DEALING WITH GEOLOGICAL HAZARDS
attributes, including soil plasticity index (PI), climate-normal annual precipitation (CNP) and normalized inter-annual rainfall extreme (NRE); each of the variables is defined in Table 1 and all of the input data are avail- able online at the pub- licly-accessible sources as cited.
For the 39 most pop-
ulous counties in Texas (i.e., ≥ 100,000 people per county), simple bivariate plots showed
that DC covaries direct- ly with PI and CNP but inversely with NRE. An unweighted com- bination of the three independent variables yields a linear trend of
DC vs. (PI + CNP)/NRE (Figure 1) with a cor- relation coefficient of R = 0.421 that surpasses the critical value of 0.325 at the 95% con- fidence level (α = 0.05 for n - 1 = 38); the null hypothesis (i.e., that no predictive relationship exists) can be excluded.
Other attempts at
both linear and non- linear multivariate analyses
alternative
produced rela-
NRE
Table 1. Variables in the Expansive-Soil Empirical Geohazard In- dex for Texas
Variable Name
DC Definition
Damage Cost for a specific type of loss caused by expansive soils
CNP
Climate-Normal Precipitation
Normalized Rainfall Extreme
Calculation or Standardization
Annual county-based road Contract Maintenance expense normalized to total
lane-miles of road ($Thousands per mile).A, B
Annual total precipitation (inches per year), averaged over the years 1981-2010, for an individual county.C
Absolute average of the maximum and minimum values (expressed as percentage of CNP) in the three-year moving average of annual precipitation excesses or deficits over the years 1996-2018.D
PI DRL Plasticity Index
Relative Likelihood of Expansive-Soil Damage
Average of all soil PI measurements reported for an individual county.E
Example for Galveston County: PI = 26.3, CNP = 51.45, NRE = 29.7. DCM = 4.19 (26.3 + 51.45) / 29.7 + 6.48 = 17.4
DRL = (17.4 – 8.99) / (18.22 – 8.99) = 0.91
Notes:
A. Alternative normalizations to daily vehicle miles (DVM) and per capita DVM did not significantly change the resultant correlations.
B. TXDOT separately reports Construction, Contract Maintenance and Non-Contract Maintenance annual expenses. Per TXDOT definitions, Contract Maintenance expenses appear to capture most of the actual road-repair costs.
tionships that were mathematically more complex but not sta- tistically more com- pelling. Indeed, the relationship in Figure 1 might be viewed as surprisingly strong considering that road maintenance costs used in the regres- sion probably were influenced by other uncontrolled variables such as absolute ages of roadways and roadbed construction methods. Therefore, based on Figure 1, the following formula can be used to relate expansive-soil road damage to soil- environment variables:
DC = 4.1946 (PI + CNP) / NRE + 6.4757 [1] Equation [1] can be used to calculate model-dependent proxy
values, re-defined as DCM, for any Texas county using readily compiled values of PI, CNP and NRE. To further refine DCM into a general-purpose, dimensionless index representing rela-
tive likelihood, denoted as DRL, the model results are scaled to an effective range with recognized lower (DE1) and upper (DE2) threshold values for expansive-soil activity:
DRL = (DCM – DE1) / (DE2 – DE1) 10 TPG •
Jul.Aug.Sep 2019 [2]
C. The 1981-2010 time period is the current definition of the climate-normal period. For the 39 counties studied, CNP ranged from 10.19 in/yr to 57.26 in/yr with an average of 34.43 in/yr.
D. The 1996-2018 time period represents the range of greatest self-consistency per measurement and reporting standards adopted by the U.S. National Weather Service in 1996. For the 39 counties studied, NRE ranged from 18.0% to 39.2% with an average of 26.2%.
E. For the 39 counties studied, average PI ranged from 14.1 to 33.9 with an overall average of 24.9; PI was directly correlated with LL with a linear R2 = 0.8718.
Engineering studies have shown that expansive-soil dam-
age typically begins at PI = 5 and is highly probable for P ≥ 35 (for example, Wang, 2016). As the lower threshold for expansive-soil activity among the Texas counties, a combina- tion of PI =5, CNP = 10 in/yr and NRE = 25% yielded a value
of DE1 = 8.99. As the upper threshold ― where expansive-soil activity would be virtually assured ― a combination of PI
=35, CNP = 35 in/yr and NRE = 25% yielded a value of DE2 = 18.22. (Note: NRE = 25% is near the average for all 39 of Texas counties that were studied.)
Application of Equation [1] and [2] gave the distribution
of dimensionless DRL values shown in Figure 2; an example calculation is included in Table 1. The horizontal distribution
of values from zero to one reflects the different degrees to which each county’s index rises toward the threshold for highly likely expansive-soil hazards; index values closer to zero are less likely to be affected whereas index values approaching
www.aipg.org
NCEI County Time Series
NCEI County Time Series
NRCS Web Soil Survey
Index
proposed in this study
Source of Data
TXDOT (2013)
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