Skip to main content
Log in

Rectangular Hyperbola Method for the Estimation of Soil Near Surface Hydraulic Conductivity Based on Short Term Infiltration Measurements

  • Published:
Eurasian Soil Science Aims and scope Submit manuscript


Disc infiltrometer can be used to characterize near saturated, soil near surface hydraulic conductivity, which is mandatory for hydrological modelling of runoff, irrigation management and artificial recharge. The hydraulic conductivity determination from the disc infiltrometer measurements requires soil-specific water retention characteristic parameters. This study proposed an alternate procedure for determining near surface near saturated soil hydraulic conductivity (K) and saturated hydraulic conductivity (Ks) for 14 soils comprising 4 different soil textures in the field. The study demonstrated the usefulness of rectangular hyperbola method (RHM) for predicting long-term final infiltration rate (if) from 50 min short-term mini disc infiltrometer (MDI) measurements. The estimated if was utilized for determining K directly. For this purpose, a multiplication factor R was proposed for four USDA surface soil textures. In addition, an empirical relationship was proposed for determining Ks from if estimated by RHM. The advantage of the proposed empirical procedure is that if, K and Ks can be determined from 50 min short-term MDI measurements without the knowledge of soil specific water retention parameters. The proposed methodology can be used to determine K and Ks of other soil textures, vegetated and organic soils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others


  1. M. A. Al-Shamrani, “Applying the hyperbolic method and Ca/Cc concept for settlement prediction of complex organic-rich soil formations,” Eng. Geol. 77, 17–34 (2005).

    Article  Google Scholar 

  2. R. Angulo-Jaramillo, V. Bagarello, M. Iovino, and L. Lassabatere, Infiltration Measurements for Soil Hydraulic Characterization (Springer International Publishing, 2016).

    Book  Google Scholar 

  3. R. Angulo-Jaramillo, D. Elrick, J. Y. Parlange, P. Gerard-Marchant, and R. Haverkamp, “Analysis of short-time single-ring infiltration under falling-head conditions with gravitational effects,” Hydrol. Days Proc., 16–23 (2003).

  4. R. Angulo-Jaramillo, J.-P. Vandervaere, S. Roulier, J.‑L. Thony, J.-P. Gaudet, and M. Vauclin, “Field measurement of soil surface hydraulic properties by disc and ring infiltrometers: A review and recent developments,” Soil Tillage Res. 55, 1–29 (2000).

    Article  Google Scholar 

  5. M. D. Ankeny, M. Ahmed, T. C. Kaspar, and R. Horton, “Simple field method for determining unsaturated hydraulic conductivity,” Soil Sci. Soc. Am. J. 55, 467–470 (1991).

    Article  Google Scholar 

  6. S. Assouline, “Infiltration into soils: conceptual approaches and solutions,” Water Resour. Res. 49, 1755–1772 (2013).

    Article  Google Scholar 

  7. ASTM D 2216-10, Standard Test Methods for Laboratory Determination of Water (Moisture) Content of Soil and Rock by Mass (ASTM International, West Conshohocken, 2010).

  8. ASTM D 6938-15, Standard Test Methods for In-Place Density and Water Content of Soil and Soil-Aggregate by Nuclear Methods (Shallow Depth) (ASTM International, West Conshohocken, 2015).

  9. ASTM D 7928-17, Standard Test Method for Particle-Size Distribution (Gradation) of Fine-Grained Soils Using the Sedimentation (Hydrometer) Analysis (ASTM International, West Conshohocken, 2017).

  10. ASTM D 854-14, Standard Test Methods for Specific Gravity of Soil Solids by Water Pycnometer (ASTM International, West Conshohocken, 2014).

  11. E. Z. Bean, W. F. Hunt, and D. A. Bidelspach, “Field survey of permeable pavement surface infiltration rates,” J. Irrig. Drain. Eng. 133 (3), 249–255 (2007).

    Article  Google Scholar 

  12. W. Bodhinayake, B. C. Si, and K. Noborio, “Determination of hydraulic properties in sloping landscapes from tension and double-ring infiltrometers,” Vadoze Zone J. 3 (3), 964–970 (2004).

    Article  Google Scholar 

  13. M. C. Boscardin, E. T. Selig, R. S. Lin, and G. R. Yang, “Hyperbolic parameters for compacted soils,” J. Geotech. Eng. 116 (1), 88–104 (1990).

    Article  Google Scholar 

  14. H. Bouwer, Intake Rate: Cylinder Infiltrometer - Methods of Soil Analysis, Ed. by A. Klute, 2nd Ed. (American Society of Agronomy and Soil Science Society of America, Madison, 1986), Part 1, pp. 825–844.

  15. R. A. Brown and M. Borst, “Evaluation of surface infiltration testing procedures in permeable pavement systems,” J. Environ. Eng. 140 (3), 04014001 (2014).

    Article  Google Scholar 

  16. R. F. Carsel and R. S. Parrish, “Developing joint probability distribution of soil water retention characteristics,” Water Resour. Res. 24, 755–769 (1988).

    Article  Google Scholar 

  17. N. Chahinian, R. Moussa, P. Andrieux, and M. Voltz, “Accounting for temporal variation in soil hydrological properties when simulated surface runoff on tilted plots,” J. Hydrol. 326, 135–152 (2006).

    Article  Google Scholar 

  18. S. G. Chung, H. J. Kweon, and W. Y. Jang, “Hyperbolic fit method for interpretation of piezocone dissipation tests,” J. Geotech. Geoenviron. Eng. 140 (1), 251–254 (2014).

    Article  Google Scholar 

  19. V. Dakshanamurthy, “A new method to predict swelling using a hyperbolic equation,” Geotech. Eng. 9, 29–38 (1978).

    Google Scholar 

  20. D. E. Elrick, G. W. Parkin, W. D. Reynolds, and D. J. Fallow, “Analysis of early-time and steady-state single-ring infiltration under falling head conditions,” Water Resour. Res. 31 (8), 1883–1893 (1995).

    Article  Google Scholar 

  21. M. Fatehnia, K. Tawfiq, and T. Abichou, “Comparison of the methods of hydraulic conductivity estimation from mini disc infiltrometer,” Electron. J. Geotech. Eng. 19 (E), 1047–1063 (2014).

  22. M. Fatehnia, K. Tawfiq, and M. Ye, “Estimation of saturated hydraulic conductivity from double-ring infiltrometer measurements,” Eur. J. Soil Sci. 67 (2), 135–147 (2016).

    Article  Google Scholar 

  23. V. K. Gadi, Y. R. Tang, A. Das, C. Monga, A. Garg, C. Berretta, and L. Sahoo, “Spatial and temporal variation of hydraulic conductivity and vegetation growth in green infrastructures using infiltrometer and visual technique,” Catena 155, 20–29 (2017).

    Article  Google Scholar 

  24. B. Ghosh and P. Sreeja “A critical evaluation of measurement induced variability in infiltration characteristics for a river sub-catchment,” Measurement 132, 47–59 (2019).

    Article  Google Scholar 

  25. B. Ghosh and P. Sreeja, “A critical evaluation of the variability induced by different mathematical equations on hydraulic conductivity determination using disc infiltrometer,” Acta Geophys. 67 (3), 863–877 (2019).

    Article  Google Scholar 

  26. C.-C. Huang, H.-Y. Hsieh, and Y.-L. Hsieh, “Hyperbolic models for a 2-D backfill and reinforcement pullout,” Geosynth. Int. 21 (3), 168 – 178 (2014).

    Article  Google Scholar 

  27. K. Kodandaramaswamy and S. N. Rao, “The prediction of settlements and heave in clays,” Can. Geotech. J. 17, 623–631 (1980).

    Article  Google Scholar 

  28. L. Lassabatere, S. Di Prima, R. Angulo-Jaramillo, S. Keesstra, and D. Salesa, “Beerkan multi-runs for characterizing water infiltration and spatial variability of soil hydraulic properties across scales,” Hydrol. Sci. J. 64 (2), 165–178 (2019).

    Article  Google Scholar 

  29. B. Latorre, D. Moret-Fernández, and C. Peña, “Applications and challenges estimate of soil hydraulic properties from disc infiltrometer three-dimensional infiltration curve: theoretical analysis and field applicability,” Procedia Environ. Sci. 19, 580–589 (2013).

    Article  Google Scholar 

  30. B. Latorre, C. Peña, L. Lassabatere, R. Angulo-Jaramillo, and D. Moret-Fernández, “Estimate of soil hydraulic properties from disc infiltrometer three-dimensional infiltration curve: numerical analysis and field application,” J. Hydrol. 527, 1–12 (2015).

    Article  Google Scholar 

  31. S. D. Logsdon and D. B. Jaynes, “Methodology for determining hydraulic conductivity with tension infiltrometers,” Soil Sci. Soc. Am. J. 57, 1426–1431 (1993).

    Article  Google Scholar 

  32. Minidisk Infiltrometer User’s Manual (METER Environment, Pullman, 2018).

  33. D. Moret-Fernández and C. González-Cebollada, “New method for monitoring soil water infiltration rates applied to a disc infiltrometers,” J. Hydrol. 379, 315–322 (2009).

    Article  Google Scholar 

  34. B. P. Naveen, P. V. Sivapullaiah, and T. G. Sitharam, “Appropriate method of determination of coefficient of consolidation for municipal solid waste,” Geotech. Test. J. 41 (6), 1026–1039 (2018).

    Article  Google Scholar 

  35. T. Pan, S. Hou, Y, Liu, and Q. Tan, “Comparison of three models fitting the soil water retention curves in a degraded alpine meadow region,” Sci. Rep. 9, 18407 (2019).

    Article  Google Scholar 

  36. S. N. Rao, K. Kodandaramaswamy, and J. R. Somayajulu, “Proposed hyperbolic relationship between settlement and time,” Geotech. Eng. 12 (1), 53–62 (1981).

    Google Scholar 

  37. P. V. Sivapullaiah, A. Sridharan, and V. K. Stalin, “Swelling behaviour of soil–bentonite mixtures,” Can. Geotech. J. 33, 808–814 (1996).

    Article  Google Scholar 

  38. A. Sridharan and A. Rao, “Rectangular hyperbola fitting method for one-dimensional consolidation,” Geotech. Test. J. 4 (4), 161–168 (1981).

    Article  Google Scholar 

  39. A. Sridharan, N. S. Murthy, and K. Prakash, “Rectangular hyperbola method of consolidation analysis,” Géotechnique 37 (3), 355–368 (1987).

  40. T. D. Stark, R. M. Ebling, and J. J. Vettel, “Hyperbolic stress–strain parameters for silts,” J. Geotech. Eng. 120 (2), 420–441 (1994).

    Article  Google Scholar 

  41. M. T. van Genuchten, “A closed-form equation for predicting the hydraulic properties of unsaturated soils,” Soil Sci. Soc. Am. J. 44, 892–898 (1980).

    Article  Google Scholar 

  42. J. P. Vandervaere, M. Vauclin, and D. E. Elrick, “Transient flow from tension infiltrometers I. The two-parameter equation,” Soil Sci. Soc. Am. J. 64 (4), 1263–1272 (2000).

    Article  Google Scholar 

  43. K. M. J. Verbist, W. M. Cornelis, S. Torfs, and D. Gabriels, “Comparing methods to determine hydraulic conductivities on stony soils,” Soil Sci. Soc. Am. J. 77, 25–42 (2013).

    Article  Google Scholar 

  44. A. W. Warrick, “Models for disk infiltrometers,” Water Resour. Res. 28 (5), 1319–1327 (1992).

    Article  Google Scholar 

  45. L. Wu, L. Pan, M. J. Roberson, and P. J. Shouse, “Numerical evaluation of ring infiltrometers under various soil conditions,” Soil Sci. 162 (11), 771–777 (1997).

    Article  Google Scholar 

  46. R. Zhang, “Determination of soil sorptivity and hydraulic conductivity from the disk infiltrometer,” Soil Sci. Soc. Am. J. 61, 1024–1030 (1997).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Sreeja Pekkat.

Ethics declarations


There is no conflict of interest in this study. The authors declare that they have no conflicts of interest.


Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghosh, B., Naik, A.P. & Pekkat, S. Rectangular Hyperbola Method for the Estimation of Soil Near Surface Hydraulic Conductivity Based on Short Term Infiltration Measurements. Eurasian Soil Sc. 55, 1761–1769 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: