5.3         Equations for Representing Laboratory Based Creep Data

Figure 5-24 shows a best-fit power equation for 517 days of laboratory creep test data obtained by Sheeley (2000). The specimens were 0.05m-cube type VIII EPS geofoam from blocks manufactured by the supplier to the I-15 project in Salt Lake City. The specimens were subjected to stresses equal to 30% and 50% of the strength of the material at 5%strain. The strain rates are shown in chapter three of this study. As was mentioned before there is no seating error correction for these specimens. Had there been seating error correction, the immediate strain and hence the total strain may be reduced by up to 0.3%. Equations 5-1 and 5-2 were derived by curve fitting for 50 and 30 percent loading, respectively.

e_t50 = 0.0092932(t)^0.0556                                   Equation 5‑1

e_t30 = 0.006489(t)^0.0615                                                 Equation 5‑2

Where:

e_t50  is dimensionless total creep strain under 30 kPa stress

e_t30  is dimensionless total creep strain under 30 kPa stress

t is the time in days

The correlation factor is 95% for both equations.

Figure 5‑1 Laboratory Creep Results

The Findley creep equation has been used to represent creep behavior of polymeric materials. The main form of the Findley equation is:

e = e_o + m (t/t_o)^nf                                              Equation 5‑3

Where:

m = m’_f sinh(s/s_mf)                                                    Equation 5‑4

e_o = e’_of sinh(s/s_ef)                                         Equation 5‑5

and,

e          is the total strain

e_o         is the immediate strain upon stress application

t           is the time in hours

t_o          is equal to 1 hour

nf         is a dimensionless Findley material parameter

m’_f       is a dimensionless Findley material parameter

e’_of       is a dimensionless Findley material parameter

s_mf        is a Findley material parameter with stress units

s_ef        is a Findley material parameter with stress units

s          is the applied stress

Obtaining the parameters values for 20kg/m³ EPS geofoam at stress levels of 50kPa or less from laboratory tests Horvath (1998) presented Findley equation in the following form:

e = 0.011 sinh(s/54.2)+0.000305sinh(s/33.0)t^0.2            Equation 5‑6

Where:

e          is the total strain

s                   is the applied stress in kPa

t           is the time in hour

Figures 5-25 through 5-33 show comparisons between creep strains predicted by equations 5-1, 5-2 and 5-6 and observing for both the south array and the middle array at the 3300 South of the I-15 project. Comparisons were done for portions of the foam layers and for the full height of the foam embankment. The equations are applied using two starting dates the start of the construction and the end of the construction. That means that the full amount of load is applied in one time; once at the start of the construction and once at the end of the construction. This is to envelop the field results. The figures show that the lab results of stresses between 30 to 50kPa contain the field results. Figure 3-34 shows an extrapolation of the equation for the expected lifetime of the embankment. 

Figure 5‑2 South Array Cumulative Portions with Lab Results

Figure 5‑3 South Array Intermediate Portions with Lab Results

Figure 5‑4 Middle Array Cumulative Portions with Lab Results

Figure 5‑5 Middle Array Intermediate Portions with Lab Results

Figure 5‑6 Findley-Horvath Equation

Figure 5‑7 South Array Cumulative Portions with Findley-Horvath Equation

Figure 5‑8 South Array Intermediate Portions with Findley-Horvath Equation

Figure 5‑9 Middle Array Cumulative Portions with Findley-Horvath Equation

Figure 5‑10 Middle Array Intermediate Portions with Findley-Horvath Equation

Figure 5‑11 20 Years Extrapolation for the Different Equations