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OCR for page 14

14
three components: (1) steel needed to resist the applied load The main differences between the simplified and the coher-
without yielding (nominal structural steel), (2) steel loss from ent gravity methods are with respect to the determination of K
corrosion (consumed steel), and (3) residual steel that was and computation of v (Berg et al., 2009). The manner in which
intended to serve as sacrificial steel, but not actually consumed reinforcement loads are computed affects the load bias used in
by corrosion. Residual steel contributes to the reinforcement the calibration of resistance factor. Allen et al. (2001 and 2005)
resistance, and consequently to the bias inherent to the design. and D'Appolonia (2007) assessed the load bias for metallic MSE
Differences between the metal loss model used in design and reinforcements using the simplified and coherent gravity meth-
the prevailing corrosion rates determine the amount of resid- ods of analysis, respectively. We have used the load bias from
ual steel at the end of the service life. Prevailing corrosion rates these references to calibrate resistance factors for LRFD.
depend on the electrochemical properties of the fill, making The maximum reinforcement tension is computed from H
fill quality an important factor to include in the calibration. based on the spacing of the reinforcements as
Reinforcement size is also important because the significance
Tmax = H SV (9)
of residual steel becomes less as the cross-sectional area of the
reinforcement increases. In consideration of these factors, the where
reliability-based calibration is performed in terms of the fol- Tmax is the maximum reinforcement tension at a given level
lowing design parameters: per unit width of wall and
SV is equal to the vertical spacing of reinforcements.
· service lives of 50, 75 and 100 years;
Equations (8) and (9) describe the demand placed on the
· different reinforcement dimensions for strips 3 mm, 4 mm,
reinforcements; the capacity is the yield resistance of the rein-
5 mm and 6 mm, or wire diameters for grids W7, W9, W11, forcements computed as
W14; and
· different backfill conditions (not all meet AASHTO speci- Fy Ac
R= (10)
fications). SH
where
Yield Limit State R is resistance per unit width of wall,
Fy is the yield strength of the steel,
Loss of cross section affects the yield resistance of MSE
Ac is the cross-sectional area of the reinforcement at the
reinforcements and is incorporated into the LRFD procedure
end of the service life, and
in terms of the yield limit state equations. The yield limit state
SH is the horizontal spacing of the reinforcements.
is reached when the reinforcement tension exceeds the yield
resistance. Therefore, calculation of loads and yield resistance For strip-type reinforcements:
contribute to the yield limit state equations. Ac = bEc (11)
Reinforcement loads may be computed via several differ-
ent methods including the coherent gravity method, tieback For steel grid-type reinforcements:
wedge method, structure stiffness method, or the simplified
D2
method (Berg et al., 2009). Most metallic reinforcements are Ac = n × × (12)
considered to be relatively inextensible, and, traditionally, 4
loads have been computed via the coherent gravity method; where
however, the structure stiffness method and the simplified b is the width of the reinforcements,
method have also been applied. For the purpose of this study Ec is the strip thickness corrected for corrosion loss;
the coherent gravity and simplified methods are considered Ec = (S - S) for S < S, and 0 for S S,
and used to compute the load bias for the calibration of resis- S is the initial thickness,
tance factor. Reinforcement loads are computed based on the S is the loss of thickness (both sides) from corrosion,
horizontal stress carried by the reinforcements computed as n is the number of longitudinal bars/wires, and
D is the diameter of the bar or wire corrected for corrosion
H = K v + H (8)
loss;
D = Di - S for S < Di, and 0 for S Di, where Di is
where
the initial diameter.
H is the horizontal stress at any depth in the reinforced zone,
K is the coefficient of lateral earth pressure, For galvanized reinforcements:
v is the factored vertical pressure at the depth of interest, and
H is the supplemental factored horizontal pressure due S = 2 × rs × ( t f - C ) For C < t f
to external surcharges. S = 0 For C t f (13a)