Published online 20 November 2006
Published in Vadose Zone J 5:1287-1292 (2006)
DOI: 10.2136/vzj2006.0098c
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
TECHNICAL NOTES
Tension Infiltrometer Measurements
Implications of Pressure Head Offset due to Contact Sand
W. D. Reynolds*
Agriculture and Agri-Food Canada, Greenhouse and Processing Crops Research Centre, 2585 County Road 20, Harrow, ON, Canada N0R 1G0
* Corresponding author (reynoldsd{at}agr.gc.ca)
Received 11 July 2006.
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ABSTRACT
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The use of contact sand to achieve good hydraulic connection between the tension infiltrometer (TI) membrane and the soil is known to introduce an offset between the pressure head set on the bubble tower (h0) and the pressure head applied to the soil surface (hs). The nature and importance of the offset are poorly understood, however. Hence, the objectives of this study were to characterize the offset and to demonstrate its impacts on TI determinations of near-saturated hydraulic conductivity, K(h), sorptive number, 
*(h), flow-weighted mean pore diameter, D(h), and number of flow-weighted mean pores per unit area, N(h). The offset, 
h = hs – h0, consists of a constant elevation component and a variable head-loss component. The elevation component increases hs relative to h0, and comprises most of the offset for low TI flux density, q(h0), and large contact sand hydraulic conductivity, Kcs. The head-loss component decreases hs relative to h0, and becomes more important as q(h0) increases or Kcs decreases. The offset has little effect on the accuracy of K(h), *(h), D(h), and N(h) when these relationships are insensitive to changes in h0. When the relationships are sensitive to changing h0, the offset can change the shapes of the relationships; cause systematic overestimates of the K(h), *(h), and D(h) values; and cause systematic underestimates of the N(h) values. The amount of overestimate and underestimate increases with increasing offset and should be corrected using a form of Darcy's law to prevent the introduction of systematic biases in TI results.
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INTRODUCTION
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THE TENSION or disk infiltrometer is now well established as a standard field and laboratory method (e.g., Reynolds, 2007; Cook, 2007; Reynolds and Elrick, 2005; Clothier and Scotter, 2002; Smettem and Smith, 2002) for measuring near-saturated soil water transmission relationships, including K(h), sorptivity, S(h), *(h), D(h), and N(h). The method applies in the "wet" or "near-saturated" end of the pore water pressure head (h) range (
–20 cm 
h 0), and has consequently been used to characterize flow effects associated with macropore infilling (White et al., 1992), macrostructure collapse (Messing and Jarvis, 1993), soil cracking (Thony et al., 1991), seasonal variation of soil structure (Angulo-Jaramillo et al., 1997), tillage (Sauer et al., 1990; Reynolds et al., 1995), root growth (White et al., 1992), faunal activity (Clothier et al., 1985), soil texture variation (Jarvis and Messing, 1995), and wheel trafficking (Ankeny et al., 1991). The method has also been used to characterize near-saturated mobile–immobile water contents (Clothier et al., 1992; Angulo-Jaramillo et al., 1996), solute transfer rate coefficients (Jaynes et al., 1995), and solute sorption isotherms (Clothier et al., 1995).
The tension infiltrometer (TI) usually consists of a 5- to 20-cm-diameter "infiltrometer plate" containing a hydrophilic porous disk (e.g., ceramic, sintered stainless steel, or porous plastic) or membrane (e.g., nylon mesh or sieve screen) connected in some fashion to a water reservoir and a Mariotte-type bubble tower (e.g., Soil Measurement Systems, Tucson, AZ; Decagon Devices, Inc., Pullman, WA; Soilmoisture Equipment Corp., Goleta, CA; ICT International, Armidale, NSW, Australia). The reservoir supplies water to the infiltrometer plate, and the bubble tower determines h0 on the plate's porous disk or membrane. When the infiltrometer is placed on an unsaturated porous medium (e.g., soil), the capillarity of the porous medium "sucks" the water out of the infiltrometer such that water infiltrates the porous medium under pressure head h0. For most field and laboratory applications, it is essential that a layer of "contact sand" (e.g., natural sand or uniform glass bead material) is placed under the infiltrometer plate to establish and maintain good hydraulic connection between the porous disk or membrane and the porous medium (Fig. 1
). Contact sand should be used regardless of whether the porous medium surface has been smoothed, leveled, or left undisturbed (e.g., Perroux and White, 1988; Bagarello et al., 2001; Vandervaere, 2002), and regardless of whether steady-state flow analyses (e.g., Reynolds, 2007; Cook, 2007; Ankeny et al., 1991; Reynolds and Elrick, 1991) or transient flow analyses (e.g., Vandervaere et al., 2000a, 2000b) are used. Otherwise, the hydraulic link between the infiltrometer and the soil may be incomplete or changing with time, and this may in turn cause erroneous or misleading results.
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Fig. 1. Schematic of the tension infiltrometer (TI) including water supply tube, infiltration disk or plate, contact sand layer, and retaining ring; Tcs and a are the thickness and radius of the contact sand layer, respectively.
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A critical requirement in both steady-state and transient TI analyses is that the pressure head applied by the infiltrometer to the soil surface must be both accurately known and constant at all infiltrometer flow rates (Reynolds, 2007; Angulo-Jaramillo et al., 2000). Walker et al. (2006) recently demonstrated, however, that under rapid flow conditions, frictional head-loss effects along the water supply tubing between the infiltrometer reservoir and membrane can cause the pressure head applied to the soil surface, hs [L], to be inconstant (flow rate dependent), and as much as 10 to 15 mm less (more negative) than the pressure head set by the bubble tower, h0 [L]. In addition, Reynolds and Zebchuk (1996) showed that contact sand introduces a pressure head "offset," h = hs – h0 [L], which consists of a constant component caused by the finite thickness of the sand layer, and a variable component caused by flow-induced head loss within the sand.
To minimize rapid-flow head loss, Walker et al. (2006) recommended increasing the diameter of the TI water supply tubing. Reynolds and Zebchuk (1996), on the other hand, developed physically based procedures for accounting for contact sand offset. They did not characterize the offset effects, however, nor did they illustrate the impacts of offset on TI results. Hence, the objectives of this study were to: (i) characterize contact sand offset in TI measurements; and (ii) demonstrate the impacts of contact sand offset on TI determinations of the K(h), *(h), D(h), and N(h) relationships. Recommendations are also given regarding desirable attributes for contact sand material.
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ANALYSIS
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Tension Infiltrometer Flow Equations
Steady flow out of a TI and into unsaturated soil can be described by the Wooding (1968) "shallow pond" expression written in the form
 | [1] |
where q(h0) [L T–1] is the steady flux density out of the infiltrometer and into the soil at membrane pressure head h = h0 [L], a [L] is the radius of the infiltration surface, G = 0.237 is a dimensionless shape factor constant (Reynolds and Elrick, 1991), *(h0) [L–1] is the sorptive number of the soil at h0, and K(h0) [L T–1] is the unsaturated soil hydraulic conductivity at h0. Equation [1] is perhaps most effectively solved for the near-saturated K(h) relationship by setting a succession of increasing (less negative) h0 values (i.e., hi where i = 1, 2, 3, ...; hi < hi+1), measuring the corresponding q(h0) values (i.e., qi where i = 1, 2, 3, ...), and then applying a "piece-wise linear" analysis (e.g., Reynolds, 2007; Ankeny et al., 1991; Reynolds and Elrick, 1991). Once K(hi) is determined, the *(h) relationship is obtained by back-substituting into the discrete form of Eq. [1], i.e.,
 | [2] |
The K(hi) and *(hi) values can then be used to calculate the D(h) and N(h) relationships using (Philip, 1987; Reynolds, 2007):
 | [3] |
 | [4] |
where 
[M T–2] is the air–pore water interfacial tension (72.75 g s–2), 
[M L–3] is the pore water density (0.9982 g cm–3), µ [M L–1 T–1] is the pore water dynamic viscosity (1.002 g cm–1 s–1), and g [L T–2] is the constant of gravitational acceleration (980.621 cm s–1). The D(hi) parameter is based on capillary rise theory and is often referred to as the effective "equivalent mean" pore diameter conducting water when infiltration occurs at h = hi. The N(hi) parameter, on the other hand, is derived from Poiseuille flow through capillary tubes and represents the number of pores of equivalent diameter, D(hi), per unit area of infiltration surface.
Hydraulic Characteristics and Flow Equation for Contact Sand
As mentioned above, a layer of contact sand is required to achieve complete and stable hydraulic connection between the TI membrane and the soil surface (Fig. 1). To function properly, the contact sand must meet three hydraulic criteria: (i) the rewet or "field-saturated" hydraulic conductivity of the sand, Kcs [L T–1], must be greater than or equal to the maximum measured K(h0) of the soil; (ii) the water-entry pressure head of the sand, hw [L], must be smaller (more negative) than the minimum pressure head set on the TI membrane (i.e., hw < all h0); and (iii) the Kcs and hw values should be stable through time and highly repeatable. These criteria ensure that flow impedance by the contact sand is minimized, that the hydraulic conductivity of the contact sand is constant and equal to Kcs for all h0 set on the TI membrane, and that Kcs is accurately known from one TI measurement site to the next.
If the contact sand layer meets the above hydraulic criteria and is contained within a retaining ring (Fig. 1), then flow through the layer is saturated and rectilinear. This allows the pressure head offset, h, to be determined via Darcy's law written in the form
 | [5] |
where Tcs [L] is the average thickness of the contact sand layer over the infiltration surface (Fig. 1). The behavior of h is perhaps best characterized by rearranging Eq. [5] into three separate expressions:
 | [6a] |
 | [6b] |
 | [6c] |
which clearly illustrate the dependence of h on q(h0), Tcs, and Kcs, respectively.
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RESULTS AND DISCUSSION
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Characteristics of Pressure Head Offset due to Contact Sand
Equation [6a] is demonstrated in Fig. 2
using Kcs, Tcs, and q(h0) values that are plausible for field measurements on dry, structured soils. Note that the pressure head offset (h) decreases linearly with increasing flux density where the slope of the relationship depends on Kcs and Tcs, and that h = Tcs occurs for the special case of q(h0) = 0 (i.e., no flow out of the TI). The offset at zero flow, which indicates that hs is greater than h0 by Tcs (i.e., hs = h0 + Tcs = h0 + 1 cm for zero flow in Fig. 2), occurs because the contact sand layer elevates the disk membrane above the soil surface by the distance Tcs (Fig. 1), thereby adding a positive "elevation" component to hs. The decrease in offset with increasing flux density, on the other hand, results from frictional head loss (flow impedance) in the contact sand; for q(h0) = 0.01 cm s–1 in Fig. 2, the decrease in hs due to head loss exactly compensates for the increase in hs due to the contact sand thickness so that h = 0 (i.e., hs = h0). Note also, however, that the offset continues to decrease with increasing flux density, and a negative offset of –1 cm is reached at q(h0) = 0.02 cm s–1 in Fig. 2, indicating that hs is now less than h0 by 1 cm. Given that Tcs 
1 cm is often required in field applications to compensate for the roughness of undisturbed soil surfaces (Thony et al., 1991), the offset between hs and h0 is often substantial at both low flux densities and high flux densities, as exemplified in Fig. 2.
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Fig. 2. Dependence of pressure head offset on flux density out of the tension infiltrometer, q(h0) (Eq. [6a]); Kcs and Tcs are the field-saturated (rewet) hydraulic conductivity and thickness, respectively, of the contact sand layer.
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Equation [6b] is plotted in Fig. 3
using the same Kcs value as in Fig. 2. As expected, the pressure head offset in Fig. 3 is zero (i.e., h = 0, hence hs = h0) for no contact sand (Tcs = 0); and the offset changes linearly with increasing contact sand thickness, with the slope of the relationship dependent on q(h0) and Kcs. Note, however, that the slope of the relationship can be positive, zero, or negative. For "low" flux densities [e.g., q(h0) = 0.004 cm s–1 in Fig. 3], the offset increases with increasing contact sand thickness (positive slope), indicating that hs becomes increasingly greater (less negative) than h0 for thicker sand layers. For "high" flux densities, on the other hand [e.g., q(h0) = 0.016 cm s–1 in Fig. 3], the offset decreases with increasing sand thickness (negative slope), indicating that hs becomes progressively lower (more negative) than h0 for thicker sand layers. This reversal occurs because of the interaction between the positive "elevation" effect imposed by the thickness of the contact sand layer, and the negative "head-loss" effect imposed by flow impedance within the contact sand. At low flux densities, the elevation effect dominates the head-loss effect, causing an increase in hs relative to h0, while at high flux densities the reverse occurs, causing a decrease in hs relative to h0. The special case of h = constant = 0 occurs when q(h0) = Kcs [i.e., at q(h0) = 0.01 cm s–1 in Fig. 3]; and this indicates an exact counterbalance of the elevation and head-loss effects as well as a hydraulic head gradient of unity through the contact sand layer. As indicated in Eq. [6b], the flux densities at which the slope changes from positive to zero to negative is determined by the hydraulic conductivity of the contact sand layer (Kcs). Note also that Reynolds and Zebchuk (1996) showed that unit hydraulic head gradient (which implies zero pressure head gradient) rarely occurs in contact sand, and hence the oft-made assumption, hs = h0, in most TI analyses is almost always incorrect.
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Fig. 3. Dependence of pressure head offset on the thickness of the contact sand layer (Eq. [6b]). The diamonds are flux density, q(h0), = 0.004 cm s–1 < field-saturated (rewet) hydraulic conductivity of the contact sand layer, Kcs; the squares are q(h0) = 0.016 cm s–1 > Kcs; and the circles are q(h0) = 0.01 cm s–1 = Kcs.
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Equation [6c] shows a linear relationship between pressure head offset and the inverse of contact sand hydraulic conductivity (Fig. 4
). The slope of the relationship is negative and depends on q(h0) and Tcs. Note also in Eq. [6c] and Fig. 4 that the pressure head offset approaches h = constant = Tcs as Kcs becomes large (i.e., as 1/Kcs becomes small). Hence, it is advantageous to have Kcs as large as possible, as this reduces the dependence of h on the TI flux density and the hydraulic properties of the contact sand. There is, of course, a practical limit on the magnitude of Kcs, however. For most readily available contact sand materials (e.g., fine glass beads, natural sands, etc.), the maximum Kcs is on the order of 0.01 to 0.05 cm s–1, as materials with greater Kcs usually have a water-entry value (hw) that is too large to maintain saturation (and thereby constant hydraulic conductivity) across the required range of h0 values (which is usually –20 cm h0 0).
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Fig. 4. Dependence of pressure head offset on the field-saturated (rewet) hydraulic conductivity of the contact sand layer, Kcs (Eq. [6c]); q(h0) parameter is the flux density out of the tension infiltrometer and Tcs is the thickness of the contact sand layer.
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Effects of Contact Sand Offset on Tension Infiltrometer Results
A TI measurement was made in situ on a cracking clay loam soil to demonstrate the effects of contact sand offset (h) on K(h), *(h), D(h), and N(h) calculations. The contact sand material (Kcs = 1.1 x 10–2 cm s–1; hw = –30 cm) was added to depth Tcs = 1.0 cm in a 25-cm inside diameter retaining ring (Fig. 1). An overhead-type dual-reservoir tension infiltrometer (Reynolds, 2007) was used, and pressure heads h0 = –16, –11, –6, –4, –2, –1, and 0 cm were set in succession on the infiltrometer membrane. The steady-flow analysis given in Reynolds (2007) was used to make the calculations, and Eq. [5] was used as per Reynolds and Zebchuk (1996) to account for the offset between the pressure head set on the TI membrane, h0, and the pressure head actually applied to the soil surface, hs.
Table 1 shows the resulting h0, hs, h, and q(h0) values, plus the elevation and head-loss components of the total pressure head offset. For h0 –6 cm, h was effectively constant at just under 1 cm, and the frictional head-loss effect (h – Tcs) comprised 0.45% of the total pressure head offset (h). This indicates that the Kcs value was large enough at the measured TI flux densities (i.e., 1.12 x 10–5 cm s–1 q(h0) 4.93 x 10–5 cm s–1) to prevent appreciable frictional head-loss effects; as a result, the total pressure head offset due to contact sand (h) consisted almost entirely of the elevation component, Tcs. At h0 > –6 cm, however, both h and the head-loss component of the offset (h – Tcs) decrease rapidly, indicating that for q(h0) 8.66 x 10–5 cm s–1 the total offset was a function of both the flow-dependent head-loss effect and the elevation effect. Note also that at the greatest measured flux density [q(h0) = 1.39 x 10–2 cm s–1], the offset due to the head-loss effect (–1.2651 cm) was greater in magnitude than the offset due to the elevation effect (1.0 cm).
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Table 1. Total pressure head offset, h = hs – h0 (h0 is the pressure head set on the bubble tower, hs is the pressure head applied to the soil surface), resulting from a tension infiltrometer (TI) measurement where a layer of contact sand (field-saturated hydraulic conductivity Kcs = 1.1 x 10–2 cm s–1; water entry value hw = –30 cm; contact sand layer thickness Tcs = 1.0 cm) was placed between the TI membrane and the infiltration surface of a dry, cracking clay loam soil; q(h0) is the steady flux density out of the TI and into the soil.
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The impact of offset on TI results is illustrated in Fig. 5
, where K(h), *(h), D(h), and N(h) are plotted using h0, which ignores the contact sand offset, and hs, which takes the offset into account. For h0 –6 cm, the K(h), *(h), D(h), and N(h) values are similar for both h0 and hs, as the plots all have low slopes in that pressure head range. For h0 > –6 cm, on the other hand, use of h0 overestimates the K(h), *(h), and D(h) values by factors of up to 3.8, 1.5, and 1.5, respectively, while the N(h) values are underestimated by as much as a factor of 3.0. Although discrepancies of these magnitudes may in some cases be considered unimportant relative to the large random variability of typical TI data sets, it should be remembered that the discrepancies are systematic and therefore impart a bias to the data set. Hence, it is always advisable to correct for elevation and head-loss offsets (by using hs rather than h0). Remember also that offset-induced bias in TI results will increase with both increasing sand thickness (greater Tcs) and increasing flow-induced head loss in the sand [due to increasing q(h0)].
Note in Fig. 5 that for h0 –4 cm, the frictional head-loss effects were sufficient to cause appreciable increases in the slopes of the K(h), *(h) and D(h) relationships. This occurs because the elevation and head-loss effects have opposing (and partially compensating) impacts, i.e., the elevation effect increases hs while the head-loss effect decreases hs (Fig. 3). It should also be noted from Fig. 5 (and Table 1) that if the TI flux densities are low enough (or Kcs large enough) to avoid appreciable head-loss effects (e.g., head-loss offset < 10% of total offset) then the contact sand offset can be readily accounted for by simply adjusting the bubble tower pressure heads by an amount equal to the thickness of the contact sand layer, Tcs. For example, if Tcs = 1 cm and hs = –15, –10, –5, –3, –1, and 0 cm are desired on the soil surface, then set the bubble tower to yield h0 = –16, –11, –6, –4, –2, and –1 cm on the TI membrane.
Desirable Attributes of Contact Sand Material
In addition to the Kcs and hw requirements described above, there are several physical attributes of contact sand material that can be considered desirable for convenient use and optimum performance. The material should ideally be composed of smooth, spherical grains with a narrow grain-size distribution. This not only facilitates spreading, leveling, and establishment of complete and stable hydraulic connection between the TI membrane and the soil surface, but it also promotes consistent and repeatable Kcs and hw values as the spheres readily fall into a highly stable "close packing" arrangement. The material should also be chemically inert with low surface area so that it neither leaches nor sorbs dissolved constituents and is thus usable for TI-based solute transport studies. Finally, the contact sand material should be easily obtained, inexpensive, and reusable if necessary.
Reynolds and Zebchuk (1996) proposed a fine "glass bead" material (Spheriglass, no. 2227, Potters Industries, LaPrairie, QC) that matches the above attributes reasonably well (Bagarello et al., 2001). The individual beads are smooth, uniform spheres of amorphous and relatively inert soda-lime glass (by weight 72.5% SiO2, 13.7% Na2O, 9.7% CaO, and 3.3% MgO), and the grain-size distribution is 99.73% (w/w) fine sand (50–250 µm). As a result, the material produces highly repeatable dry bulk density, hw, and Kcs values of 1.495 Mg m–3 (SD = 0.014), –30 cm (SD = 3), and 1.1 x 10–2 cm s–1 (SD = 8.0 x 10–4), respectively. In addition, the hw value should be adequate for the usual pressure head range of tension infiltrometers (i.e., –20 cm h0 0), while the Kcs value should be large enough for use on most agricultural soils. The material is also easily leveled even under humid conditions; it can be dried, sieved, and reused; and it is inexpensive and readily available as it is widely used in plastics manufacture.
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CONCLUSIONS
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Placing a layer of contact sand under a TI introduces an offset between the pressure head set on the infiltrometer membrane, h0, and the pressure head applied to the soil surface, hs. The offset, h = hs – h0, consists of an "elevation" component and a frictional "head-loss" component. The elevation component is constant and equal to the thickness of the contact sand layer, Tcs, while the head-loss component is variable and depends on the flux density out of the infiltrometer, q(h0), and the saturated (rewet) hydraulic conductivity of the sand, Kcs. The elevation component increases hs relative to h0, while the head-loss component decreases hs, thus causing the two components to counteract each other to varying degrees. The relative importance of the two offset components is determined by q(h0) and Kcs; i.e., the elevation component dominates for low q(h0) and large Kcs, while the head-loss component becomes progressively more important as q(h0) increases or Kcs decreases.
Contact sand offset has varying impacts on the relationships describing near-saturated hydraulic conductivity, K(h), sorptive number, *(h), flow-weighted mean pore diameter, D(h), and number of flow-weighted mean pores per unit area, N(h). Where the relationships have low slopes (insensitive to change in h0), contact sand offset has little effect on the accuracy of the K(h), *(h), D(h), and N(h) values. Where the relationships have steep slopes (sensitive to change in h0), however, the offset can change the shapes of the relationships, cause systematic overestimates of the K(h), *(h), and D(h) values, and cause systematic underestimates of the N(h) values. The amount of overestimate and underestimate increases with the degree of offset, and should be corrected using Eq. [5] to prevent the introduction of systematic biases in the TI results.
Essential hydraulic properties of contact sand include: (i) a saturated (rewet) hydraulic conductivity, Kcs, that is greater than or equal to the maximum measured hydraulic conductivity of the soil, K(h0); (ii) a water-entry value, hw, that is smaller (more negative) than the minimum h0 set in the TI membrane; and (iii) Kcs and hw values that are stable with time and highly repeatable among measurement sites. Desirable physical attributes of contact sand include fine, single-grain structure that readily makes a complete and stable hydraulic connection between the infiltrometer membrane and the soil surface; easy spreading and leveling characteristics; chemical inertness; low cost and ready availability; and the ability to be dried, sieved, and reused if necessary.
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ACKNOWLEDGMENTS
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The assistance of J. Gignac in collection of the tension infiltrometer data is greatly appreciated. Funding for this work was provided by Agriculture and Agri-Food Canada.
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ABSTRACT
INTRODUCTION
