Effective stress¶

Terzaghi's principle — the cornerstone of all soil mechanics:

\[ \boxed{\;\sigma' = \sigma - u\;} \]

The module's stress functions are deliberately thin wrappers over this rule, so you can compose them however your problem requires.

Quick example¶

Python

import geoeq as ge

# Layered total stress
ge.total_stress([17, 19, 20], [2, 3, 5])     # 191 kPa

# Hydrostatic pore pressure
ge.pore_pressure(5.0, z_w=2.0)               # 29.43 kPa
ge.pore_pressure([0, 2, 5, 10], z_w=2)       # vectorised

# Terzaghi effective stress
ge.effective_stress(154.0, 58.86)            # 95.14 kPa

For multi-layer integration, prefer the SoilProfile object — it handles the bookkeeping of which layer is above / below the water table for you.

Capillary rise¶

Python

ge.capillary_rise(D10=0.05, e=0.7)           # 0.57 m for a fine sand

Uses the Hazen-type estimate \(h_c = C / (e \, D_{10}^{\text{cm}})\) with \(C = 0.2\) by default. Reference: Das (2010) Eq. 5.8.

API reference¶

total_stress ¶

Python

total_stress(gamma: Union[float, Sequence[float]], depth: Union[float, Sequence[float]]) -> float

Total vertical stress sigma_v = sum(gamma_i * H_i).

PARAMETER	DESCRIPTION
`gamma`	Unit weight(s) of each layer (kN/m^3). TYPE: `float or sequence`
`depth`	Either a single depth (with scalar gamma) -- returns gammadepth -- or layer thicknesses matching `gamma` -- returns sum(gamma_i H_i). TYPE: `float or sequence`

RETURNS	DESCRIPTION
`sigma`	Total vertical stress (kPa). TYPE: `float`

Reference

Das (2010) Eq. 5.1; Terzaghi (1943).

Source code in geoeq/design/stress.py

Python
def total_stress(
    gamma: Union[float, Sequence[float]],
    depth: Union[float, Sequence[float]],
) -> float:
    """Total vertical stress sigma_v = sum(gamma_i * H_i).

    Parameters
    ----------
    gamma : float or sequence
        Unit weight(s) of each layer (kN/m^3).
    depth : float or sequence
        Either a single depth (with scalar gamma) -- returns gamma*depth --
        or layer thicknesses matching ``gamma`` -- returns sum(gamma_i * H_i).

    Returns
    -------
    sigma : float
        Total vertical stress (kPa).

    Reference
    ---------
    Das (2010) Eq. 5.1; Terzaghi (1943).
    """
    g = np.atleast_1d(np.asarray(gamma, dtype=float))
    d = np.atleast_1d(np.asarray(depth, dtype=float))
    check_positive(g, "gamma")
    check_non_negative(d, "depth")
    if g.size == 1 and d.size == 1:
        return float(g[0] * d[0])
    if g.size != d.size:
        raise ValueError(
            "gamma and depth must have equal length (one entry per layer).")
    return float(np.sum(g * d))

pore_pressure ¶

Python

pore_pressure(z: Union[float, Iterable[float]], z_w: float = 0.0, gamma_w: float = GAMMA_WATER) -> Union[float, np.ndarray]

Hydrostatic pore pressure u = gamma_w * (z - z_w), clipped at 0.

PARAMETER	DESCRIPTION
`z`	Depth(s) of interest (m, positive downward). TYPE: `float or array`
`z_w`	Depth of the water table (m). Default 0 (water table at surface). TYPE: `float` DEFAULT: `0.0`
`gamma_w`	Unit weight of water (kN/m^3). Default 9.81. TYPE: `float` DEFAULT: `GAMMA_WATER`

RETURNS	DESCRIPTION
`u`	Pore pressure (kPa). Zero above the water table. TYPE: `float or array`

Reference

Das (2010) Eq. 5.2.

Source code in geoeq/design/stress.py

Python
def pore_pressure(
    z: Union[float, Iterable[float]],
    z_w: float = 0.0,
    gamma_w: float = GAMMA_WATER,
) -> Union[float, np.ndarray]:
    """Hydrostatic pore pressure u = gamma_w * (z - z_w), clipped at 0.

    Parameters
    ----------
    z : float or array
        Depth(s) of interest (m, positive downward).
    z_w : float
        Depth of the water table (m). Default 0 (water table at surface).
    gamma_w : float
        Unit weight of water (kN/m^3). Default 9.81.

    Returns
    -------
    u : float or array
        Pore pressure (kPa). Zero above the water table.

    Reference
    ---------
    Das (2010) Eq. 5.2.
    """
    check_positive(gamma_w, "gamma_w")
    z_arr = np.asarray(z, dtype=float)
    u = gamma_w * np.maximum(0.0, z_arr - z_w)
    return float(u) if u.ndim == 0 else u