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

[R16]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.