Abstract
Parameter selection is always a critical issue for the numerical modeling of many geotechnical problems. In this work, an idea of non-parameterized numerical analysis is demonstrated by incorporating tri-axial data as the input into the distinct lattice spring model (DLSM). An automatic parameter acquisition procedure is developed to determine the parameters of a modified Duncan–Chang (DC) model which is implemented in the DLSM through the further development of an incremental DLSM and a fabric stress calculation scheme. These newly developed algorithms are verified against available numerical results and experimental counterparts. Then, the discrete feature of the DC-DLSM is explored and discussed through the numerical modeling of large-scale tri-axial tests and a fracturing test. Finally, a real rockfill dam project is analyzed by using the DC-DLSM with the available tri-axial data as the input, and a reasonable fitting is obtained, which shows the possibility for the numerical modeling of the DLSM with no parameter selection burden.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a :
-
The model constant of the Duncan–Chang model
- \(b\) :
-
The model constant of the Duncan–Chang model
- \(c\) :
-
The cohesion
- \(D\) :
-
The dimensionless constant of the Duncan–Chang model
- \(E_{\text{i}}\) :
-
The initial tangent elastic modulus
- \(E_{\text{t}}\) :
-
The tangent elastic modulus
- \(f_{\text{i}}\) :
-
The bond force component
- \(F\) :
-
The dimensionless constant of the Duncan–Chang model
- \({\mathbf{F}}_{ij}^{n,t}\) :
-
The normal interaction forces at t
- \({\mathbf{F}}_{ij}^{n,t - \Delta t}\) :
-
The normal interaction forces at \(t - \Delta t\)
- \({\mathbf{F}}_{ij}^{s,t}\) :
-
The shear interaction forces at t
- \({\mathbf{F}}_{ij}^{s,t - \Delta t}\) :
-
The shear interaction forces at \(t - \Delta t\)
- \(\sum {\mathbf{F}}_{i}^{(t)}\) :
-
The sum of the forces acting on the particle i
- \(F_{y}^{T} (t)\) :
-
The reaction force in the y-direction
- \(G\) :
-
The dimensionless constant of the Duncan–Chang model
- \(k_{\text{n}}\) :
-
The normal stiffness
- \(k_{\text{s}}\) :
-
The shear stiffness
- \(K_{\text{i}}\) :
-
The dimensionless modulus number of the Duncan–Chang model
- \(l\) :
-
The bond length
- \(l_{i}^{0}\) :
-
The initial length of the ith bond
- \(L\) :
-
The length of the cubic specimen
- \(L^{*}\) :
-
The effective length of the cubic specimen
- \(m_{\text{p}}\) :
-
The particle mass
- \(n\) :
-
The dimensionless modulus exponent of the Duncan–Chang model
- \({\mathbf{n}}\) :
-
The normal unit vector
- \(p_{\text{a}}\) :
-
The atmospheric pressure
- \(q\) :
-
The deviatoric stress
- \(q_{j}^{*}\) :
-
The ultimate deviation stress
- \(r_{i}\) :
-
The radius of particle i
- \(r_{j}\) :
-
The radius of particle j
- \(R_{f}\) :
-
The failure ratio
- \({\mathbf{u}}_{i}^{(t + \Delta t)}\) :
-
The displacement of particle i at \(\left( {t + \Delta t} \right)\)
- \({\mathbf{u}}_{i}^{(t)}\) :
-
The displacement of particle i at t
- \({\dot{\mathbf{u}}}_{i}\) :
-
The velocity of particle i
- \({\dot{\mathbf{u}}}_{i}^{(t + \Delta t)}\) :
-
The velocity of particle i at \(\left( {t + \Delta t} \right)\)
- \({\dot{\mathbf{u}}}_{i}^{(t)}\) :
-
The velocity of particle i at t
- \({\dot{\mathbf{u}}}_{ij}\) :
-
The relative velocity between particle \(i\) and particle \(j\)
- \({\dot{\mathbf{u}}}_{ij}^{n}\) :
-
The normal relative velocity between particle \(i\) and particle \(j\)
- \({\dot{\mathbf{u}}}_{ij}^{s}\) :
-
The shear relative velocity between particle \(i\) and particle \(j\)
- \({\dot{\mathbf{u}}}_{j}\) :
-
The velocity of particle j
- \(u_{\text{n}}\) :
-
The normal deformation of the springs
- \(u_{\text{s}}\) :
-
The shear deformation of the springs
- \(u_{\text{n}}^{*}\) :
-
The ultimate deformation of the springs
- \(u_{\text{s}}^{*}\) :
-
The shear deformation of the springs
- \(u_{x}^{L} (t)\) :
-
The average displacement of the cubic left surface in the x-direction
- \(u_{x}^{R} (t)\) :
-
The average displacement of the cubic right surface in the x-direction
- \(u_{y}^{B} (t)\) :
-
The average displacement of the cubic bottom surface in the y-direction
- \(u_{y}^{T} (t)\) :
-
The average displacement of the cubic top surface in the y-direction
- \(u_{z}^{B} (t)\) :
-
The average displacement of the cubic back surface in the z-direction
- \(u_{z}^{F} (t)\) :
-
The average displacement of the cubic front surface in the z-direction
- \(V\) :
-
The volume of the computational model
- \(V^{\prime}\) :
-
The particle’s represented volume
- \({\mathbf{x}}_{i}\) :
-
The coordinate of particle i
- \({\mathbf{x}}_{j}\) :
-
The coordinate of particle j
- \({\mathbf{x}}_{i}^{0}\) :
-
The initial coordinate of particle i
- \({\mathbf{x}}_{j}^{0}\) :
-
The initial coordinate of particle j
- \(\alpha\) :
-
The coefficient of the elastic modulus
- \(\alpha^{ 3D}\) :
-
The lattice geometry coefficient
- \(\beta\) :
-
The translation coefficient of the weight function
- \(\gamma\) :
-
The scaling coefficient of the weight function
- \(\varepsilon_{1}\) :
-
The axial strain
- \(\varepsilon_{v}\) :
-
The volumetric strain
- \(\varepsilon_{x}\) :
-
The strain in the x-direction
- \(\varepsilon_{y}\) :
-
The strain in the y-direction
- \(\varepsilon_{z}\) :
-
The strain in the z-direction
- \([\dot{\varepsilon }]_{\text{bond}}\) :
-
The local strain rate of a spring bond
- \([\dot{\varepsilon }]_{i}\) :
-
The strain rate of particle i
- \([\dot{\varepsilon }]_{j}\) :
-
The strain rate of particle j
- \(\nu_{t}\) :
-
The tangent Poisson
- \(\nu_{t}^{'}\) :
-
The modified tangent Poisson ratio
- \(\nu^{*}\) :
-
The upper limit of the Poisson ratio
- \(\sigma_{1}\) :
-
The major principal stress
- \((\sigma_{1} - \sigma_{3} )_{f}\) :
-
The failure strength
- \(\sigma_{1,j}^{*}\) :
-
The failure first principle stress
- \(\sigma_{3}\) :
-
The minor principal stress
- \(\sigma_{3,j}^{0}\) :
-
The confining pressures
- \(\sigma_{ij}^{{}}\) :
-
The stress of the particle
- \(\sigma_{y}\) :
-
The stress in the y-direction
- \(\varphi\) :
-
The internal friction angle
- \(\chi\) :
-
The dimensionless damping constant
- ∆t :
-
The time step
- \(\xi_{i}\) :
-
The ith component of the normal vector of the lattice bond
- \(\prod\) :
-
The strain energy
- \(\lambda\) :
-
The ratio of horizontal acceleration to gravitational acceleration
References
Abdollahipour A, Marji MF, Bafghi AY, Gholamnejad J (2016) DEM simulation of confining pressure effects on crack opening displacement in hydraulic fracturing. Int J Min Sci Tech 26(4):557–561
Chen YF, Hu R, Lu WB, Li DQ, Zhou CB (2011) Modeling coupled processes of non-steady seepage flow and non-linear deformation for a concrete-faced rockfill dam. Comput Struct 89(13–14):1333–1351
Dong W, Hu L, Yu YZ, Lv H (2013) Comparison between Duncan and Chang’s EB model and the generalized plasticity model in the analysis of a high earth-rockfill dam. J Appl Math 20:1–12
Duncan JM, Chang CY (1970) Nonlinear analysis of stress and strain in soils. J Soil Mech Found Div 96(SM5):1629–1653
Fan LF, Yi XW, Ma GW (2013) Numerical manifold method (NMM) simulation of stress wave propagation through fractured rock mass. Int J Appl Mech 5(02):1350022
Fu M, Hu ZF, Yuan J (2018) Comparative study on deformation analysis of rockfill dam with two models. Energy Res Manag 37(04):61–64 (in Chinese)
Guo PY, Li WC (2012) Development and implementation of Duncan–Chang constitutive model in GeoStudio2007. Proced Eng 31(1):395–402
Hopkins JK, Reid JM, Mccarey J, Bray C (2010) Roadford Dam-20 years of monitoring-managing dams challenges in a time of change. Thomas Telford Ltd, London, pp 187–198
Jiang C, Zhao GF (2018) Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials. Int J Numer Anal Methods 42(4):674–693
Jiang C, Zhao GF, Khalili N (2017) On crack propagation in brittle material using the distinct lattice spring model. Int J Solids Struct 118–119:41–57
Juang CH, Gong WP, Martin JR, Chen QS (2018) Model selection in geological and geotechnical engineering in the face of uncertainty—does a complex model always outperform a simple model? Eng Geol 242:184–196
Kazerani T, Zhao J (2014) A microstructure-based model to characterize micromechanical parameters controlling compressive and tensile failure in crystallized rock. Rock Mech Rock Eng 47(2):435–452
Kolda T (2014) What kind of science is computational science? A rebuttal. https://sinews.siam.org/Details-Page/what-kind-of-science-is-computational-science-a-rebuttal
Kuniyuki M, Norio T, Kazuo A, Tsutoma Y (2012) A nonlinear elastic model for triaxial compressive properties of artificial methane-hydrate-bearing sediment samples. Energies 5:4057–4075
Li JC (2013) Wave propagation across non-linear rock joints based on time-domain recursive method. Geophys J Int 193(2):970–985
Li JC, Ma GW, Zhao J (2010) An equivalent viscoelastic model for rock mass with parallel joints. J Geophys Res-Sol Earth 115:B3
Li JC, Li HB, Ma GW, Zhao J (2012) A time-domain recursive method to analyse transient wave propagation across rock joints. Geophys J Int 188(2):631–644
Li JC, Li HB, Ma GW, Zhou YX (2013) Assessment of underground tunnel stability to adjacent tunnel explosion. Tunn Undergr Sp Tech 35:227–234
Liang YC, Feng DP, Liu GR, Yang XW, Han X (2003) Neural identification of rock parameters using fuzzy adaptive learning parameters. Comput Struct 81(24–25):2373–2382
Russell AR, Khalili N (2004) A bounding surface plasticity model for sands exhibiting particle crushing. Can Geotech J 41(6):1179–1192
Shi C, Yang WK, Yang JX, Chen X (2019) Calibration of micro-scaled mechanical parameters of granite based on a bonded-particle model with 2D particle flow code. Granul Matter 21(2):38
Su JB, Shao GJ, Chu WJ (2008) Sensitivity analysis of soil parameters based on interval. Appl Math Mech 29(12):1651–1662
Wang ZL, Song MT, Yin ZZ (2004) Analyses of parameters sensitivity of Duncan–Chang model in settlement calculation of embankment. Rock Soil Mech 25(7):1135–1138 (in Chinese)
Wang ZL, Li YC, Shen RF (2007) Correction of soil parameters in calculation of embankment settlement using BP network back-analysis model. Eng Geol 91(2–4):168–177
Wang ZJ, Liu XR, Yang X, Fu Y (2017) An improved Duncan–Chang constitutive model for sandstone subjected to drying-wetting cycles and secondary development of the model in FLAC3D. Arab J Sci Eng 42(3):1265–1282
Wu HM, Shu YM, Zhu JG (2011) Implementation and verification of interface constitutive model in FLAC3D. Water Sci Eng 4(3):305–316
Yan C, Jiao Y-Y, Zheng H (2018) A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing. Comput Geotech 96:73–89
Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min 44(6):871–889
Zhang M, Song E, Chen Z (1999) Ground movement analysis of soil nailing construction by three-dimensional (3-D) finite element modeling (FEM). Comput Geotech 25(4):191–204
Zhang ZH, Deng JH, Zhu JB (2018) A rapid and nondestructive method to determine normal and shear stiffness of a single joint based on 1D wave-propagation theory. Geophysics 83(1):WA89–WA100
Zhao GF (2017) Developing a four-dimensional lattice spring model for mechanical responses of solids. Comput Method Appl Mech 315:881–895
Zhao GF, Khalili N (2012) A lattice spring model for coupled fluid flow and deformation problems in geomechanics. Rock Mech Rock Eng 45(5):781–799
Zhao GF, Fang J, Zhao J (2011) A 3D distinct lattice spring model for elasticity and dynamic failure. Int J Numer Anal Methods 35(8):859–885
Zhao GF, Yin Q, Russell AR, Li YC, Wu W, Li Q (2018) On the linear elastic responses of the 2D bonded discrete element model. Int J Numer Anal Methods 43(1):166–182
Zhao GF, Lian J, Russell A, Khalili N (2019) Implementation of a modified Drucker–Prager model in the lattice spring model for plasticity and fracture. Comput Geotech 107:97–109
Zhou W, Hua JJ, Chang XL, Zhou CB (2011) Settlement analysis of the Shuibuya concrete-face rockfill dam. Comput Geotech 38(2):269–280
Acknowledgements
This research is financially supported by the National Key R&D Program of China (under # 2018YFC0406800) and National Natural Science Foundation of China (Grant no. 11772221).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhao, GF., Wei, XD., Liu, F. et al. Non-parameterized Numerical Analysis Using the Distinct Lattice Spring Model by Implementing the Duncan–Chang Model. Rock Mech Rock Eng 53, 2365–2380 (2020). https://doi.org/10.1007/s00603-020-02047-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-020-02047-w