###### Abstract  
This paper presents an improved earth pressure method that considers the capacity of a wall toe to carry an earth load to predict the connection loads of GRS segmental walls constructed with cohesionless backfills on competent foundations. In this method, a response surface model (RSM) of the lateral earth pressure coefficient replaces the Coulomb active earth pressure coefficient. The parameters of the RSM were determined from numerical studies on the impacts of toe restraint, wall geometry, and backfill properties on the distribution of earth loads between the toe and reinforcement layers. The unknown coefficients of the RSM were obtained through a regression analysis of 705 reinforcement load values from 65 simulated walls. The proposed method was compared to the earth pressure method and the stiffness method using measured connection loads from field and centrifuge GRS segmental walls. The results show that the predictions of the proposed RSM method are in better agreement with the measurements than those of the stiffness method and the earth pressure method, whether under a typical or poor toe restraint condition. geosynthetics; segmental retaining walls; reinforcement connection load; toe load; response surface method; numerical modeling +
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This indicates that the connection load may be the largest within the reinforcement layer and an important design parameter for GRS walls in both the working stress and limit states. There are a few methods for predicting reinforcement connection loads. [PERSON] et al. [14] considered that the earth pressure method, specified in the FHWA (2009) [15] standard, can be used to predict \(T_{\text{con}}\) for GRS bridge abutments based on a comparison between measured connection loads and theoretical calculations. The earth pressure method is the most widely used for predicting \(T_{\text{bmax}}\); in this approach, \(T_{\text{bmax}}\) is equated with the active earth pressure calculated using [PERSON]'s theory within the contributory area of each reinforcement layer. However, this method seriously overestimates the \(T_{\text{bmax}}\) of GRS walls under working stress conditions, since it ignores the effects of toe resistance, facing stiffness, reinforcement stiffness, and backfill soil cohesion on the reinforcement loads [16]. Overestimation was also observed in the calculated values of the earth pressure method when comparing it to \(T_{\text{con}}\) under working stress conditions [10; 11]. A number of experimental and numerical studies have shown that a significant portion of earth pressures acting on the facing column are counterbalanced by toe resistance [17; 18; 19; 20; 21]. Considering the effects of toe resistance on reinforcement loads, [PERSON] et al. [22] presented a limit equilibrium method to calculate \(T_{\text{con}}\) for both GRS walls and slopes, in which toe resistance was regarded as a function of the normal load and the interface friction angle at the base of the facing column. [PERSON] et al. [23] included toe resistance in the earth pressure method to estimate \(T_{\text{con}}\). In this method, toe resistance was calculated using the equilibrium of the forces and bending moments of the vertical facing column. Some methods for predicting \(T_{\text{bmax}}\) also included the influence of toe resistance [24; 25; 26; 27]. Among them, the stiffness method proposed by [PERSON] [25], which was previously known as the simplified stiffness method, has been adopted in the latest AASHTO (2020) code [28]. It has been shown that the magnitude of toe resistance is affected by a variety of factors, such as toe restraint, wall height, facing batter, facing stiffness, reinforcement spacing, etc. [29; 30; 31; 32; 33]. It is not easy to determine the relationship between toe resistance or \(T_{\text{con}}\) 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.