Allen and Bathurst (2001) developed a new methodology for estimating reinforcement loads in both steel and geosynthetic reinforced soil walls known as the K0-Stiffness Method. Figure 8.44a and b, for polymeric and metal reinforcements, respectively, are provided for estimating the reinforcement load distribution with respect to the magnitude of maximum reinforcement tension from the top to the bottom of the wall. The soil reinforcement load distribution factor (D, max) in these two figures was determined empirically from all of the available field wall case histories. There were empirical databases consisting of measured reinforcement strains and loads from nine full-scale field geosynthetic wall cases (13 different wall sections and surcharge conditions, and 58 individual data points) and 19 full-scale field steel reinforced soil wall cases
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FIGURE 8.44 Distribution of maximum tension force in a reinforcement layer Tmax with normalized depth below top of wall. (a) For geosynthetic-reinforced soil walls; (b) for steel-reinforced soil walls. (From Research Report WA-RD 528.1, Washington State Department of Transportation, Olympia, Wash., with permission) |
(24 different wall sections and surcharge conditions, and 102 individual data points). The resulting factor is shown in Fig. 8.44a for geosynthetic-reinforced soil walls and in Fig. 8.44b for steel-reinforced soil walls. This factor, D, , is the ratio of the
‘max
maximum tension force Tmax in a reinforcement layer to the maximum reinforcement loads in the wall, T (the maximum value of T within the wall). The two parts of Fig. 8.44 provide the distributions of load, but the magnitude of Tmax is evaluated by the equations of the ^-Stiffness Method in Art. 8.5.13. Empirical reinforcement load distributions provided in Fig. 8.44a and b apply only to walls constructed on a firm soil foundation. The distributions that would result for a rock or soft-soil foundation may differ from those shown. The two parts of the figure demonstrate the differences in reinforcement load distributions between geosynthetic — and steel-reinforced soil walls. The long recognized fact of nontriangular load distribution is clarified, especially for the geosynthetic-reinforced soil wall. Though two different drawings have been used to determine the reinforcement load distribution, this new method provides an improved load estimation for both steel — and geosynthetic-reinforced soil walls and a unified approach.
This new method was developed empirically through analyses of many full-scale wall case histories. In most cases, reinforcement loads had to be estimated from measured reinforcement strain converted to load through a properly estimated reinforcement modulus. For metal-reinforced soil walls, the use of Young’s modulus to convert strain to stress and load is relatively straightforward. However, to accurately determine the
reinforcement loads for geosynthetic-reinforced soil walls, the correct modulus, considering time and temperature effects, had to be estimated accurately. The creep modulus generated from long-term laboratory creep data through regular product analysis was considered accurate enough for estimating reinforcement loads from measured strains.
Once the correct load levels in the reinforcement layers were established, the reinforcement loads obtained from the full-scale walls were compared to what would be predicted with the new method and the current methodologies found in design guidelines and design codes, including the simplified coherent gravity approach in article 5.8.4.1 of AASHTO. All existing design methodologies were found to provide inaccurate load predictions, especially for geosynthetic-reinforced walls. Considering all available case histories, Allen and Bathurst (2001) reported that the average and coefficient of variation (COV) of the ratio of the predicted to measured Tmax, the peak reinforcement load in each layer, for the simplified method were as follows: 2.9 and 85.9 percent, respectively, for geosynthetic walls, and 0.9 and 50.6 percent, respectively, for steel-reinforced soil walls. The average and COV of the ratio for the K0-Stiffness Method were as follows: 1.12 and 40.8 percent, respectively, for geosynthetic walls, and 1.12 and 35.1 percent, respectively, for steel-reinforced soil walls. This indicates a marked improvement and shows that the calculated loads can be estimated more closely with the D, factors
‘max
and the K0-Stiffness Method.
In the determination of the magnitude of Tmax in the wall, the stiffness of all wall components (facing type, facing batter, reinforcement stiffness, and spacing) relative to soil stiffness is evaluated. By the nature of extensibility of soil reinforcement, the reinforcement load distributions (D, max) are differentiated by two unique figures. From working load to ultimate load up to incipient soil failure, this methodology covers the full range of strain and load predictions. The method is workable to estimate reinforcement responses for both the serviceability and strength limit state. It also includes the estimate of wall deformation from reinforcement strain prediction, load, and resistance factors that account for the uncertainty in the method and material properties.
