Summary on Integrating Climate into Mechanistic-Empirical Design Procedures

Posted: August 26th, 2021

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Summary on Integrating Climate into Mechanistic-Empirical Design Procedures

Model to Represent Climate (TMI Model)

Thornthwaite Moisture Index (TMI) is a model that seeks to establish the climate conditions of soil by bringing about a balance between the amount of rainfall and the evapotranspiration. TMI is given by an equation 75[]+ 10, where P is the annual precipitation, and PE considered as the evapotranspiration function of the involved temperature levels (Zapata, 2016). A positive value of TMI implies a wetter climate, whereas a negative amount of the same signifies a dryer climate. TMI measures relative aridity or humidity of a particular climate condition of a soil type, which seemed affected by the following factors, namely precipitation, soil type, air temperature, evapotranspiration, and solar radiation. Among these factors, establishing the potential evapotranspiration seems a more useful variable to measure the relative humidity or aridity of a soil-climate condition as quantified by the following mathematical formula (Zapata 2016).

PE = 1.6(^a

Where H_yequals to annual heat index; t_iequates to the mean monthly temperature in degree Celsius. On the other hand, the annual heat index is obtained by the following equation.

H_y=

H_i = (0.2t_i)^1.514

PE_i= PE_i

            Wherethe variable D_iis a day length correction concerning latitude as well asthe sunshine of the day (Zapata, 2016).

Translating Climate into Stress State of the Soil (Suction State) – TMI-Suction Models

Surface tension and matrix suction are variables of unsaturated soil associated with translating climate into the stress state of the soil (Zapata &Houston, 2009). The entire procedure is done through the TMI suction model that measures void spaces in the soil, thus regarding them as similar to the capillary tube shown below (fig.1).

Figure 1. Capillary tube measuring air temperature of unsaturated soil type

            Therefore, translating climate into the stress state of the soil involves matric suction that measures the pressure difference on the air-water interface. The pressure on the air surface needs to be more than the pressure on the water surface in a bid to measure both the tension and stress attached to unsaturated soils. The following equation ascribes to the TMI-suction model (Zapata &Houston, 2009).

(U_a – U_w) =

Where (U_a – U_w) equates to the matrix suction, T_S is given as the surface tension, whereas R relates to the radius of curvature.

From the equation, it is clear to state that there would be a higher capillary rise in case the capillary tube and radius of curvature are smaller in sizes. Therefore, the whole concept implies that the developed MTI suction model would record a higher value due to the utilization of a smaller size pore and an effective radius of curvature (Zapata &Houston 209). In studying the suction state, clay soil has been found out to sustain more excellent matric suction as compared to sand because it contains smaller pores. As an example, when soil tends to dry, the contents of water recede into the pores as the radius of curvature decreases, hence leading to an increase in the soil matric suction. Consequently, fine-grained type of soils encompasses a higher air pressure to occasion air and water enter into the pores than the coarse-grained ones. In this regard, the matric suction is regarded as an independent stress state that equally measures the behavior of the unsaturated soil as it affects the following factors (Zapata, 2016). They include the effects of the total head flow, hydraulic conductivity, and regulating the retention rate of soil moisture contents.

Figure 2. TMI-P₂₀₀ Model for granular bases of soil

Thus, the TMI effectiveness is associated with quantifying the environmental factor underneath a covered soil due to its ease of using the model to predict the tension state of soils.

Relationship between the Suction Stress and Water Content of the Soil (SWCC Models)

Soil Water Characteristics Curve (SWCC) is a predictive model of unsaturated soils. The model aims tat studying the quantity of air about the amount of water in the soil and its further relativity to the radius curvature of the water content. For example, it is established that a higher suction matrix of the soil means decreased levels of water coupled with a reduced radius of curvature (Zapata, 2016). Therefore, the SWCC is critical in impacting effectively that a drier soil type exhibits superior matrix suction and vice versa. In making the SWCC model effective, it is essential to understand that matrix suction and net normal stress are involved variables that aid in regulating the volume and shear strength of the unsaturated soil.

Figure 3. A graph of SWCC

            Figure 3 is a graph of SWCC intended to measure the water contents of an unsaturated type of soil concerning the volumetric water content (Ø_W) given by the following equation.

Ø_W= (V_W/V_T) X 100%

In this equation, V_Wequates to the water volume, while V_Tsignifies the total amount of the soil.

            Therefore, the SWCC graph above seeks to study how the moisture contents of the soil relate to the matrix suction under prescribed equilibrium conditions. Where suction necessitates the existence of moisture retention in soil, there is a need to find out the stress state of the soil gradient, especially when the fluid flow has not undergone 100% saturation, as demonstrated in figure 3. The Ø_Sas a descriptive parameter of SWCC, it helps in defining the porosity of the soil, mainly when the pores are filled with water. Also, the air-entry value of the soil matrix suction needs to be exceeded before air could get inside the pores (Zapata, 2016). Thus, the relationship between soil matrix suction and the content of water seems non-linear, and indeed resembles more or less the sigmoidal curve in the sense that a more wetted soil demonstrates a negative the pore-water pressure (U_W)

Relationship between Water Content and Resilient Modulus (Environmental Factor)

The environmental factor is useful in impacting the adjustment of water content for the resilient modulus (M_R). In this whole scenario, the resilient modulus is a function of the multiplication of the environmental factor by the optimal resilient modulus of the adjusted soil content. In 2003, Andrei and Witczac modeled a sigmoid graph attached to normalizing the M_Rbased on the optimal adjustment of the environmental factors (fig. 4).

Figure 4. M_R moisture model for coarse-grained soil types

Figure 5. M_R moisture model for fine-grained soil types

            Therefore, the model graph helps predict the change in resilient modulus comparativeto the adjustment of the contents of water under the influence of varied environmental factors.

Figure 6. A graph showing effects of the moisture contents on the resilient modulus

            The figure exhibiting the moisture contents of the M_Rencompasses both the dry and wet of optimum adjustments based on the water content of the soil types, either fine or coarse-grained particles (Zapata et al., 2007). The modeling of fig.6 is predictive with the expansion of the M_R –moisture model as follows.

            In the modeling equation above, M_R equates to the resilient modulus at usual point S, where M_Ropt equals the resilient modulus at an optimal position, and F_Uentails the adjusted factor associated with the unfrozen material (Zapata, 2016). Consequently, a, b, and k_mconsist of the regression parameters of the resilient modulus equation. On the other hand, ß signifies the intercepted value of the moisture content when the y-intercept seems (0,1).

Works Cited

Zapata, Claudia, and Perera Houston. “Matric Suction Prediction Model Used in the New AASHTO Mechanistic-Empirical Pavement Design Guide.”Transportation Research Record: J. of the Transportation Research Board, No. 2101, Geology and Properties of Earth Materials, 2009, pp. 53-62.

Zapata, Claudia E. “AASHTO Implementation – State of the Art.” Geotechnical Aspects of Pavements Design, 2016, pp. 1-37.

Zapata, Claudia E. “Empirical Approach for the Use of Unsaturated Soil Mechanics in Pavement Design.” Transport Geotechnical Systems of Built Environment, 2016, pp. 1-25.

Zapata, Claudia E. “Environmental Effects on Material Stiffness.” Geotechnical Aspects of Pavements, CEE 598, 2016, pp. 1-96.

Zapata, Claudia et al. “Incorporation of Environmental Effects in Pavement Design.”Int. J. of Road Materials and Pavement Design, vol. 8, no. 4, 2007, pp. 667-693.