Skip to main content
SpringerLink
Log in

Modified Green–Ampt Model Considering Vegetation Root Effect and Redistribution Characteristics for Slope Stability Analysis

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

The Green–Ampt (GA) model is widely applied in practice because of its simplicity and relatively few parameters. However, the GA model and its modifications are mostly only suitable for uniform rainfall, and rarely account for the effect of water uptake by vegetation roots. In this study, a modified GA model that accounts for both roots and moisture redistribution is proposed to assess slope stability. Compared with the numerical solution, the modified GA model slightly overestimates the wetting front depth and underestimates the moisture content of surface soil. The hydrological and mechanical effects of vegetation roots on slope stability are also incorporated in the proposed model. Parametric analyses are performed to investigate the effects of parameters including rainfall intensity on the safety factor (Fs). The results show that the wetting front depth decreases/increases with the increase of slope angle/rainfall intensity, and Fs of the slope decreases with the increase of slope angle and rainfall intensity. The safety factor of the slope is negatively correlated with rainfall duration and initial moisture content. Exponential and triangular roots have more significant effect on reinforcing shallow soils than uniform roots. The safety factor of the shrub-covered slope is 1.45 times that of the bare slope. The proposed method has the advantages of simplicity and few parameters.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Availability of Data and Materials

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

Abbreviations

q t :

Evaporation rate

z r :

Root depth

H :

Soil thickness

β :

Slope angle

k s :

Saturated permeability coefficient

s f :

Suction head of the wetting front

z f :

Wetting front depth

t p :

Ponding water time

θ s and θ i :

Saturated moisture content and initial moisture content

θ r :

Residual moisture content

ψ b :

Air entry pressure

λ :

Pore distribution index

c r :

Cohesion related to the vegetation roots

c ′ and φ ′ :

Effective cohesion and the effective internal frictional angle

φ b :

Angle of internal friction related to suction

σ n :

Normal stress

u w and u a :

Pore-water pressure and pore-air pressure

ξ :

Correction factor

T r :

Root tensile strength

R f :

Root orientation factor

RAR :

Root area ratio

γ d and γ w :

Dry unit weights of soil and water

References

  • Aires URV, da Silva DD, Moreira MC, Ribeiro CAAS, Ribeiro CBM (2020) The use of the normalized difference vegetation index to analyze the influence of vegetation cover changes on the streamflow in the Manhuaçu River Basin, Brazil. Water Resour Manage 34(6):1933–1949

    Article  Google Scholar 

  • Brakensiek DL, Onstad CA (1977) Parameter estimation of the Green and Ampt infiltration equation. Water Resour Res 13(6):1009–1012

    Article  Google Scholar 

  • Brooks R, Corey T (1964) HYDRAU properties of porous media. Hydrology Papers, Colorado State University 24:37

    Google Scholar 

  • Chen L, Young MH (2006) Green-Ampt infiltration model for sloping surfaces. Water Resour Res 42(7):887–896

    Article  Google Scholar 

  • Chu ST (1978) Infiltration during an unsteady rain. Water Resour Res 14(3):461–466

    Article  Google Scholar 

  • Corradini C, Melone F, Smith RE (1994) Modeling infiltration during complex rainfall sequences. Water Resour Res 30(10):2777–2784

    Article  Google Scholar 

  • Corradini C, Melone F, Smith RE (1997) A unified model for infiltration and redistribution during complex rainfall patterns. J Hydrol 192(1–4):104–124

    Article  Google Scholar 

  • D’Aniello A, Cimorelli L, Cozzolino L (2019) The influence of soil stochastic heterogeneity and facility dimensions on stormwater infiltration facilities performance. Water Resour Manage 33:2399–2415

    Article  Google Scholar 

  • Dorofki M, Elshafie AH, Jaafar O, Karim OA, Abdullah SMS (2014) A GIS-ANN-based approach for enhancing the effect of slope in the modified Green-Ampt model. Water Resour Manage 28(2):391–406

    Article  Google Scholar 

  • Dou HQ, Han TC, Gong XN, Zhang J (2014) Probabilistic slope stability analysis considering the variability of hydraulic conductivity under rainfall infiltration-redistribution conditions. Eng Geol 183:1–13

    Article  Google Scholar 

  • Durner W, Jansen U, Iden SC (2008) Effective hydraulic properties of layered soils at the lysimeter scale determined by inverse modelling. Eur J Soil Sci 59(1):114–124

    Google Scholar 

  • El Harraki W, Ouazar D, Bouziane A, El Harraki I, Hasnaoui D (2021) Streamflow prediction upstream of a dam using swat and assessment of the impact of land use spatial resolution on model performance. Environ Process 8:1165–1186

    Article  Google Scholar 

  • Emadi-Tafti M, Ataie-Ashtiani B, Hosseini SM (2021) Integrated impacts of vegetation and soil type on slope stability: a case study of Kheyrud Forest, Iran. Ecol Model 446:109498

  • Essig ET, Corradini C, Morbidelli R, Govindaraju RS (2009) Infiltration and deep flow over sloping surfaces: Comparison of numerical and experimental results. J Hydrol 374(1–2):30–42

    Article  Google Scholar 

  • Feng S, Liu HW, Ng CWW (2020) Analytical analysis of the mechanical and hydrological effects of vegetation on shallow slope stability. Comput Geotech 118:103335

  • Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. John Wiley and Sons

    Book  Google Scholar 

  • Ghestem M, Sidle RC, Stokes A (2011) The influence of plant root systems on subsurface flow: Implications for slope stability. Bioscience 61(11):869–879

    Article  Google Scholar 

  • Green WH, Ampt GA (1911) Studies on soil physics, 1. The flow of air and water through soils. J Agric Sci 4:1–24

    Google Scholar 

  • Greenway D (1987) Vegetation and slope stability. In: Anderson MG, Richards KS (Eds.), Slope stability: Geotechnical engineering and geomorphology. John Wiley and Sons Ltd, Hoboken, NJ, USA

  • Grimaldi S, Petroselli A, Romano N (2013) Curve-number/Green-Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis. Hydrol Process 27(8):1265–1275

    Article  Google Scholar 

  • Jornet JM, Akyildiz IF (2014) Femtosecond-long pulse-based modulation for Terahertz band communication in Nanonetworks. IEEE Trans Commun 62(5):1742–1754

    Article  Google Scholar 

  • Kale RV, Sahoo B (2011) Green-Ampt infiltration models for varied field conditions: a revisit. Water Resour Manage 25(14):3505–3536

    Article  Google Scholar 

  • Li CD, Tang HM, Ge Y, Hu X, Wang L (2014) Application of back-propagation neural network on bank destruction forecasting for accumulative landslides in the three Gorges Reservoir Region, China. Stoch Env Res Risk Assess 28(6):1465–1477

    Article  Google Scholar 

  • Liu HW, Feng S, Ng CWW (2016) Analytical analysis of hydraulic effect of vegetation on shallow slope stability with different root architectures. Comput Geotech 80:115–120

    Article  Google Scholar 

  • Lynch J (1995) Root architecture and plant productivity. Plant Physiol 109(1):7–13

    Article  Google Scholar 

  • Mao L, Li Y, Hao W, Zhou X, Xu C, Lei T (2016) A new method to estimate soil water infiltration based on a modified Green-Ampt model. Soil and Tillage Research 161:31–37

    Article  Google Scholar 

  • Mein RG, Larson CL (1973) Modeling infiltration during a steady rain. Water Resour Res 9(2):384–394

    Article  Google Scholar 

  • Meng C, Zhou J, Dai M, Zhu S, Xue X, Ye L (2017) Variable infiltration capacity model with BGSA-based wavelet neural network. Stoch Env Res Risk Assess 31(7):1871–1885

    Article  Google Scholar 

  • Morbidelli R, Saltalippi C, Flammini A, Govindaraju RS (2018) Role of slope on infiltration: a review. J Hydrol 557:878–886

    Article  Google Scholar 

  • Morbidelli R, Saltalippi C, Flammini A, Cifrodelli M, Corradini C, Govindaraju RS (2015) Infiltration on sloping surfaces: Laboratory experimental evidence and implications for infiltration modeling. J Hydrol 523:79–85. https://doi.org/10.1016/j.jhydrol.2015.01.041

    Article  Google Scholar 

  • Morbidelli R, Saltalippi C, Flammini A, Cifrodelli M, Picciafuoco T, Corradini C, Govindaraju RS (2016) Laboratory investigation on the role of slope on infiltration over grassy soils. J Hydrol 543:542–547

    Article  Google Scholar 

  • Ng CWW, Liu HW, Feng S (2015) Analytical solutions for calculating pore water pressure in an infinite unsaturated slope with different root architectures. Can Geotech J 52:1981–1992

    Article  Google Scholar 

  • Nyambayo VP, Potts DM (2010) Numerical simulation of evapotranspiration using a root water uptake model. Comput Geotech 37(1):175–186

    Article  Google Scholar 

  • Ogden FL, Saghafian B (1997) Green and Ampt Infiltration with Redistribution. J Irrig Drain Eng 123(5):386–393

    Article  Google Scholar 

  • Pham BT, Khosravi K, Prakash I (2017) Application and comparison of decision tree-based machine learning methods in landside susceptibility assessment at Pauri Garhwal Area, Uttarakhand, India. Environ Process 4:711–730

    Article  Google Scholar 

  • Preti F, Schwarz M (2006) On root reinforcement modelling. Geophysical research 436 abstracts, vol. 8, EGU General Assembly, 2–7 April, ISSN: 1029–7006

  • Raats PAC (1979) The distribution of the uptake of water by plants: inference from hydraulic and salinity data. Seminaires Sur L’irrigation Localisée 1:35–46

    Google Scholar 

  • Rahardjo H, Leong EC, Rezaur RB (2008) Effect of antecedent rainfall on pore-water pressure distribution characteristics in residual soil slopes under tropical rainfall. Hydrol Process 22(4):506–523

    Article  Google Scholar 

  • Rasool T, Dar AQ, Wani MA (2021) Development of a predictive equation for modelling the infiltration process using gene expression programming. Water Resour Manage 35:1871–1888

    Article  Google Scholar 

  • Ribolzi O, Patin J, Bresson L, Latsachack K, Mouche E, Sengtaheuanghoung O, Silvera N, Thiébaux JP, Valentin C (2011) Impact of slope gradient on soil surface features and infiltration on steep slopes in northern Laos. Geomorphology 127(1–2):53–63

    Article  Google Scholar 

  • Rees SW, Ali N (2012) Tree induced soil suction and slope stability. Geomech Geoeng 7(2):103–113

    Article  Google Scholar 

  • Sihag P, Singh B, Sepah Vand A, Mehdipour V (2018) Modeling the infltration process with soft computing techniques. ISH J Hydraul Eng 26(2):138–152

    Article  Google Scholar 

  • Smith RE, Corradini C, Melone F (1993) Modeling infiltration for multistorm runoff events. Water Resour Res 29(1):133–144

    Article  Google Scholar 

  • Srivastava A, Kumari N, Maza M (2020) Hydrological response to agricultural land use heterogeneity using variable infiltration capacity model. Water Resour Manage 34:3779–3794

    Article  Google Scholar 

  • Srivastava R, Yeh TCJ (1991) Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils. Water Resour Res 27(5):753–762

    Article  Google Scholar 

  • Talsma T, Parlange JY (1972) One-dimensional vertical infiltration. Aust J Soil Res 10(2):143–150

    Article  Google Scholar 

  • Vahedifard F, Leshchinsky D, Mortezaei K, Lu N (2016) Effective stress-based limit-equilibrium analysis for homogeneous unsaturated slopes. Int J Geomech 16(6):D4016003

    Article  Google Scholar 

  • Vanapalli SK, Fredlund DG, Pufahl DE, Clifton AW (1996) Model for the prediction of shear strength with respect to soil suction. Can Geotech J 33(3):379–392

    Article  Google Scholar 

  • Waldron LJ (1977) The shear resistance of root-permeated homogeneous and stratified soil. Soil Sci Soc Am J 41(5):843–849

    Article  Google Scholar 

  • Wu LZ, Huang J, Fan W, Li X (2020) Hydro-mechanical coupling in unsaturated soils covering a non-deformable structure. Comput Geotech 117:103287

  • Wu LZ, Zhang LM, Zhou Y, Xu Q, Yu B, Liu GG, Bai LY (2018) Theoretical analysis and model test for rainfall-induced shallow landslides in the red-bed area of Sichuan. Bull Eng Geol Environ 77:1343–1353

    Article  Google Scholar 

  • Wu LZ, Zhou Y, Sun P, Shi JS, Liu GG, Bai LY (2017) Laboratory characterization of rainfall-induced loess slope failure. Catena 150:1–8

    Article  Google Scholar 

  • Wu TH (1976) Investigation of landslides on Prince of Wales Island. Ohio State University, Alaska

    Google Scholar 

  • Xu QJ, Zhang LM (2010) The mechanism of a railway landslide caused by rainfall. Landslides 7(2):149–156

    Article  Google Scholar 

  • Yuan W, Liu M, Wan F (2019) Calculation of critical rainfall for small-watershed flash floods based on the HEC-HMS hydrological model. Water Resour Manage 33:2555–2575

    Article  Google Scholar 

  • Zaibon S, Anderson SH, Thompson AL, Kitchen NR, Gantzer CJ, Haruna SI (2017) Soil water infiltration affected by topsoil thickness in row crop and switchgrass production systems. Geoderma 286:46–53

    Article  Google Scholar 

  • Zhang QY, Chen WW, Zhang YM (2019) Modification and evaluation of Green-Ampt model: Dynamic capillary pressure and broken-line wetting profile. J Hydrol 575:1123–1132

    Article  Google Scholar 

  • Zhang S, Xu Q, Zhang Q (2017) Failure characteristics of gently inclined shallow landslides in Nanjiang, southwest of China. Eng Geol 217:1–11

    Article  Google Scholar 

  • Zhu J, Wang YQ, Wang YJ, Mao Z, Langendoen EJ (2019) How does root biodegradation after plant felling change root reinforcement to soil? Plant Soil 446:211–227

    Article  Google Scholar 

  • Zhu SR, Wu LZ, Huang JS (2022a) Application of an improved P(m)-SOR iteration method for flow in partially saturated soils. Comput Geosci 26(1):131–145

    Article  Google Scholar 

  • Zhu SR, Wu LZ, Song XL. (2022b) An improved matrix split-iteration method for analyzing underground water flow. Eng Comput. https://doi.org/10.1007/s00366-021-01551-z

Download references

Funding

We thank the National Natural Science Foundation of China (41790432) and the National Key Research and Development Program of China (No. 2021YFB2600026).

Author information

Authors and Affiliations

  1. State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Shaohong Li & Lizhou Wu

  2. Key Laboratory for Mountain Hazards and Earth Surface Process, Institute of Mountain Hazards and Environment, CAS, Chengdu, 610041, Sichuan, China

    Peng Cui

  3. College of Environment and Civil Engineering, Chengdu University of Technology, Chengdu, 610059, Sichuan, China

    Ping Cheng

Authors
  1. Shaohong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lizhou Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Shaohong Li: Conceptualization, Code Developer, Writing—original draft. Peng Cui: Methodology, Formal analysis, Writing- original draft. Ping Cheng: Code Developer, Review & Editing. Lizhou Wu: Supervision, Methodology, Review & Editing.

Corresponding author

Correspondence to Lizhou Wu.

Ethics declarations

Ethics Approval

All authors kept the ‘Ethical Responsibilities of Authors’.

Consent to Participate

All authors gave explicit consent to participate in this work.

Consent to Publish

All authors gave explicit consent to publish this manuscript.

Competing of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, S., Cui, P., Cheng, P. et al. Modified Green–Ampt Model Considering Vegetation Root Effect and Redistribution Characteristics for Slope Stability Analysis. Water Resour Manage 36, 2395–2410 (2022). https://doi.org/10.1007/s11269-022-03149-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-022-03149-6

Keywords

Search

Navigation