Deterministic and probabilistic assessment of margins of safety for internal stability of as-built PET strap reinforced soil walls

doi:10.1016/j.geotexmem.2020.06.001

Geotextiles and Geomembranes

Volume 48, Issue 6, December 2020, Pages 780-792

https://doi.org/10.1016/j.geotexmem.2020.06.001 Get rights and content

Highlights

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Describes deterministic and reliability-based analyses of internal limit states for PET strap walls.
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Reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet.
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Three PET strap MSE wall case studies are used to demonstrate the reliability-based assessment approach.
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Most critical limit state is the soil failure limit state which is used in the Simplified Stiffness Method.
•
General approach is applicable to MSE walls with extensible and inextensible reinforcement materials.

Abstract

The paper demonstrates deterministic and reliability-based assessment of strength limit states (tensile resistance and pullout) and the service limit state for soil failure for mechanically stabilized earth (MSE) walls constructed with polyester (PET) strap reinforcement. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty in the estimate of nominal load and resistance values at time of design. Reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet. Three PET strap MSE wall case studies are used to demonstrate the reliability-based assessment approach and to compare margins of safety using different load and resistance model combinations. In some walls using the Coherent Gravity Method to compute loads, the recommended nominal factors of safety for tensile strength and pullout limit states were not satisfied. However, reliability analyses showed that the walls satisfy recommended minimum target reliability index values for the limit states investigated, usually by large amounts. The most critical limit state is the soil failure limit state which is used in the Simplified Stiffness Method to keep the reinforced soil zone at working stress conditions assumed for geosynthetic MSE walls under operational conditions.

Introduction

Mechanically stabilized earth (MSE) walls constructed with polyester (PET) strap soil reinforcement are becoming more common to perform the earth retaining wall function. Nevertheless, at the time of this paper only the French code (AFNOR, 2009) and the recent AASHTO (2020) specifications in the USA offer guidance on the design of PET strap walls. Current design codes in Canada (CSA, 2019), the UK (BSI, 2010), Japan (PWRC, 2013) and Hong Kong (Geoguide 6, 2002) remain silent.

Miyata et al. (2018) collected reinforcement load measurements from eight instrumented PET strap walls at end of construction. The reinforcement was identified as relatively inextensible in some case study sources, and thus treated similar to steel reinforcement products, while in the other cases the PET strap reinforcement was classified as an extensible geosynthetic type. This distinction is important for the internal stability design of MSE walls because the Coherent Gravity Method (e.g., AASHTO, 2020; BSI, 2010; CSA, 2019) and variants are recommended in design codes for relatively inextensible reinforcement, while the AASHTO (2017) Simplified Method and variants are recommended for extensible geosynthetic reinforced MSE wall systems. Only the Simplified Stiffness Method (Allen and Bathurst, 2015, 2018) provides a seamless transition between inextensible and extensible reinforcement classifications for the internal stability design of MSE walls. Using the global reinforcement stiffness value that appears in the Simplified Stiffness Method, Miyata et al. (2018) concluded that PET strap walls fall into the extensible (geosynthetic) wall category along with geogrids and geotextiles (or at least at the stiffer end of these walls) rather than MSE walls with relatively inextensible (steel) reinforcement.

Miyata et al. (2018) assessed the accuracy of load predictions using the Coherent Gravity Method, the Simplified Method and the Simplified Stiffness Method by comparing predicted loads with those deduced from reinforcement strain measurements from the eight wall cases in their study. The Coherent Gravity Method and the Simplified Method resulted in conservative (safe) estimates of reinforcement loads under operational conditions on average. However, the Simplified Stiffness Method was the most accurate and did not result in an excessive level of conservativeness.

Miyata et al. (2019) carried out a complementary investigation of the accuracy of different pullout models for the ultimate (failure) pullout capacity for PET strap reinforcement. The models were taken from the research literature and default models specified in design codes for steel and geosynthetic reinforcement materials. The accuracy of these models and new models developed by the authors was investigated by comparing pullout capacity predictions with measured values in the database of pullout tests compiled by the authors from many sources.

The accuracy of the reinforcement load and pullout models in the two studies described above was determined from analysis of bias statistics where bias is the ratio of measured (observed) value to predicted (calculated) value. The same collections of bias values can be used to carry out reliability-based (probabilistic) assessment of internal stability tensile and pullout strength limit states and the service limit state for soil failure of PET strap MSE walls at the time of design or for as-built structures.

This paper demonstrates for the first time a rigorous reliability assessment approach for the limit states identified above using three examples of as-built PET strap walls taken from the study of Miyata et al. (2018) and the collections of load and resistance bias values mentioned above. The assessment of margin of safety is based on the deterministic nominal factor of safety and the reliability index (or probability of failure) that are computed using different load and pullout model combinations. The design limit state for the connection between the reinforcement straps and the concrete facing panels is not considered in this investigation.

The assessment of margins of safety in terms of probability that an internal limit state is not satisfied (i.e., failure) provides the designer with a more nuanced appreciation of margins of safety during design than can be gained from allowable (working) stress (factor of safety) design used in past practice and current load and resistance factor design (LRFD).

Reliability analyses of the case study walls in this study are based on the problem geometry and parameters shown in Fig. 1. The details of these figures are described later in the paper. The simple geometry and reinforcement arrangement for the example walls have the advantage of a vertical face, horizontal back-slope and a single reinforcement type.

The current study is timely because the latest edition of the AASHTO (LRFD) Bridge Design Specifications in the USA (AASHTO, 2020), adopts the Simplified Stiffness Method as the primary method for internal stability design of geosynthetic MSE walls, including those constructed with PET strap reinforcement. In the new AASHTO specifications, the Simplified Stiffness Method is called the “Stiffness Method” for brevity and the polymeric straps are called “geostrips”.

Section snippets

General

The three load models introduced in the previous section are briefly reviewed here for the case of frictional (cohesionless) soils only. All three load models are empirically based using loads estimated from reinforcement strain measurements taken from instrumented structures under operational conditions. The Coherent Gravity and Simplified Methods estimate loads considering soil strength and reinforcement type, whereas the Simplified Stiffness Method is largely based on the reinforcement

Pullout models

The general form of the PET strap pullout models in this study is:P_c = 2f*σ_v L_e R_c

Here, P_c = peak pullout capacity (e.g., units of kN/m), f* = dimensionless interaction coefficient (the equivalent symbol F* is used in US design practice), σ_v = vertical stress acting at the elevation of the reinforcement layer in the resistant zone, L_e = anchorage length of the reinforcement element, and R_c = coverage ratio = b_w/S_h where b_w = width of the reinforcement element and S_h = horizontal

Tensile strength

In this investigation the ultimate tensile strength (rupture) capacity of the reinforcement is taken as the nominal long-term tensile strength (AASHTO, 2020; CSA, 2019) computed as: $T_{al} = \frac{T_{ult}}{RF} = \frac{T_{ult}}{{RF}_{ID} \times {RF}_{CR} \times {RF}_{D}}$

The numerator is a reference laboratory ultimate tensile strength (T_ult), typically a minimum average roll value (MARV). This reference tensile strength is reduced by factors that account for loss of strength over the design life of the reinforcement due to installation damage (RF_ID),

Soil failure (Simplified Stiffness Method)

A key feature of the Simplified Stiffness Method is the soil failure limit state which applies to MSE walls constructed with extensible geosynthetic reinforcement materials. Satisfying this limit state ensures that the strain in each reinforcement layer under operational conditions does not exceed a value that will cause a contiguous zone of shear stress to develop in the reinforced soil zone that is equal to the soil peak strength. This constraint is required if working stress conditions

General approach

The general form of the limit state design equations in this investigation is: $g = \frac{R_{m}}{Q_{m}} - 1 = \frac{λ_{R} R_{n}}{λ_{Q} Q_{n}} - 1$

Here R_m and Q_m are the measured (observed) resistance and measured (observed) load, respectively. Parameters λ_R and λ_Q are resistance and load method bias (or bias values for brevity), respectively, and are used to transform nominal values (R_n and Q_n) to corresponding measured values, hence:λ_R = R_m/R_nλ_Q = Q_m/Q_n

Bias values can be understood to account for over- or under-estimation of observed

Example walls

Three well-documented case histories of full-scale instrumented PET strap MSE walls are used in this study to demonstrate reliability analyses for the three limit states introduced earlier. The Delaware wall was constructed in the USA in 2012. The Nagasaki wall was constructed in Japan in 2015 and the Sao Paulo wall in Brazil in 2011. These three examples were selected to provide a wide geographical coverage and a range of soil properties and reinforcement arrangement. Wall geometry and

Bias statistics

Bias statistics for load and resistance models were collected (or computed) from data reported in previous studies by the authors (Miyata et al., 2018, 2019; Allen and Bathurst, 2019). They are summarized in Tables S1, S2 and S3 in the Supplemental Material for the maximum tensile load, tensile strength and maximum pullout capacity, respectively.

Two sets of load bias value statistics are shown in Table S1 for each load model; one set of bias values was computed for walls constructed with c−ϕ

Results

Selected results from all three walls are presented here to demonstrate the main outcomes. The results of all analyses can be found in the Supplemental Material for this paper. Unless noted otherwise, the plots in the figures to follow are computed taking COV_Qn = COV_Rn = 0, implying that there is no uncertainty in the “level of understanding” of the limit states, project conditions and material properties at the time of design. Nevertheless, differences in computed β values using nominal COV

Conclusions

This paper has focused on the calculation of margins of safety for three internal stability limit states for three full-scale instrumented walls constructed with PET strap reinforcement products. The connection limit state was not investigated in this study. Margins of safety for the reinforcement layers in these structures were expressed by (deterministic) nominal factor of safety, operational factor of safety and reliability index (or matching probability of failure). These calculations were

Acknowledgements

The authors are grateful for financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant Number: 94344-2013), the Ministry of Transportation of Ontario (MTO) Highway Infrastructure Innovations Funding Program (Grant Number: 9017-R-0030) and the Japan Ministry of Education, Culture, Sports, Science and Technology (Grant-in-Aid for Scientific Research (B) No. 17H03309).

References (41)

R.J. Bathurst et al.
Reinforcement loads in geosynthetic walls and the case for a new working stress design method
Geotext. Geomembranes
(2005)
N. Bozorgzadeh et al.
Influence of corrosion on reliability-based design of steel grid MSE walls
Struct. Saf.
(2020)
Y. Miyata et al.
Evaluation of K-Stiffness method for vertical geosynthetic reinforced granular soil walls in Japan
Soils Found.
(2007)
Y. Miyata et al.
Analysis and calibration of default steel strip pullout models used in Japan
Soils Found.
(2012)
T.M. Allen et al.
An improved simplified method for prediction of loads in reinforced soil walls
ASCE J. Geotech. Geoenviron. Eng.
(2015)
T.M. Allen et al.
Application of the Simplified Stiffness Method to design of reinforced soil walls
ASCE J. Geotech. Geoenviron. Eng.
(2018)
T.M. Allen et al.
Geosynthetic reinforcement stiffness characterization for MSE wall design
Geosynth. Int.
(2019)
T.M. Allen et al.
A new working stress method for prediction of reinforcement loads in geosynthetic walls
Can. Geotech. J.
(2003)
T.M. Allen et al.
A new working stress method for prediction of loads in steel reinforced soil walls
ASCE J. Geotech. Geoenviron. Eng.
(2004)
T.M. Allen et al.
Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design
(2005)

AASHTO

NTPEP Report 8508.1. Final Product Qualification Report for Linear Composites Paraweb/Paralink and Paragrid Product Line. National Testing and Product Evaluation Program (NTPEP) Report Series, Laboratory Evaluation of Geosynthetic Reinforcement

(2010)

AASHTO

Standard Practice R69-15. Determination of Long-Term Strength for Geosynthetic Reinforcement

(2015)

AASHTO

LRFD Bridge Design Specifications

(2017)

AASHTO

LRFD Bridge Design Specifications

(2020)

AFNOR

NF P94-270: Renforcement des sols. Ouvrages en sol rapporté renforcé par armatures ou nappes extensibles et souples. Dimensionnement (Association Française de Normalisation). La Plaine Saint Denis cedex – France

(2009)

A. Azizinamini et al.

Bridges for Service Life beyond 100 Years: Innovative Systems, Subsystems, and Components. (No. SHRP 2 Report S2-R19a-RW-1) Transportation Research Board, Washington, DC

(2014)

R.J. Bathurst et al.

LRFD calibration of internal limit states for geogrid MSE walls

ASCE J. Geotech. Geoenviron. Eng.

(2019)

R.J. Bathurst et al.

Calibration concepts for load and resistance factor design (LRFD) of reinforced soil walls

Can. Geotech. J.

(2008)

R.J. Bathurst et al.

Influence of model type, bias and input parameter variability on reliability analysis for simple limit states in soil-structure interaction problems

Georisk

(2017)

R.J. Bathurst et al.

Reliability-based design of internal limit states for mechanically stabilized earth walls using geosynthetic reinforcement

Can. Geotech. J.

(2019)

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Deterministic and probabilistic assessment of margins of safety for internal stability of as-built PET strap reinforced soil walls

Highlights

Abstract

Introduction

Section snippets

General

Pullout models

Tensile strength

Soil failure (Simplified Stiffness Method)

General approach

Example walls

Bias statistics

Results

Conclusions

Acknowledgements

Geotext. Geomembranes

Struct. Saf.

Soils Found.

Soils Found.

An improved simplified method for prediction of loads in reinforced soil walls

ASCE J. Geotech. Geoenviron. Eng.

Application of the Simplified Stiffness Method to design of reinforced soil walls

ASCE J. Geotech. Geoenviron. Eng.

Geosynthetic reinforcement stiffness characterization for MSE wall design

Geosynth. Int.

A new working stress method for prediction of reinforcement loads in geosynthetic walls

Can. Geotech. J.

A new working stress method for prediction of loads in steel reinforced soil walls

ASCE J. Geotech. Geoenviron. Eng.

Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design

NTPEP Report 8508.1. Final Product Qualification Report for Linear Composites Paraweb/Paralink and Paragrid Product Line. National Testing and Product Evaluation Program (NTPEP) Report Series, Laboratory Evaluation of Geosynthetic Reinforcement

Standard Practice R69-15. Determination of Long-Term Strength for Geosynthetic Reinforcement

LRFD Bridge Design Specifications

LRFD Bridge Design Specifications

NF P94-270: Renforcement des sols. Ouvrages en sol rapporté renforcé par armatures ou nappes extensibles et souples. Dimensionnement (Association Française de Normalisation). La Plaine Saint Denis cedex – France

Bridges for Service Life beyond 100 Years: Innovative Systems, Subsystems, and Components. (No. SHRP 2 Report S2-R19a-RW-1) Transportation Research Board, Washington, DC

LRFD calibration of internal limit states for geogrid MSE walls

ASCE J. Geotech. Geoenviron. Eng.

Calibration concepts for load and resistance factor design (LRFD) of reinforced soil walls

Can. Geotech. J.

Influence of model type, bias and input parameter variability on reliability analysis for simple limit states in soil-structure interaction problems

Georisk

Reliability-based design of internal limit states for mechanically stabilized earth walls using geosynthetic reinforcement

Can. Geotech. J.