Assessment of Reliability-Based Serviceability Limit State Procedures using Full-Scale Loading Tests

Assessment of Reliability-based Serviceability

Limit State Procedures using Full-Scale Loading

Tests

Jonathan C. HUFFMAN a, John P. MARTIN b and Armin W. STUEDLEIN c a

Graduate Student, Foundation Engineering, Inc., and School of Civil and Construction Engineering, Oregon State University, USA

b

Graduate Student, Oregon State University, USA c

Assistant Professor and Loosley Faculty Fellow, Oregon State University, USA

Abstract. Geotechnical reliability-based limit state design methodologies are rapidly evolving to meet the demands of various applications. However, the accuracy of these new procedures should be independently assessed and improved as new loading test data is made available. This paper focuses on the assessment of two relatively new serviceability limit state (SLS) procedures developed for immediate displacement of spread footings supported on clay and on aggregate pier improved clay. These procedures were developed using a database of full-scale loading tests reported in the literature, and incorporate estimates of and variability associated with the bearing capacity, or ultimate limit state (ULS) and bivariate normalized bearing pressure-displacement models. Independent evaluations of these two SLS models are made using new full-scale loading tests on unimproved ground and aggregate pier improved ground. Comparison of observed and expected normalized bearing pressure-displacement curves and empirical cumulative distribution functions highlight the importance of footing/soil representation in the source databases and the impact and importance of differentiating between intra- and inter-site variability.

Keywords. Reliability-based Design, Serviceability Limit State, Full-Scale Loading Tests, probability of failure

1. Introduction

Geotechnical limit state design methodologies are rapidly evolving to meet the demand for reliability-based assessment of structural performance. Examples include applications for deep foundations (e.g., Paikowsky 2004, Phoon and Kulhawy 2008, Dithinde et al. 2011, Stuedlein et al. 2012, and Li et al. 2013), shallow foundations (e.g., Uzieli and Mayne 2011, Huffman and Stuedlein 2014), and reinforced soil walls (e.g., Bathhurst et al. 2008), among others. Calibration of a suitable geotechnical reliability-based limit state model will typically employ a database of full-scale tests in order to characterize applicable resistance parameters for a given model and to evaluate load and resistance factors. However, the development of a suitable database for the calibration of such models is difficult owing to the expense of large-scale testing and subsequent scarcity of high-quality loading test data. Therefore, the accuracy of the reliability-based model and those procedures

used to develop it should be evaluated independently, and improved, as new loading test data becomes available.

This paper uses the results of new full-scale loading test data to provide an unbiased assessment of two recently developed serviceability limit state (SLS) procedures for the immediate (i.e., initial or distortion) displacement of spread footings supported on clayey soil and on aggregate pier improved clayey soil. First, two previously developed SLS models are introduced and their procedures described. Next, the new loading tests are described, including a description of the test site and soil profile, and pertinent footing and improved ground geometry. The new loading test data and empirical distributions are then compared to the probabilistic estimates of bearing pressure-displacement performance and variability anticipated from the reliability-based SLS models. This comparison provides a framework to evaluate existing SLS procedures © 2015 The authors and IOS Press.

This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License.

for the assessment of the accuracy of reliability-based SLS procedures.

2. Serviceability Limit State Models

2.1. Footings on Clay (Unimproved)

Huffman et al. (2015) developed an SLS procedure to address the immediate displacement of spread footings supported on plastic, fine-grained soils. This procedure was introduced to provide an SLS design methodology for spread footings on clayey soils that may prove helpful for meeting the requirements of existing design codes (e.g., AASHTO, 2012; Eurocode 7 [Orr and Breysse, 2008]).

The SLS procedure was developed based on a database of full-scale footing loading tests reported by Strahler and Stuedlein (2014). The immediate displacement was found to be related to a reference slope-tangent capacity that is a function of the bearing capacity, qult, or ultimate limit state (ULS) for undrained loading:

qd qs q f cd cs c u ult

s

N

D

N

q

O

O



J

O

O

(1) where su is the undrained shear strength, J is the unit weight, Df is the footing embedment depth, Nc and Nq are the bearing capacity factors, and

Ocs, Oqs, Ocd and Oqd are the Brinch Hansen (1970) shape and depth factors, respectively.

The mobilized resistance, qmob, at a pre-determined serviceability-level footing disp-lacement, G, is defined in terms of a hyperbolic function (Huffman et al. 2015):

ult STC mob M q k k q

K

K

2 1 (2)

where K is the normalized footing displacement and equal to G/B’ and B’ is the equivalent footing diameter (e.g., Mayne and Poulos 1999), k1 and k2 are the correlated bivariate hyperbolic

Table 1. Summary of fitted normalized resistance model parameters for Eq. (1) and Eq. (5).

Parameter Mean COV (%) Model Distribution k1 0.013 53.0 Gamma k2 0.701 16.1 Inv. Gaussian MSTC 0.643 18.7 Lognormal k3 3.088 0.407 Lognormal k4 0.454 0.233 Lognormal

model parameters and MSTC is the factor that relates the bearing capacity to a reference slope tangent capacity estimated from the results of the database loading tests. The hyperbolic model parameters and MSTC were calibrated for each loading test in the database. The mean values and statistical distributions of the SLS model parameters are summarized in Table 1.

Figure 1. Definition of the slope tangent capacity with an offset set at 3 percent of normalized footing displacement.

A “lumped” load and resistance factor, \q, was calibrated for the SLS model using MCS with distributions of the resistance parameters estimated from Table 1. The MCS also accounted for dependence between model parameters and variability in applied loading, among other factors. The load and resistance factor was found equal to (Huffman et al., 2015):

 

» » » » » ¼ º « « « « « ¬ ª  ¸¸¹ · ¨¨© § _¸ ¹ · ¨ © §      c b a f e d q K K K E \ exp 1 ln ln exp 2 (3)

where a through f are best-fit coefficients that depend on the expected variability of the allowable structure displacement and the applied foundation load, and E is equal to the reliability index associated with the target probability of failure, pf. Refer to Huffman et al. (2015) for tabulated values of a through f.

The mobilized resistance calculated from Eq. (2) is multiplied by 1/\q to obtain the allowable bearing pressure that will not exceed the serviceability-level footing displacement within the predetermined level of reliability based on the selected E value.

2.2. Footings on Aggregate Pier Improved Clay An SLS procedure to calculate the immediate displacement of spread footings supported on aggregate pier improved clay was developed by Huffman and Stuedlein (2014) based on a database of full-scale footing loading tests discussed in detail by Stuedlein and Holtz (2013). The immediate serviceability-level displacement is represented as a function of the bearing capacity, qult, which is calculated as (Stuedlein and Holtz, 2013): mp mp rp f r rp ult b bS ba bD S b b q ) _{0 1 2 3 4}

W

1 ₅

W

ln(       (4) where Sr is the slenderness ratio of the aggregate pier(s) defined as Sr = Lp/Dp (i.e., ratio of pier length to pier diameter), ar is the area replacement ratio and equal to the ratio of pier area to foundation area, and Wm is the matrix soil shear mass participation factor given by

Wm = su/ar, where su is the undrained shear strength of the matrix soil. Fitted model coefficients were determined equal to b0 = 4.756, b1 = 0.013, b2 = 1.914, b3 = 0.070, b4 = -13.71, and b5 = 0.005.

The mobilized resistance, qmob, is modeled using a power law function of the form (Huffman and Stuedlein 2014):





ult k mob

k

q

q

4 3

K

(5)

where k3 and k4 are the correlated bivariate power law model factors calibrated from the loading tests and K is the normalized

displacement. The mean values and statistical distributions of k3 and k4 are summarized in Table 1.

A lumped load and resistance factor, \q, was calibrated using MCS with distribution parameters from Table 1 and similar means as described above. The load and resistance factor was found equal to (Huffman and Stuedlein 2014):

 

 

»

_¼

º

«

¬

ª







0 0 0 0

ln

ln

exp

b

a

d

c

q

K

K

E

\

(6)

where a0 through d0 are best-fit coefficients that depend on the expected variability of the allowable structure displacement and the applied foundation load; refer to Huffman and Stuedlein (2014) for tabulated values of a0 through d0.

3. New Full-Scale Loading Tests

New full-scale loading tests were recently completed at the Oregon State University (OSU) geotechnical field test site on unimproved and aggregate pier-improved soils. A layout of the site is shown in Figure 2(a). The loading tests were completed during two seasons (Spring and Fall) in order to observe potential differences in the undrained shear response of the foundation soils with seasonal changes in the natural moisture content and groundwater table elevation.

Subsurface explorations were completed in conjunction with the loading tests and included three soil borings and five cone penetrometer (CPT) tests. The soil profile underlying the site consists of stiff, dilative clayey silt to silty clay extending to a depth of 4 to 4.5 m, followed by loose to medium dense silty to clayey sand to a depth of 5.5 to 6 m. The sand is underlain by stiff clayey silt with some sand extending to at least 10 m. Representative cross-sections interpolated from the explorations are shown in Figure 2(b) and 2(c).

The performance of the footings was controlled by the upper clayey silt to silty clay layer. This soil has medium plasticity, with USCS classifications ranging from CL (low plasticity clay) to ML and MH (low and high plasticity silt). The undrained shear strength (su)

of this stratum within the depth of influence beneath the footings was estimated from triaxial CU tests and back-calculations with the CPT cone tip resistance (qt). During the Spring test series, su was estimated equal to 50 kPa; su was estimated equal to 65 kPa during the Fall test series when the groundwater table was deeper.

The testing program included two loading tests on unimproved soil and eight tests on aggregate pier improved soil (test G4DS in Figure 2(a) has not yet been conducted). A summary of the test designations and pertinent soil parameters and footing and pier dimensions are summarized in Table 2. The bearing capacity provided in Table 2 was calculated using Eq. (1) for the footings on unimproved soil or Eq. (4) for the footings on aggregate pier improved soil.

The test footings consisted of rigid concrete foundations, formed and constructed in place. All but one of the tests consisted of a circular footing with a base diameter of 0.76 m. The remaining test (G4DF) consisted of a 2.44 m square footing. The circular footings supported on reinforced soil were constructed on a single aggregate pier with the same diameter as the footing (i.e., ar = 100%). Test G4DF was constructed on 4 aggregate piers resulting in ar = 31%.

The aggregate piers supporting the different loading tests extended to varying depths corresponding to pier lengths of 2, 3, 4 and 5 Dp. The bottom of the deepest aggregate piers (i.e., those with a pier length of 5 Dp) extended into the silty to clayey sand layer. However, the loading test results suggest that this pier exhibited a bulging failure consistent with

aggregate piers with large slenderness ratios (Stuedlein and Holtz 2013). The results of the loading tests are shown in Figure 3, grouped to show tests with similar geometries and test conditions. For comparison, the expected bearing pressure-displacement response calculated using Eq. (2) for the footings on unimproved soil and Eq. (5) for footings on aggregate pier improved soil is shown in Figure 3.

4. Performance of the Reliability-based SLS

Models

In order to better assess the performance of the SLS models proposed by Huffman and Stuedlein (2014) and Huffman et al. (2015) in terms of reliability, the bearing pressure-displacement data from the new loading tests are normalized as dictated by the respective SLS procedures. Figure 4 compares these normalized bearing pressure-displacement curves with the mean predicted responses (i.e., the expected response) and ±1 standard deviation, whereas Figure 5 presents the comparison empirical cumulative distribution functions (CDFs) of normalized capacity at a given normalized displacement to those dictated by the reliability-based SLS design procedures. The mean and ±1 standard deviation curves were generated from 5,000 new MCS based on the resistance model parameters given in Table 1 and the relevant bivariate model parameter correlation structures discussed in Huffman et al. (2015) and Huffman and Stuedlein (2014). As shown in Figure 4(a), the

0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 Depth (m ) Distance(m)

SPT N (blow/0.3 m) and QT(MPa) QT(MPa) 4/7/14

9/19/14

Stiff silty CLAY to clayey SILT, some sand (CL to ML/MH)

Loose to medium dense silty SAND to clayey SAND (SM to SC)

Stiff clayey SILT, some sand (CL to ML/MH) (b) 0 25 50 C-1F 0 25 50 C-1S B-1S 0 25 50 C-3F 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 Depth (m )

SPT N (blow/0.3 m) and QT(MPa) 4/7/14 9/19/14

Stiff silty CLAY to clayey SILT, some sand (CL to ML/MH)

Loose to medium dense silty SAND to clayey SAND (SM to SC)

Stiff clayey SILT, some sand (CL to ML/MH) ? ? (c) 0 25 50 C-3F 0 25 50 C-2F B-1F 0 25 50 C-2S B-2S (a)

Figure 2. Test site with (a) site layout, (b) subsurface cross-section A-A’ and (c) subsurface cross-section B-B’. Note: B-xx = exploratory boring, C-xx = cone penetration test, VST-xx = vane shear test, MW = monitoring well, F = Fall, S = Spring.

Table 2. Summary of pertinent soil information, ground improvement geometry, and footing dimensions. Loading Test su (kPa) B’ (m) Df (m) Dp (m) Lp (m) ar (%) qult (kPa) BS 50 0.76 0.76 - - - 419 BF 65 0.76 0.76 - - - 541 T2DS 50 0.76 0.46 0.76 1.52 100 842 T3DS 50 0.76 0.46 0.76 2.28 100 881 T4DS 50 0.76 0.46 0.76 3.04 100 922 T5DS 50 0.76 0.46 0.76 3.80 100 965 T3DF 65 0.76 0.46 0.76 2.28 100 1,013 T4DF 65 0.76 0.46 0.76 3.04 100 1,060 T5DF 65 0.76 0.46 0.76 3.80 100 1,109 G4DF 65 2.75 0.30 0.76 3.04 30.5 652

Figure 3. Comparison of observed and expected bearing pressure-displacement curvs for footings on (a) 2Dp piers, (b) 3 Dp piers,

(c) 4 Dp piers, (d) 5 Dp piers, and (e) unimproved soil.

observed footing response for the improved ground falls within the bounds of one standard deviation of that expected. The expected response is particularly accurate at normalized bearing pressures less than approximately 0.7qult; with increased displacements, the SLS model tends to over-predict the bearing resistance. However, typical SLS design requirements target allowable bearing pressures less than 0.5qult. Accordingly, the empirical CDFs of normalized capacity compare quite well to those implied by the SLS procedure for aggregate pier-improved clay at the lower normalized displacements (Figure 5). Only at larger K, say 0.05, does the empirical CDF begins to diverge from the expected CDF.

On the other hand, the capacity of the new baseline footings appear to be consistently over-predicted as a function of displacements as shown in Figures 4b and 5, not-withstanding the extremely low sample number (i.e., two). The database used to form the proposed reliability-based SLS procedures for footings on plastic, fine-grained soils included just one footing constructed in the dilative clayey silt deposit as the new footings. Thus, it could be expected that the under-representation of the conditions associated with the current footing loading tests in the database could lead to less accurate estimates than footing responses in other deposits. This comparison highlights the need to revisit

and re-calibrate reliability-based SLS procedures as newer loading test data becomes available.

Separately, these tests highlight the need to identify and quantify the relative contributions of intra-site or intra-deposit variability and inter-site or inter-deposit variability. Concentrating on the footing loading tests derived from the aggregate pier-reinforced clay owing to the much larger sample size, it is observed that the empirical CDF represents significantly less dispersion than that expected from the reliability-based SLS procedures (i.e., the CDF is steeper than

expected). This is because the SLS procedures incorporated data from many test sites, contributing to larger overall variability. Thus, when assessing the differential settlement at a given site, reliability-based SLS procedures relying on data from multiple geologic units will tend to under-predict the actual reliability (differences in the controlling soil layer thickness aside), as it will account for greater dispersion than anticipated due to the implicit incorporation of non-applicable inter-site variability.

Figure 4. Normalized bearing pressure-displacement curves with mean predicted response and ±1 standard deviation for (a) footings on aggregate pier improved soil, and (b) footings on unimproved soil.

Figure 5. Comparison of the observed and expected cumulative distribution functions of the normalized resistance at normalized displacements, K = G/B’ of (a) 0.01, (b) 0.02, (c) 0.03 and (d) 0.05.

5. Conclusions

This study used the results of new full scale loading tests to assess recently developed SLS models for immediate displacement of footings on unimproved and aggregate pier-improved soil. The results of the loading tests compared favorably with the response expected from the SLS model for footings on aggregate pier improved ground. However, the response observed from the footings on unreinforced ground was consistently over-predicted, owing to an under-representation of footing loading test data in similar dilative clayey silt soil. This study emphasizes the need to continuously refine reliability-based design procedures based on full-scale loading tests, and the need to study source contributions of variability stemming from intra- and inter-site uncertainty. Parallel with these efforts, continued improvement of the mechanical models for estimating footing displacement is encouraged.

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