shanetal2012¶
Function summary¶
_integral_for_exp_loading () |
equ 75 from shan et al 2012 for exponential loading |
_integral_for_exp_loading_dt () |
equ 75 from shan et al 2012 for exponential loading diff wrt time |
_integral_for_homogenous_case_linear_initial_condition () |
equ 52 from shan et al 2012 for depth-linear initial conditon |
_integral_for_sin_loading () |
equ 75 from shan et al 2012 for sin loading |
_integral_for_sin_loading_dt () |
equ 75 from shan et al 2012 for sin loading diff wrt time |
shanetal2012 (z, t, H, Cw, Cvw, Ca, Cva[, …]) |
1D unsaturated consolidation |
Module listing¶
Shan et al (2012) “Exact solutions for one-dimensional consolidation of single-layer unsaturated soil”.
-
geotecha.consolidation.shanetal2012.
shanetal2012
(z, t, H, Cw, Cvw, Ca, Cva, drn=1, Csw=0, Csa=0, uwi=(0, 0), uai=(0, 0), nterms=100, f=None, f1=None, f2=None, f3=None, f4=None)[source]¶ 1D unsaturated consolidation
Features:
- Unsaturated soil.
- Vertical flow.
- Soil properties constant with time.
- Initial pore pressure distribution is linear with depth. Load is uniform with depth but can be sinusoidal with time, or exponential with time.
- Drainage boundaries in air and water phase can be pervious, impervious or piecewise linear with time or sinusoidal with time or exponential with time.
- Pore pressure vs depth in air and water at various times.
Parameters: - z : float or 1d array/list of float
Depth values for output.
- t : float or 1d array/list of float
Time values for output
- H : float
Drainage path length.
- Cw : float
Cw = (1 - (m2w/m1kw)) / (m2w - m1kw)
- Cvw : float
Cvw = kw / (gamw * m2w)
- Ca : float
Ca = (m2a/m1ka) / (1 - m2a/m1ka - n(1-S)/(ua_*m1ka))
- Cva : float
Cva = ka / {(wa/(R*T)) * m1ka*ua_*[1 - m2a/m1ka - n(1-S)/(ua_*m1ka)]} where wa=molecular mass of air= 28.966e-3 kg/mol for air, R=universal gas constant=8.31432 J/(mol.K), T = absolute temperature in Kelvin=273.16+t0 (K), t0=temperature in celsius, ua_= absolute air pressure=ua+uatm (kPa), ua=guage air pressure, uatm= atmospheric air pressure=101 kPa. When ua is small or rapidly dissipates during consolidation ua_ can be considered a constant; so let ua_=uatm
- drn : int, optional
Drainage condition. drn=0 is PTPB, drn=1 is PTIB. Default drn=1.
- Csw : float, optional
Csw = m1kw/m2w default=0.
- Csa : float, optional
Csa = (m2a/m1ka) / (1 - m2a/m1ka - n(1-S)/(ua_*m1ka)) Default=0,
- uwi : 2-element tuple, optioanl
Initial pore water pressure at top and bottom of soil. Initial pore water pressure within soil is assumed to vary linearly between the top and bottom values. Default uwi=(0,0).
- uai : 2-element tuple, optioanl
Initial pore air pressure at top and bottom of soil. Initial pore air pressure within soil is assumed to vary linearly between the top and bottom values. Default uai=(0,0).
- nterms : int, optional
Number of terms to use in solution. Default nterms=100.
- f : dict, optional
Ditionary describing a loading function. Default f=None i.e. no load e.g. f = {‘type’: ‘exp’, ‘q0’: 100, ‘b’: 0.00005} is a load described by q(t) = q0 * exp[-b * t]. f = {‘type’: ‘sin’, ‘q0’: 100, ‘omega’: 2*np.pi/1e8} is a load described by q(t) = q0 * sin(omega*t).
- f1, f2 : dict, optional
dict describing loading function for uwtop and uatop. Default f1=f2==None i.e. no load.
- f3, f4 : dict, optional
dict describing loading function for uwbot and uabot. Default f3=f4==None i.e. no load.
Returns: - porw, pora : 2d array of float
Pore pressure at depth and time in water and air phase por is an array of size (len(z), len(t)).
References
[1] Shan, Zhendong, Daosheng Ling, and Haojiang Ding. 2012. ‘Exact Solutions for One-dimensional Consolidation of Single-layer Unsaturated Soil’. International Journal for Numerical and Analytical Methods in Geomechanics 36 (6): 708-22. doi:10.1002/nag.1026.