Prediction of Reinforcement Connection Loads in Geosynthetic Reinforced Segmental Retaining Walls Using Response Surface Method

Round 1

Reviewer 1 Report

applsci-2427194

Prediction of reinforcement connection loads in geosynthetic reinforced segmental retaining walls using response surface method

Wan Zhang & JianFeng Chen

The objective of this study was that of proposing a criterion for predicting the tensile load in the connections of the reinforcements in reinforced earth structures provided of segmental wall (GRS). To this purpose, numerical investigation was first carried out in order to appreciate the role of the wall foundation in carrying part of the active earth load: in this case were examined the influence of the toe restraint, the wall height, the facing inclination, the reinforcement spacing and the soil friction angle. The comparison between the results of the numerical models and of a full-scale instrumented GRS wall, allowed a new method for predicting the connection tensile load by replacing the Coulomb active earth pressure coefficient with a reduced earth pressure coefficient because of the strength of the foundation. Finally, the proposed method was compared with the classical Earth Pressure Method and the Stiffness Method (which are not recalled to the reader) using the measured connection loads on reinforcement with reference to two full height walls and three centrifuge model walls.

This article may be considered interesting for the users of the journal and may accepted for publication. However, some aspects appear neglected and need more explanation and/or revision of the text.

For example, the difference between the plane strain soil strength compared to the triaxial condition is pointed out, but the intercept cohesion is neglected, which can give a significant contribution to soil strength in mechanically compacted embankments. An examination of equation 5 shows that the Coulomb formula has been applied assuming null the friction angle between the segmental face and the soil; this assumption is a highly reductive for works of this nature. The block-block interface is schematized as a simple frictional contact, whereas local block overturning is possible; geosynthetic creep may have a role in the term distribution of tensile load in the reinforcements. Authors should clarify and discuss these aspects to raise awareness of the static behaviour of reinforced earth structures of this nature. It should also be specified that reducing the Coulomb active thrust due to the foundation strength must be carefully analysed in the light of the possible differential settlements at the level of the foundation in high-rise works and in bridge abutments built with these technologies.

applsci-2427194

Prediction of reinforcement connection loads in geosynthetic reinforced segmental retaining walls using response surface method

Wan Zhang & JianFeng Chen

The objective of this study was that of proposing a criterion for predicting the tensile load in the connections of the reinforcements in reinforced earth structures provided of segmental wall (GRS). To this purpose, numerical investigation was first carried out in order to appreciate the role of the wall foundation in carrying part of the active earth load: in this case were examined the influence of the toe restraint, the wall height, the facing inclination, the reinforcement spacing and the soil friction angle. The comparison between the results of the numerical models and of a full-scale instrumented GRS wall, allowed a new method for predicting the connection tensile load by replacing the Coulomb active earth pressure coefficient with a reduced earth pressure coefficient because of the strength of the foundation. Finally, the proposed method was compared with the classical Earth Pressure Method and the Stiffness Method (which are not recalled to the reader) using the measured connection loads on reinforcement with reference to two full height walls and three centrifuge model walls.

This article may be considered interesting for the users of the journal and may accepted for publication. However, some aspects appear neglected and need more explanation and/or revision of the text.

For example, the difference between the plane strain soil strength compared to the triaxial condition is pointed out, but the intercept cohesion is neglected, which can give a significant contribution to soil strength in mechanically compacted embankments. An examination of equation 5 shows that the Coulomb formula has been applied assuming null the friction angle between the segmental face and the soil; this assumption is a highly reductive for works of this nature. The block-block interface is schematized as a simple frictional contact, whereas local block overturning is possible; geosynthetic creep may have a role in the term distribution of tensile load in the reinforcements. Authors should clarify and discuss these aspects to raise awareness of the static behaviour of reinforced earth structures of this nature. It should also be specified that reducing the Coulomb active thrust due to the foundation strength must be carefully analysed in the light of the possible differential settlements at the level of the foundation in high-rise works and in bridge abutments built with these technologies.

 

Author Response

1. For example, the difference between the plane strain soil strength compared to the triaxial condition is pointed out, but the intercept cohesion is neglected, which can give a significant contribution to soil strength in mechanically compacted embankments.

Reply:

Thank you for your comment. In the design of GRS walls, the cohesionless backfill is recommended (FHWA, 2009). Thus, the object of this study is the GRS segmental walls with cohesionless backfill. The cohesion of the cohesionless backfill is usually assumed to be 0. The adopting of a small value for backfill cohesion in the current work instead of 0 is only to avoid numerical instability.

In Introduction, we have pointed out that the object of this study is the cohesionless reinforced fill walls (see Lines 82-84 in revised paper).

Reference:

FHWA, 2009. Design of mechanically stabilized earth walls and reinforced slopes. In: Berg, R.R., Christopher, B.R., Samtani, N.C. (Eds.), No. FHWA-NHI-10-024 Vol I. Federal Highway Administration, Washington, DC., USA.

2. An examination of equation 5 shows that the Coulomb formula has been applied assuming null the friction angle between the segmental face and the soil; this assumption is a highly reductive for works of this nature.

Reply:

Thank you for your comment. We agree the reviewer’s point that Equation 5 is reductive. Nevertheless, this equation for active earth pressure coefficient is recommended by FHWA standard, which considers that the friction between the facing column and the backfill can be ignored. The reductive equation will induce conservative results (i.e., lager reinforcement tensile forces than actual values). The Equation 5 is just used for comparing the numerically calculated active thrust against facing column with the theoretically calculated one, instead of calculating reinforcement tensile forces. In fact, the numerical values are indeed smaller than the theoretical values. The proposed method for calculating reinforcement connection loads in this paper is back-analyzed based on the numerical results. Thus, the calculated earth pressure using Equation 5 has no influence on the results of this paper.

An explanation for the simplification of Equation 5 has been added in the revised manuscript (see Lines 295-297, 305-306 in revised paper).

3. The block-block interface is schematized as a simple frictional contact, whereas local block overturning is possible; geosynthetic creep may have a role in the term distribution of tensile load in the reinforcements. Authors should clarify and discuss these aspects to raise awareness of the static behaviour of reinforced earth structures of this nature.

Reply:

Thank you for your comment. We agree the reviewer’s point that local block overturning is possible. In fact, we also pointed out that the reinforcement connection load is generally the maximum tensile force along a reinforcement layer partially due to the down-drag force caused by rotation of facing column. The effect of block overturning is difficult to be quantified in theoretical equations. However, in our numerical modeling, the block overturning can be simulated as show in the following figure (please see attachment). Thus, the effect of block overturning has been considered in the proposed method for calculating reinforcement loads. Relevant content has been stated in the manuscript (see Lines 565-570 in revised paper). The effect of geosynthetic creep was considered in the proposed method by using the creep stiffness for the reinforcement layers in the numerical modeling (see Lines 253-255 in revised paper).

4. It should also be specified that reducing the Coulomb active thrust due to the foundation strength must be carefully analysed in the light of the possible differential settlements at the level of the foundation in high-rise works and in bridge abutments built with these technologies.

Reply:

Thank you for your suggestion. The foundation stiffness is considered to have a great influence on the reinforcement connection loads, which has been pointed out several times in the paper (see Lines 40-43, 565-566 in revised paper). This paper only focuses on the reinforced soil walls constructed on the competent foundation, considering that this is common cases. The influence of foundation stiffness will be analyzed in our future work.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Use reference - explain about the high value of the angle of internal friction of the soil in Table 1.

The exact reason for considering the model has not been specified precisely.  Please explain.

What is the connection between wall number 1-4-5 and references 12-17-50 on page 21?

The percentage of difference in the data is suggested in figure 19 to 23.

please explain to use of this method about the effects of the cohesion of backfill soil and the down-drag force induced by differential settlement of foundations.

Please check the relationship parameters 7 to 10. Some may be undefined.

 

 

It is suggested to review the use of technical words in the article.

Author Response

1. Use reference - explain about the high value of the angle of internal friction of the soil in Table 1.

Reply:

Thank you for your suggestion. The wall used for numerical validation in this paper was reported by Allen and Bathurst (2014). The friction angle of 54° was calculated from the triaxial ones using the equation by Lade and Lee (1976):

                                       φ_{ps=1.5φtx-17}

where φ_ps = plane strain friction angle; φ_tx = triaxial friction angle. The triaxial friction angle of backfill soil is 47°, which was determined by triaxial tests (Allen and Bathurst, 2014). The reference of Allen and Bathurst, 2014 has been added in the revised manuscript (see Lines 131 in revised paper).

Reference:

Allen, T.M., Bathurst, R.J., 2014. Design and performance of 6.3-m-high, block-faced geogrid wall design using K-stiffness method. Journal of Geotechnical and Geoenvironmental Engineering, 140 (2), 04013016.

Lade, P.V., Lee, K.L., 1976. Engineering properties of soils. Report UCLA-ENG-7652, University of California, Los Angeles, Calif.

2. The exact reason for considering the model has not been specified precisely. Please explain.

Reply:

Thank you for your comment. The reinforcement connection loads are difficult to calculate using theorical method, because it is affected by the down-drag forces caused by backfill compaction, rotation of facing column and differential settlement of foundation. However, these influence factors can be considered in numerical modeling of reinforced soil walls. Thus, we constructed the database of reinforcement connection load through a number of numerical simulations. The numerical study shows that the connection loads are affected by a variety of factors, such as toe restraint, wall height, facing batter, facing stiffness, reinforcement spacing, etc. It is not easy to establish the relationship between the connection load and the enumerated influence factors analytically. This problem can be effectively solved using the response surface method, whereby the relationship can be approximated with a polynomial. Thus, we proposed the response surface model of connection load based on the database of connection load. Relevant content has been stated in the manuscript (see Lines 73-78, 565-570 in revised paper).

3. What is the connection between wall number 1-4-5 and references 12-17-50 on page 21?

Reply:

Thank you for your comment. Both Walls 1, 4 and 5 and the walls reported by References 12, 17 and 50 are the walls under working stress conditions. The distribution shapes of predicted connection loads in Walls 1, 4 and 5 are similar with those in the walls reported by References 12, 17 and 50, which shows the reliability of the proposed response surface method.

4. The percentage of difference in the data is suggested in figure 19 to 23.

Reply:

Thank you for your suggestion. The difference in the data in Figures 19 to 23 has been quantified the revised manuscript (see Lines 529-531, 534-536, 540-541, 546-548, 550 in revised paper).

5. Please explain to use of this method about the effects of the cohesion of backfill soil and the down-drag force induced by differential settlement of foundations.

Reply:

Thank you for your comment. The proposed method applies to the cohesionless reinforced fill walls constructed on competent foundations, which is required by FHWA standard and is common case. The effect of more unfavorable cases, such as cohesive backfill and compressible foundation, needs further study and will be included in the proposed model in our future work.

Reference:

FHWA, 2009. Design of mechanically stabilized earth walls and reinforced slopes. In: Berg, R.R., Christopher, B.R., Samtani, N.C. (Eds.), No. FHWA-NHI-10-024 Vol I. Federal Highway Administration, Washington, DC., USA.

6. Please check the relationship parameters 7 to 10. Some may be undefined.

Reply:

Thank you for your comment. Partial parameters in Equations 7-10 have been defined earlier (see Lines 427-438 in revised paper) and thus they have not been redefined after Equations 7-10.

Author Response File: Author Response.docx