting behind the soil block are explicitly considered. Unlike with overall stability scenarios for SNWs, loads in this limit state are assigned load factors ≥ 1.0 because destabilizing effects are clearly separated from stabilizing effects.
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for the verification of sliding limit states, any external load, Q, acting behind the retaining structure must be considered to extend outside the block of soil, i.e., up to the vertical dashed line shown in Figure 3-8. The nominal soil sliding resistance can be calculated as: where c = the cohesive resistance of the soil at the base of the block of soil, BL = the base length (considered herein a horizontal slip surface)
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In addition, based on the instrumentation of soil nails in various in-service SNWs, the following range for To-s can be used (Byrne at al., 1998)
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However, to simplify calculations, the distribution is commonly assumed to be constant along the pullout length; therefore, the nominal bond resistance qU is considered an apparent, average value. For a given pullout length, LP, occurring behind the slip surface, the resulting nominal pullout resistance, RPO, is: Adequate nail pullout resistance is provided when: where φPO is the resistance factor for pullout resistance and Tmax is the maximum tensile force on the bar, as calculated in stability, limit-equilibrium analyses.
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Limit states in soil nail wall facings.
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The calculation of the resistance RFF is presented in Equation 3-54. For the flexural limit state, it must be verified that: where φFF = the resistance factor for flexure in the facing; RFF = the nominal resistance for facing flexure (considered a force herein)
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Connectors installed at the nail head may be subjected to a punching-shear limit state, which may occur if the nominal shear resistance of the reinforced shotcrete section around the nails is exceeded. The nominal punching-shear resistance must be evaluated for both temporary and permanent facings (Figure 3-13)
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Limit states for punching-shear in facing -- horizontal cross sections.
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Headed-Stud Tensile Resistance in Permanent Facings. The tensile resistance of headed-stud connectors in permanent facings, RFH, must comply with: where φFH is the resistance factor for headed-stud tensile resistance.
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3.4.5 Seismic Considerations in Extreme-Event Limit States of Soil Nail Walls 3.4.5.1 Introduction Seismic forces must be considered in SNW design in areas with moderate to high seismic exposure and, according to the LRFD Bridge Design Specifications, seismic effects must be considered in the design of bridge substructures as an extreme-event limit state. In general, the response of SNWs to past strong ground motions has been very good to excellent.
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3.4.6 Design for Service Limit States (Displacements) 3.4.6.1 Introduction As part of the design of SNWs, the maximum lateral and vertical movements of the wall must be estimated and verified to be less than the tolerable deformation limits of the wall.
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From page 34... ...
Finally, Section 3.5.6 presents a summary of resistance factors to be considered for the design of SNWs in the LRFD. 3.5.2 Common Load Factors in Earth-Retaining Structures As mentioned previously, load factors are established for specific limit states and load types.
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Extreme-Event Loads BR = vehicular braking force CT = vehicular collision force CE = vehicular centrifugal force CV = vessel collision force CR = creep EQ = earthquake FR = friction IC = ice load IM = vehicular dynamic load allowance LL = vehicular live load (4) Load factors for permanent loads vary w ith load type.
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From page 36... ...
Based on the provisions for earth-retaining structures included in Article 11.5, Load Combinations and Load Factors of AASHTO (2007) , the most common limit states for SNWs can be: • Service limit states (e.g., Service I Limit State, which involves overall stability)
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From page 37... ...
that this approach is an interim solution due to the current lack of a satisfactory methodology and calibration data for applying LRFD methods to stability analysis computations. 3.5.3 Resistance Factors for Sliding, Basal Heave, Overall Stability, and Seismic Limit States 3.5.3.1 Introduction This section provides a discussion of the resistance factors used for sliding, basal heave, overall stability, and seismic limit states that are associated with SNWs.
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3.5.4 Resistance Factors for Structural Limit States 3.5.4.1 Resistance Factors for Tension in Soil Nails The tensile resistance factor to be used in SNWs selected in this document is consistent for the case of load factors in overall stability or γ = 1.0. To this end, the resistance factor is adopted as follows: for nail bars of mild steel (i.e., ASTM A 615)
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From page 39... ...
In the case of the pullout resistance of soil nails, this factor can be computed from the LRFD equation assuming that nail loads are directly affected by the load factors, or: If loads are comprised of permanent dead (QDC) and live loads (QLL)
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Equations 3-74 and 3-75 can be employed to derive resistance factors for a load combination of permanent dead loads and live loads per AASHTO (2007) Strength I Limit State (from γDC = 1.25 and γLL = 1.75)
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From page 41... ...
For these types of soil nails, the nominal bond resistance is affected by numerous factors, including: • Conditions of the ground around soil nails, including: – Soil type; – Soil characteristics; – Magnitude of overburden; and • Conditions at time of soil nail installation, including: – Drilling method (e.g., rotary drilled, driven casing, etc.) ; – Drill-hole cleaning procedure; 41 Limit State Resistance Condition ResistanceFactor Value Sliding All φτ 0.90 Soil Failure Basal Heave All φb 0.70 Slope does not support a structure φ s 0.75 (1)
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From page 42... ...
Estimations of the nominal bond resistance of soil nails from various sources are discussed below. 3.6.2.2 Typical Values Published in Literature Typical values of bond resistance have been presented in the literature for drilled and gravity-grouted soil nails installed in various types of soils/rocks and for different drilling methods.
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Estimated nominal bond resistance for soil nails in soil and rock. a Material Type b Sand 6.90 119 0.390 Gravel 5.87 122 0.469 Clays 5.89 120 0.461 Weathered Rock 6.33 177 0.595 Notes: (1)
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0 20 40 60 80 100 120 Blow Count, N (bpf)
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Weathered Rock Range Figure 3-20. Relationship between qu, pL, and N for weathered rock.
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3.6.3 Background of Soil Nail Load Testing 3.6.3.1 General Load testing of soil nails consists of applying a tensile force to selected, individual bars in a controlled manner while measuring the developed forces and bar elongations with the purpose of verifying the pullout resistance along the bonded, grouted bar length. Note that soil nails are only partially grouted for testing purposes.
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. With this assumption, the nominal bond resistance, qu, is the average of the mobilized stress distribution at the limit state.
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Reduction of soil nail load-test data.
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The review showed that it was not possible to derive complete or strong correlations between measured bond resistances and field test data because either the variability was excessive or the data was incomplete, unreliable, or inconsistent. Therefore, the database of soil nail pullout resistance was developed for various soil/rock types solely based on soil nail load-test results, which were obtained from a wide variety of sources.
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From page 50... ...
The statistical parameters for these curves, which are summarized in Table 3-11, are used subsequently to perform the calibration of the pullout resistance factors. 3.6.5 Database of Soil Nail Loads The statistics of the bias for loads to be used for the calibration of the pullout resistance factor were derived by examining 11 instrumented SNWs in the United States and abroad (Byrne et al., 1998; Oregon DOT, 1999)
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Measured and predicted pullout resistance -- rock.
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0.5 1 1.5 2 2.5 Bias λR of TPO -3 -2 -1 0 1 2 3 St an da rd N or m al V ar ia bl e, z Clay Figure 3-27. Bias R of pullout resistance -- clay.
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0.5 1 1.5 2 2.5 Bias λR of TPO -3 -2 -1 0 1 2 3 St an da rd N or m al V ar ia bl e, z All Figure 3-29. Bias R of pullout resistance -- all materials.
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Monte Carlo simulations were conducted to improve initial values presented previously in this chapter. 3.7.2 Description of Calibration Process The calibration was performed using the following steps: Step 1: Establish a limit state function; Step 2: Develop PDFs and statistical parameters for loads and resistances; Step 3: Select a target reliability index for SNW design; Step 4: Establish load factors; Step 5: Best-fit cumulative density functions to data points; Step 6: Conduct Monte Carlo simulation; Step 7: Compare computed and target reliability indices; and
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From page 55... ...
Step 1: Establish a Limit State Function The limit state function, M, for nail pullout is defined as: where φPO = the resistance factor for pullout, RPO = a random variable representing the nominal pullout resistance, γQ = a load factor, and Tmax = a random variable representing the load in a nail. At the limit state (i.e., M = 0)
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From page 56... ...
TBC 1.4 x 1 1.4 x 1 1.8 x 1.8 1.5 x 1.5 1.5 x 1.25 0.75 x 0.75 0.75 x .75 1.5 x 1.5 1.5 x 1.2 1.5 x 1.5 Table 3-12. Characteristics of monitored soil nail walls.
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Bias Q for maximum load in soil nails.
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Resistance factors for pullout were calculated for this series of load factors. Step 5: Best-Fit Cumulative Density Functions to Data Points CDFs for loads and resistances were generated via Monte Carlo simulations using the statistics for load and resistances.
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Figure 3-36. Monte Carlo curve fitting of load and resistance -- all soil types.
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Pullout resistance factors were calculated for the range of γQ listed in Step 4. Figures 3-33 through 3-36 present the curvefitting analysis using Monte Carlo for different soils and for γQ = 1.75.
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From page 61... ...
. Because of the values of the calibrated resistance factors for pullout, it is expected that a LRFD-based SNW design that uses this range of resistance factors would not produce significant differences in results (i.e., in terms of soil nails, nail bar diameter, etc.)
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From page 62... ...
λQ Number of Points in Database Mean of Bias Standard Deviation Coefficient of Variation Log Mean of Bias Log Standard Deviation 1.75 1.60 1.50 1.35 1.00 Material N Distribution Type λR σR COVR μln σln φR = φPO Sand/Sandy Gravel 82 Lognormal 1.05 0.25 0.24 0.02 0.24 0.82 0.75 0.70 0.63 0.47 Clay/FineGrained 41 Lognormal 1.03 0.05 0.05 0.03 0.05 0.90 0.82 0.77 0.69 0.51 Rock 26 Lognormal 0.92 0.18 0.19 –0.10 0.19 0.79 0.72 0.68 0.61 0.45 All 149 Lognormal 1.05 0.22 0.21 0.03 0.21 0.85 0.78 0.73 0.66 0.49 Table 3-15. Summary of calibration of resistance factors for soil nail pullout for various load factors.
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