Optimization of anchor trench design for solar evaporation ponds.
Geosynthetics | October 2010
By Richard Thie
A series of 10-hectare (25-acre), geomembrane-lined ponds were planned to evaporate potash salt. The ponds were designed with 1(V):2(H) sideslopes ranging in height from 2m–12m. The sideslopes would have the geomembrane exposed.
One of the value-engineering goals was to design the anchor trenches to involve minimal construction effort while resisting pullout due to possible wind forces. The estimated wind forces were calculated using the Giroud et al. (1995) method for a 145km/hr wind speed.
From the Euler-Eytelwein equation presented in Figure 2, we have the corner force relationship: 
Defining 
we have: 
Figure 4 presents a free-body diagram (FBD) and a force polygon of the bottom trench corner.
The resultant force R3 can be solved using the law of cosines as: 
Where: 
The angle b can be solved using the law of sines as: 
The x- and y- directions for R3 can now be resolved as: 
Referring to Figure 5, and summing forces in the x- and y- directions, yields the following: 
Rearranging Equation (9) yields the following (not all steps are shown to save space): 
Where: 
Rearranging Equation (10) yields the following: 
Where W2 can easily be calculated from the unit weight and geometry, and where: 
Having solved for T'3 in Equation (13) allows for calculation of T3 and N2 (and therefore S21 and S22, as well) using Equations (2) and (11), respectively. This then allows calculation of T'2 as: 
Using Equations (2) and (3) in a similar fashion for corner number 2 as was used for corner number 3, and defining K2 = e(?1)tand2, we obtain: 
This now allows for the calculation of T1 as: 