# 3.6 Specific Yield and Specific Retention

If the water that fills the connected pores of a sample is allowed to drain under gravitational force, not all of the water occupying the voids is released. The volume of water that drains is less than the volume of water in the interconnected pore space because some of the water clings to the solids due to capillary forces. The term specific yield, Sy, is used to describe the ratio of the water that drains by gravity, VD, to the total volume of sample, VT, as shown by Equation 11.

 (11)

where:

 Sy = specific yield (dimensionless) VD = volume of water that drains by gravity (L3) VT = volume of sample (L3)

The water that does not drain remains as coatings on the surfaces of the solid material bordering the pore spaces or “hangs” in the pore spaces and is referred to as pendular water or residual water. The volume of retained water or pendular water depends on the number and size of the pore spaces, which essentially reflect the relative amount of surface area of the grains available to hold the water. The term specific retention, Sr, describes the fractional volume left behind after gravity drains a porous material and is the ratio of the volume retained, VR, and the total sample volume, VT (Equation 12). The volume retained, VR, is the volume of water in the effective pore space minus the volume drained, (VIVD). The specific retention can also be computed as the effective porosity minus the specific yield (Sr = neSy).

 (12)

where:

 Sr = specific retention (dimensionless) VR = volume of water retained against gravity after drainage ceases (L3) VT = volume of sample (L3)

Effective porosity, specific yield and specific retention each represent a ratio of a volume of water to the total volume of an earth material, and are related as indicated in Equation 13 and Figure 13. When any two of the parameters are known the third can be calculated.

 (13)

The specific yield of an earth material is of interest to the groundwater professional because it represents the volume of water that enters a groundwater system by recharge (a rise in the water table) or is drained from a system when a well is pumped. For example, consider an area that is 1000 m by 1000 m, in which the sand has an effective porosity of 25% and a specific yield of 15%. Now suppose the water table over that area is lowered by four meters. How much water would be drained from the sand? The total volume of drained sand is 4 m × 1000 m × 1000 m or 4,000,000 m3 and the volume of water in the sand is 25% of the total volume of drained sand (ne = VT = VI = 1,000,000 m3). However, the actual volume of groundwater that would drain from this area with a 4 m lowering of the water table is only 15% of the total volume (Sy VT = VD = 600,000 m3).

Next consider how much water is left clinging to the sand grains against the force of gravity by capillary tension after drainage. The sand contains 25% interconnected pore space, ne, and 15% of the total volume drained, Sy = 15%. It follows that that 10% of the total volume is retained water (Sr = neSy), so 400,000 m3 of water remains on the grain surfaces in the drained pores.

To give some more thought to specific yield and specific retention, let’s go back to the example of the two rooms, one filled with solid glass spheres the size of soccer balls and one filled with 1 cm diameter marbles. Both sets of balls are packed in the same cubic arrangement, and thus the rooms have equal porosity (48%). Now let’s examine the specific yield of each room. When the rooms are saturated with water and then allowed to drain, the room with the soccer-ball-sized glass spheres would produce a larger volume of drained water than the room full of marbles. This is because even though the pore volume is the same in both rooms, the pores in the marble room are smaller and there is substantially more surface area associated with the small, but numerous, solids than there is the room full of large glass spheres. Once again, the larger surface area of the marbles retains more water though capillary forces.

The water retained as a fraction of the total volume after drainage, Sr, is sometimes referred to as the field capacity. It is synonymous with the terms soil water holding capacity and water retention capacity and is used to describe the water available to plants once excess water has drained from the soil. Plants have the ability to lower porewater pressure (increase tension) in the vicinity of their roots so they can draw water from the surrounding soil. As time passes, if air is circulating in the partially saturated earth material (vadose zone), some water may evaporate and further decrease the moisture content. When the moisture content falls below the specific retention of the soil because of plant use or evaporation, the soil is below field capacity.

Specific yield measurements from several lab and field methods are compiled in Table 3 to provide insight on the range of specific yield of common earth materials. Specific yield can also be determined by measuring the response of the water table to pumping of wells and analyzing the changes of water levels with equations and models.

Table 3 –Summary of specific yield values of common earth materials compiled by Morris and Johnson (1967) with additional data from Rivera (2014), Freeze and Cherry (1979) and Domenico and Schwartz (1998). “NA” represents not available.

 Measurements of Specific Yield for Some Common Earth Materials (Percent) Material Number of Samples Range of Specific Yield % Unconsolidated Sediments Clay 27 1 – 18 Silt 299 1 – 40 Loess 5 14 – 22 Eolian sand 14 32 – 47 Sand (fine) 287 1 – 46 Sand (medium) 297 16 – 46 Sand (coarse) 143 18 – 43 Gravel (fine) 33 13 – 40 Gravel (medium) 13 17 – 44 Gravel (coarse) 9 13 – 25 Consolidated Sediments Shale NA 0.5 – 5 Siltstone 13 1 – 33 Sandstone (fine-grained) 47 2 – 40 Sandstone (medium-grained) 10 12 – 41 Limestone and dolomite 32 0 – 36 Karstic limestone NA 2 – 15 Igneous and Metamorphic Rocks Fresh granite and gneiss NA <0.1 Weathered granite/gneiss NA 0.5 – 5 Fractured basalt NA 2 – 10 Vesicular basalt NA 5 – 15 Tuff 90 2 – 47