The internal stability requirements for MSE walls dictate the extent of the reinforcement elements into the backfill, as well as their vertical and (if strips are used) horizontal spacing.
Figure 10.22 represents a generic cross section of an MSE wall. Based on the existing or assumed vertical spacing, the vertical stresses are calculated at each reinforcement depth (z).
The corresponding horizontal stress,σh,z, is then computed accordingly, assuming active earth pressure conditions. The horizontal earth pressure at depthzis calculated from:
σh,z=Kaσv,z
(10.18) In the absence of any surcharge loading, the vertical stress is equal to the unit weight of the soil times the depth. Additional stresses resulting from surcharges at the surface may be calculated from a variety of methods such as elastic solutions and charts when applicable. The maximum tensile force in the reinforcement layer is calculated by multiplying the horizontal stress by the cross sectional “area of influence” of the reinforcement element. In the case of reinforcement strips, the area of influence is equal tosv×sh,wheresvandshare the vertical and horizontal spacing between the reinforcement strips, respectively. In the case of geogrid and geotextile reinforcement, a unit width of the reinforcement is considered in lieu of the horizontal spacing, sh. In this case, the calculation output is a force per unit length.
The factor of safety against yielding of the reinforcement is then calculated for each layer by dividing the yield strength of the reinforcement material by the maximum tensile strength:
(10.19)
FIGURE 10.22
Cross section of MSE wall.
whereFmaxis the maximum design tensile resistance of the reinforcement element. In the case of galvanized steel, the yield strength may be used. However, in the case of geosynthetic reinforcement, the yield strength must be multiplied by a number of reduction factors to account for environmental conditions. As such, the maximum design strength of geosynthetic reinforcement is calculated from:
Fmax=Fyield×RFCR×RFID×RFCD×RFBD
(10.20) where RFCR, RFID, RFCD, and RFBDare reduction factors for creep deformation, installation damage, chemical degradation, and biological degradation, respectively. These values depend on the properties of the geosynthetic as well as the environmental conditions during operation and can vary within a very significant range. It is not uncommon for these factors to amount to an overall reduction factor of 10 or 20.
The second component of internal stability is the resistance to pullout, which dictates the extent of the reinforcement into the backfill. For design purposes, a potential Rankine-type failure wedge (θ=45+φ/2) is considered to originate at the toe of the wall (Figure 10.22). The length of reinforcement within the Rankine wedge,LR,is calculated from
LR=(H−z)tan(45−φ/2)
(10.21) Experimental evidence has shown that a Rankine wedge may not be representative of the actual potential failure surface, so more sophisticated design procedures may consider more realistic surfaces, such as curved or bilinear failure wedges. Since the failure wedge is
assumed to be rigid, no internal deformations develop, and the length of reinforcement within this zone(LR)does not contribute to resisting pullout. Instead, the effective length of
reinforcement (Le)is measured from the back end of the Rankine wedge. The factor of safety
maximum tensile force in the reinforcement for each reinforcement layer:
(10.22)
wherew is the width of the reinforcement element andφiis the interface friction angle between the soil and the reinforcement. It is noted that a multiplier of 2 is included in the numerator to account for frictional stresses developing on both top and bottom faces of the embedded reinforcement. The total length,LT,of the reinforcement for each layer is then calculated by adding the Rankine length,LR,to the effective length,Le.
For reinforcement elements distributed at uniform spacing, it is inevitable that design calculations will result in different required yield strength and length for each layer of reinforcement. However, from a constructability perspective, it is imperative to specify a constant set of values, corresponding to the most critical layer. As a result, the finished design ends up being overly conservative and extremely redundant in safety. In large projects where tall MSE walls are constructed, and when strict quality control measures are implemented in the field, it is possible to specify multiple sets of parameters over certain heights of the wall.
For instance, it is not uncommon to use tighter vertical reinforcement spacing within the bottom half of a wall, where tensile forces are highest.