**1. Introduction**

Reinforced earth achieves reinforcement with high-tensile strength, and it has been used as a method to improve the stability of various geotechnical structures by decreasing the earth pressure and by increasing the shear strength [1–13]. Among the various structures, mechanically stabilized earth (MSE) walls are mainly divided in panel and block types, depending on the type of the facing wall. Because the inhibition of horizontal deformation in the facing wall is required for vertical MSE walls using reinforced earth, various reinforcements have been developed. Reinforcements that are applied to MSE walls are classified as inextensible and extensible reinforcements, depending on the material, and extensible reinforcements, such as geogrids and geosynthetic strips, have been mainly used in the late stages. In South Korea, in particular, block-type MSE walls with geogrids have been mainly applied owing to their economic feasibility and appearance, and geosynthetic strips that are applicable to block-type facing walls have been developed.

The design of the MSE walls was based on internal and external stability. To achieve internal stability, fracture and failure are determined by the tensile strength of the reinforcement. The pullout failure of the resistance area is based on the soil-reinforcement interaction, which is very important for the behavior of MSE walls. The mechanism associated with this failure is very complex because it depends on the characteristics of the

**Citation:** Park, J.; Hong, G. Effective Length Prediction and Pullout Design of Geosynthetic Strips Based on Pullout Resistance. *Materials* **2021**, *14*, 6151. https://doi.org/10.3390/ ma14206151

Academic Editor: Krzysztof Schabowicz

Received: 23 September 2021 Accepted: 14 October 2021 Published: 16 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

soil-reinforcement interaction [14]. In particular, because embedded extensible reinforcement may exhibit tensile deformation owing to load transfer during the pullout process, load transfer must be considered in pullout resistance evaluation. Therefore, it is necessary to analyze the pullout behavior of the reinforcement to secure the stability of the MSE walls and to calculate reasonable design parameters. Many studies have been conducted on the reinforcement interaction. Experimental studies have been conducted on the pullout behavior of grid-type inextensible and extensible reinforcements applied in sand and cohesive soil [15–22]. In addition, studies on methods for evaluating the pullout resistance of reinforcement have been conducted based on experimental research [23–25], and a number of studies on the theoretical and numerical analysis of the soil-reinforcement interaction have also been conducted [26–29]. Studies have been conducted on the influence of soil conditions on the pullout resistance of reinforcement [30–32]. Additional studies have been conducted on the shear resistance of reinforced soil and on interactions using mixed soil [33–35]. Grid-type reinforcement has been used in many studies, but studies on the pullout behavior of geosynthetic strips have been conducted to extend the applicability of geosynthetic strips [27,28,36,37].

In this study, pullout tests on geosynthetic strips were conducted to ensure the design applicability of these strips to block-type facing walls. Based on the test results, the pullout displacement–pullout load relationship was analyzed to evaluate the pullout behavior of the geosynthetic strips. In addition, the effective length that induced the pullout resistance of a geosynthetic strip in the soil was predicted. The pullout parameters were derived using the predicted effective length, and they were applied to a design case to evaluate the effective length prediction method.

#### **2. Theoretical Background of Reinforcement Pullout**

#### *2.1. Soil-Reinforcement Interaction under Pullout Condition*

The interaction between the soil and embedded reinforcement consists of two mechanisms: the shear resistance (friction resistance) on the top and bottom surfaces of the reinforcement, and the bearing resistance of the supporting member. The pullout resistance that uses these mechanisms is expressed by Equation (1) by FHWA [38].

$$P\_r = 2\ L\_\varepsilon \ \sigma\_v' \propto F^\* \ , \tag{1}$$

where *Le* is the embedded length in the resistant zone; *σ*- *<sup>v</sup>* is effective vertical stress at soil-reinforcement interfaces, *<sup>α</sup>* is the scale effect correction factor, *<sup>F</sup>*∗(= *fb*·*tan*<sup>∅</sup> <sup>=</sup> *tanδ*) is the pullout resistance factor, *fb* is the soil-reinforcement bond coefficient, ∅ is the internal friction angle of soil, and *δ* is the soil-reinforcement interface friction angle.

The pullout resistance factor includes both friction and bearing resistance elements. Because geosynthetic strips develop pullout resistance owing to friction, the pullout resistance factor is identical to the friction angle of the soil-reinforcement interface. The pullout resistance factor is determined by the bond coefficient (*fb*, soil-reinforcement bond coefficient) caused by the soil-reinforcement interaction. The bond coefficient is defined as the ratio of the shear strength on the soil-reinforcement interface to the shear strength of the soil, as shown by Equation (2) [33].

$$f\_b = \frac{\tau\_p}{\tau} = \frac{c\_p + \sigma\_v' \tan \delta}{c + \sigma\_v' \tan \mathcal{Q}} \,\tag{2}$$

where *τ<sup>p</sup>* is the shear strength at the soil-reinforcement interface, *τ* is the shear strength of the soil, *cp* is the soil-reinforcement interface adhesion, and *c* is the cohesion in the soil.

In this instance, the shear strength at the soil-reinforcement interface can be calculated using the surface area of the reinforcement and the pullout force from the pullout test results. The mechanism of soil-reinforcement interaction can be confirmed in detail through schematic diagrams in previous studies [33,38].
