def capacity_sp_meyerhof_and_hanna_1978(sp, fd, verbose=0):
"""
Calculates the two-layered foundation capacity according Meyerhof and Hanna (1978)
:param sp: Soil profile object
:param fd: Foundation object
:param wtl: water table level
:param verbose: verbosity
:return: ultimate bearing stress
"""
assert isinstance(sp, sm.SoilProfile)
if fd.length > fd.width: # TODO: deal with plane strain
fd_length = fd.length
fd_width = fd.width
else:
fd_length = fd.width
fd_width = fd.length
sl_0 = sp.layer(1)
sl_1 = sp.layer(2)
h0 = sp.layer_depth(2)
gwl = sp.gwl
sl_0.nq_factor_0 = (
(np.tan(np.pi / 4 + np.deg2rad(sl_0.phi / 2))) ** 2 * np.exp(np.pi * np.tan(np.deg2rad(sl_0.phi))))
if sl_0.phi == 0:
sl_0.nc_factor_0 = 5.14
else:
sl_0.nc_factor_0 = (sl_0.nq_factor_0 - 1) / np.tan(np.deg2rad(sl_0.phi))
sl_0.ng_factor_0 = (sl_0.nq_factor_0 - 1) * np.tan(1.4 * np.deg2rad(sl_0.phi))
sl_1.nq_factor_1 = (
(np.tan(np.pi / 4 + np.deg2rad(sl_1.phi / 2))) ** 2 * np.exp(np.pi * np.tan(np.deg2rad(sl_1.phi))))
if sl_1.phi == 0:
sl_1.nc_factor_1 = 5.14
else:
sl_1.nc_factor_1 = (sl_1.nq_factor_1 - 1) / np.tan(np.deg2rad(sl_1.phi))
sl_1.ng_factor_1 = (sl_1.nq_factor_1 - 1) * np.tan(1.4 * np.deg2rad(sl_1.phi))
if verbose:
log("Nc: ", sl_1.nc_factor_1)
log("Nq: ", sl_1.nq_factor_1)
log("Ng: ", sl_1.ng_factor_1)
sl_0.kp_0 = (np.tan(np.pi / 4 + np.deg2rad(sl_0.phi / 2))) ** 2
sl_1.kp_1 = (np.tan(np.pi / 4 + np.deg2rad(sl_1.phi / 2))) ** 2
# shape factors
if sl_0.phi >= 10:
sl_0.s_c_0 = 1 + 0.2 * sl_0.kp_0 * (fd_width / fd_length)
sl_0.s_q_0 = 1.0 + 0.1 * sl_0.kp_0 * (fd_width / fd_length)
else:
sl_0.s_c_0 = 1 + 0.2 * (fd_width / fd_length)
sl_0.s_q_0 = 1.0
sl_0.s_g_0 = sl_0.s_q_0
if sl_1.phi >= 10:
sl_1.s_c_1 = 1 + 0.2 * sl_1.kp_1 * (fd_width / fd_length)
sl_1.s_q_1 = 1.0 + 0.1 * sl_1.kp_1 * (fd_width / fd_length)
else:
sl_1.s_c_1 = 1 + 0.2 * (fd_width / fd_length)
sl_1.s_q_1 = 1.0
sl_1.s_g_1 = sl_1.s_q_1
# Note: this method explicitly accounts for the foundation depth, so there are no depth factors
# TODO: inclination factors, see doi.org/10.1139/t78-060
# Capacity
a = 1 # assumed to be one but can range between 1.1 and 1.27 for square footings according to Das (1999) Ch 4
s = 1
r = 1 + (fd_width / fd_length)
# put the same things before that condition
# effective weight not in the soil object
if gwl == 0: # case 1: GWL at surface
q_at_interface = sl_0.unit_bouy_weight * h0
unit_eff_weight_0_at_fd_depth = sl_0.unit_bouy_weight
unit_eff_weight_0_at_interface = sl_0.unit_bouy_weight
unit_eff_weight_1_below_foundation = sl_1.unit_bouy_weight
elif 0 < gwl <= fd.depth: # Case 2: GWL at between foundation depth and surface
q_at_interface = (sl_0.unit_dry_weight * gwl) + (sl_0.unit_bouy_weight * (h0 - gwl))
q_d = (sl_0.unit_dry_weight * gwl) + (sl_0.unit_bouy_weight * (fd.depth - gwl))
unit_eff_weight_0_at_fd_depth = q_d / fd.depth
unit_eff_weight_0_at_interface = sl_0.unit_bouy_weight
unit_eff_weight_1_below_foundation = sl_1.unit_bouy_weight
elif fd.depth < gwl <= fd_width + fd.depth:
if gwl < h0: # Case 3: GWL at between foundation depth and foundation depth plus width, and GWL < layer 1 depth
average_unit_bouy_weight = sl_0.unit_bouy_weight + (
((gwl - fd.depth) / fd_width) * (sl_0.unit_dry_weight - sl_0.unit_bouy_weight))
q_at_interface = (sl_0.unit_dry_weight * gwl) + (sl_0.unit_bouy_weight * (h0 - gwl))
unit_eff_weight_0_at_fd_depth = sl_0.unit_dry_weight
unit_eff_weight_0_at_interface = average_unit_bouy_weight
unit_eff_weight_1_below_foundation = sl_1.unit_bouy_weight
else: # Case 4: GWL at between foundation depth and foundation depth plus width, and GWL > layer 1 depth
average_unit_bouy_weight = sl_1.unit_bouy_weight + (
((gwl - h0) / fd_width) * (sl_1.unit_dry_weight - sl_1.unit_bouy_weight))
q_at_interface = sl_0.unit_dry_weight * h0
unit_eff_weight_0_at_fd_depth = sl_0.unit_dry_weight
unit_eff_weight_0_at_interface = sl_0.unit_dry_weight
unit_eff_weight_1_below_foundation = average_unit_bouy_weight
elif gwl > fd.depth + fd_width: # Case 5: GWL beyond foundation depth plus width
q_at_interface = sl_0.unit_dry_weight * h0
unit_eff_weight_0_at_fd_depth = sl_0.unit_dry_weight
unit_eff_weight_0_at_interface = sl_0.unit_dry_weight
unit_eff_weight_1_below_foundation = sl_1.unit_dry_weight
else:
raise ValueError("Could not interpret inputs") # never reached
# maximum value (qu <= qt)
q_ult6 = q_at_interface - unit_eff_weight_0_at_fd_depth * fd.depth
q_0 = (sl_0.cohesion * sl_0.nc_factor_0) + (0.5 * unit_eff_weight_0_at_interface * fd_width * sl_0.ng_factor_0)
q_b2 = (q_at_interface * sl_1.nq_factor_1 * sl_1.s_q_1)
q_1 = (sl_1.cohesion * sl_1.nc_factor_1) + (0.5 * unit_eff_weight_1_below_foundation * fd_width * sl_1.ng_factor_1)
q_b3 = (unit_eff_weight_1_below_foundation * fd_width * sl_1.ng_factor_1 * sl_1.s_g_1 / 2)
q_ult5 = r * (unit_eff_weight_0_at_interface * ((h0 - fd.depth) ** 2)) * (1 + (2 * fd.depth / (h0 - fd.depth))) * (
np.tan(np.deg2rad(sl_0.phi)) / fd_width) * s
q_t2 = (unit_eff_weight_0_at_fd_depth * fd.depth * sl_0.nq_factor_0 * sl_0.s_q_0)
q_t3 = (unit_eff_weight_0_at_interface * fd_width * sl_0.ng_factor_0 * sl_0.s_g_0 / 2)
# qb
q_b1 = (sl_1.cohesion * sl_1.nc_factor_1 * sl_1.s_c_1)
q_b = q_b1 + q_b2 + q_b3
q1_q0 = q_1 / q_0
# calculate the ca factor
# if sl_0.cohesion == 0:
# c1_c0 = 0
# else:
# c1_c0 = sl_1.cohesion / sl_0.cohesion
x = np.array([0.000, 0.082, 0.206, 0.298, 0.404, 0.509, 0.598, 0.685, 0.772])
y = np.array([0.627, 0.700, 0.794, 0.855, 0.912, 0.948, 0.968, 0.983, 0.997])
# raise Warning("ca should be interpolated using q1/q2 not cohesion, see Figure 4 in MH1978")
ca_c0 = np.interp(q1_q0, x, y)
ca = ca_c0 * sl_0.cohesion
# ks
x_0 = np.array([0, 20.08, 22.42, 25.08, 27.58, 30.08, 32.58, 34.92, 37.83, 40.00, 42.67, 45.00, 47.00, 49.75])
y_0 = np.array([0.93, 0.93, 0.93, 0.93, 1.01, 1.17, 1.32, 1.56, 1.87, 2.26, 2.72, 3.35, 3.81, 4.82])
x_2 = np.array([0, 20.08, 22.50, 25.08, 27.58, 30.08, 32.50, 35.00, 37.67, 40.17, 42.67, 45.00, 47.50, 50.00])
y_2 = np.array([1.55, 1.55, 1.71, 1.86, 2.10, 2.33, 2.72, 3.11, 3.81, 4.43, 5.28, 6.14, 7.46, 9.24])
x_4 = np.array([0, 20.00, 22.51, 25.10, 27.69, 30.11, 32.45, 35.04, 37.88, 40.14, 42.65, 45.07, 47.33, 50.08])
y_4 = np.array([2.49, 2.49, 2.64, 2.87, 3.34, 3.81, 4.43, 5.20, 6.29, 7.38, 9.01, 11.11, 14.29, 19.34])
x_10 = np.array([0, 20.00, 22.50, 25.08, 28.00, 30.00, 32.50, 34.92, 37.50, 40.17, 42.42, 45.00, 47.17, 50.08])
y_10 = np.array([3.27, 3.27, 3.74, 4.44, 5.37, 6.07, 7.16, 8.33, 10.04, 12.30, 15.95, 21.17, 27.47, 40.00])
x_int = sl_0.phi
if sl_0.phi < 1:
fd.ks = 0
else:
if q1_q0 == 0:
fd.ks = np.interp(x_int, x_0, y_0)
elif q1_q0 == 0.2:
fd.ks = np.interp(x_int, x_2, y_2)
elif q1_q0 == 0.4:
fd.ks = np.interp(x_int, x_4, y_4)
elif q1_q0 == 1.0:
fd.ks = np.interp(x_int, x_10, y_10)
elif 0 < q1_q0 < 0.2:
ks_1 = np.interp(x_int, x_0, y_0)
ks_2 = np.interp(x_int, x_2, y_2)
fd.ks = (((ks_2 - ks_1) * q1_q0) / 0.2) + ks_1
elif 0.2 < q1_q0 < 0.4:
ks_1 = np.interp(x_int, x_2, y_2)
ks_2 = np.interp(x_int, x_4, y_4)
fd.ks = (((ks_2 - ks_1) * (q1_q0 - 0.2)) / 0.2) + ks_1
elif 0.4 < q1_q0 < 1.0:
ks_1 = np.interp(x_int, x_4, y_4)
ks_2 = np.interp(x_int, x_10, y_10)
fd.ks = (((ks_2 - ks_1) * (q1_q0 - 0.4)) / 0.6) + ks_1
else:
raise DesignError(
"Cannot compute 'ks', bearing ratio out-of-range (q1_q0 = %.3f) required: 0-1." % q1_q0)
# qu
q_ult4 = (r * (2 * ca * (h0 - fd.depth) / fd_width) * a)
q_ult5_ks = q_ult5 * fd.ks
q_ult = q_b + q_ult4 + q_ult5_ks - q_ult6
q_t1 = (sl_0.cohesion * sl_0.nc_factor_0 * sl_0.s_c_0)
q_t = q_t1 + q_t2 + q_t3
if q_ult > q_t:
if h0 > fd_width/2:
fd.q_ult = q_t
else:
vert_eff_stress_interface = sp.get_v_eff_stress_at_depth(h0)
vert_eff_stress_lowest = sp.get_v_eff_stress_at_depth(fd_width+fd.depth)
average_eff_stress = (vert_eff_stress_interface + vert_eff_stress_lowest) / 2
c_2_eff = sl_1.cohesion + average_eff_stress * np.tan(np.radians(sl_1.phi))
if sl_0.cohesion > c_2_eff:
fd.q_ult = q_t
else:
# vd = {}
# vd[1] =[1, 1, 1, 1, 1]
# vd[0.667] = [1, 1.033, 1.064, 1.088, 1.109]
# vd[0.5] = [1, 1.056, 1.107, 1.152, 1.193]
# vd[0.333] = [1, 1.088, 1.167, 1.241, 1.311]
# vd[0.25] = [1, 1.107, 1.208, 1.302, 1.389]
# vd[0.2] = [1, 1.121, 1.235, 1.342, 1.444]
# vd[0.1] = [1, 1.154, 1.302, 1.446, 1.584]
h_over_b = (h0 - fd.depth) / fd_width
c1_over_c2 = sl_0.cohesion/c_2_eff
c_1_over_c_2 = [0.1, 0.2, 0.25, 0.333, 0.5, 0.667, 1.]
m_1 = [1.584, 1.444, 1.389, 1.311, 1.193, 1.109, 1.]
m_125 = [1.446, 1.342, 1.302, 1.241, 1.152, 1.088, 1.]
m_167 = [1.302, 1.235, 1.208, 1.167, 1.107, 1.064, 1.]
m_25 = [1.154, 1.121, 1.107, 1.088, 1.056, 1.033, 1.]
m_5 = [1, 1, 1, 1, 1, 1, 1]
if h_over_b == 0.1:
m = np.interp(c1_over_c2, c_1_over_c_2, m_1)
elif h_over_b == 0.125:
m = np.interp(c1_over_c2, c_1_over_c_2, m_125)
elif h_over_b == 0.167:
m = np.interp(c1_over_c2, c_1_over_c_2, m_167)
elif h_over_b == 0.250:
m = np.interp(c1_over_c2, c_1_over_c_2, m_25)
elif h_over_b >= 0.5:
m = np.interp(c1_over_c2, c_1_over_c_2, m_5)
elif 0.1 < h_over_b < 0.125:
m_a = np.interp(c1_over_c2, c_1_over_c_2, m_1)
m_b = np.interp(c1_over_c2, c_1_over_c_2, m_125)
m = np.interp(h_over_b, [0.1,0.125], [m_a,m_b])
elif 0.125 < h_over_b < 0.167:
m_a = np.interp(c1_over_c2, c_1_over_c_2, m_125)
m_b = np.interp(c1_over_c2, c_1_over_c_2, m_167)
m = np.interp(h_over_b, [0.125, 0.167], [m_a, m_b])
elif 0.167 < h_over_b < 0.25:
m_a = np.interp(c1_over_c2, c_1_over_c_2, m_167)
m_b = np.interp(c1_over_c2, c_1_over_c_2, m_25)
m = np.interp(h_over_b, [0.167, 0.250], [m_a, m_b])
elif 0.25 < h_over_b < 0.5:
m_a = np.interp(c1_over_c2, c_1_over_c_2, m_25)
m_b = np.interp(c1_over_c2, c_1_over_c_2, m_5)
m = np.interp(h_over_b, [0.250, 0.500], [m_a, m_b])
fd.q_ult = (sl_0.cohesion * m * sl_0.nc_factor_0) + (unit_eff_weight_0_at_fd_depth * fd.depth)
else:
fd.q_ult = q_ult
return fd.q_ult
def settlement_schmertmann(sp, fd, load, youngs_modulus_soil, **kwargs):
"""
Calculates the settlement of a shallow foundation (Schmertmann, 19XX).
:param sp: Soil Profile object
:param fd: Foundation object
:param load:
:param youngs_modulus_soil: The Young's modulus of the soil.
:param kwargs:
:return: float, the settlement.
"""
length = float(fd.length)
breadth = float(fd.width)
depth = float(fd.depth)
load = float(load)
sp.gwl = kwargs.get("gwl", sp.gwl)
sp.unit_sat_weight = kwargs.get("unit_sat_weight", sp.unit_sat_weight)
verbose = kwargs.get("verbose", 0)
years = kwargs.get("years", 0)
q = load / (length * breadth)
sigma_v0_eff = (sp.unit_dry_weight * min(depth, sp.gwl) +
(sp.unit_sat_weight - 9.8) * max([0, depth - sp.gwl]))
delta_q = q - sigma_v0_eff
# EMBEDMENT FACTOR
c_1 = max(1 - 0.5 * (sigma_v0_eff / delta_q), 0.5)
# CREEP FACTOR
if years == 0:
c_2 = 1.0
else:
c_2 = 1.0 + 0.2 * np.log10(years / 0.1)
# SHAPE FACTOR
long = max(length, breadth)
short = min(length, breadth)
c_3 = max(1.03 - 0.03 * (long / short), 0.73)
# Peak settlement index
if long / short > 10:
zp = short + depth
z_top = 0.2
z_bottom = 4 * short + depth
else:
z_top = 0.1
zp = 0.5 * short + depth
z_bottom = 2 * short + depth
sigma_vp_eff = (sp.unit_dry_weight * min(zp, sp.gwl) +
(sp.unit_sat_weight - 9.8) * max([0, zp - sp.gwl]))
i_zp = 0.5 + 0.1 * (delta_q / sigma_vp_eff)**0.5
i_z_top = (i_zp + z_top) / 2
i_z_bottom = i_zp / 2
settlement = (c_1 * c_2 * c_3 * delta_q *
(i_z_top * (zp - depth) + i_z_bottom *
(z_bottom - zp)) / youngs_modulus_soil)
if verbose:
log("delta_q:", delta_q)
log("c_1:", c_1)
log("c_2:", c_2)
log("c_3:", c_3)
log("zp:", zp)
log("sigma_vp_eff:", sigma_vp_eff)
log("i_zp:", i_zp)
log("i_z_top:", i_z_top)
log("i_z_bottom:", i_z_bottom)
log("settlement:", settlement)
return settlement
def size_footing_for_capacity(sl, vertical_load, fos=1.0, length_to_width=1.0, verbose=0, unit_weight=0, **kwargs):
"""
Determine the size of a footing given an aspect ratio and a load
:param sl: Soil object
:param vertical_load: The applied load to the foundation
:param fos: The target factor of safety
:param length_to_width: The desired length to width ratio of the foundation
:param verbose: verbosity
:return: a Foundation object
"""
method = kwargs.get("method", 'vesic')
depth_to_width = kwargs.get("depth_to_width", 0)
depth = kwargs.get("depth", 0)
use_depth_to_width = 0
if not depth:
use_depth_to_width = 1
# Find approximate size
fd = models.RaftFoundation()
fd.width = .5 # start with B=1.0m
for i in range(50):
fd.length = length_to_width * fd.width
if use_depth_to_width:
fd.depth = depth_to_width * fd.width
else:
fd.depth = depth
capacity_method_selector(sl, fd, method)
q = fd.q_ult
bearing_capacity = q * fd.length * fd.width
fs_actual = bearing_capacity / (vertical_load + unit_weight * fd.area * fd.depth)
if fs_actual < fos:
# Need to increase foundation sizes
fd.width += 0.5
else:
if verbose:
log("fs_actual: ", fs_actual)
log("fd.width: ", fd.width)
break
# at this stage the current size should be too big
width_array = []
fs_array = []
for j in range(11):
width_array.append(fd.width)
fd.length = length_to_width * fd.width
if use_depth_to_width:
fd.depth = depth_to_width * fd.width
capacity_method_selector(sl, fd, method)
q = fd.q_ult
capacity = q * fd.length * fd.width
fs_array.append(capacity / (vertical_load + unit_weight * fd.area * fd.depth))
fd.width = fd.width - 0.5 / 10
# search the array until FS satisfied:
if verbose:
log("reqFS: ", fos)
log("width array: \n", width_array)
log("FS array: \n", fs_array)
for fs in range(len(fs_array)):
if fs_array[fs] < fos:
fd.width = width_array[fs - 1]
fd.length = length_to_width * fd.width
if use_depth_to_width:
fd.depth = depth_to_width * fd.width
capacity_method_selector(sl, fd, method)
break
if fs == len(fs_array) - 1:
DesignError("No suitable foundation sizes could be determined!")
return fd
def capacity_vesic_1975(sl, fd, h_l=0, h_b=0, vertical_load=1, slope=0, base_tilt=0, verbose=0, gwl=1e6, **kwargs):
"""
Calculates the foundation capacity according Vesics(1975)
#Gunaratne, Manjriker. 2006. "Spread Footings: Analysis and Design."
Ref: http://geo.cv.nctu.edu.tw/foundation/download/
BearingCapacityOfFoundations.pdf
:param sl: Soil object
:param fd: Foundation object
:param h_l: Horizontal load parallel to length
:param h_b: Horizontal load parallel to width
:param vertical_load: Vertical load
:param slope: ground slope
:param base_tilt: The slope of the underside of the foundation
:param verbose: verbosity
:return: ultimate bearing stress
"""
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
if fd.length > fd.width: # TODO: deal with plane strain
fd_length = fd.length
fd_width = fd.width
else:
fd_length = fd.width
fd_width = fd.length
area_foundation = fd_length * fd_width
c_a = 0.6 - 1.0 * sl.cohesion
horizontal_load = np.sqrt(h_l ** 2 + h_b ** 2)
fd.nq_factor = ((np.tan(np.pi / 4 + sl.phi_r / 2)) ** 2 * np.exp(np.pi * np.tan(sl.phi_r)))
if sl.phi_r == 0:
fd.nc_factor = 5.14
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
fd.ng_factor = 2.0 * (fd.nq_factor + 1) * np.tan(sl.phi_r)
print('Nq-faktor', fd.nq_factor)
print('Ng-faktor', fd.ng_factor)
# shape factors:
s_c = 1.0 + fd.nq_factor / fd.nc_factor * fd_width / fd_length
s_q = 1 + fd_width / fd_length * np.tan(sl.phi_r)
s_g = max(1.0 - 0.4 * fd_width / fd_length, 0.6) # add limit of 0.6 based on Vesic
# depth factors:
if fd.depth / fd_width > 1:
k = np.arctan(fd.depth / fd_width)
else:
k = fd.depth / fd_width
d_c = 1 + 0.4 * k
d_q = 1 + 2 * np.tan(sl.phi_r) * (1 - np.sin(sl.phi_r)) ** 2 * k
d_g = 1.0
# load inclination factors
m__b = (2.0 + fd_width / fd_length) / (1 + fd_width / fd_length)
m_l = (2.0 + fd_length / fd_width) / (1 + fd_length / fd_width)
m = np.sqrt(m__b ** 2 + m_l ** 2)
if sl.phi_r == 0:
i_q = 1.0
i_g = 1.0
else:
i_q = (1.0 - horizontal_load / (vertical_load + area_foundation *
c_a / np.tan(sl.phi_r))) ** m
i_g = (1.0 - horizontal_load / (vertical_load + area_foundation *
c_a / np.tan(sl.phi_r))) ** (m + 1)
i_c = i_q - (1 - i_q) / (fd.nq_factor - 1)
check_i_c = 1 - m * horizontal_load / (area_foundation * c_a * fd.nc_factor)
if abs(check_i_c - i_c) / i_c > 0.001:
raise DesignError
# ground slope factors:
if sl.phi_r == 0:
# g_c = slope / 5.14
g_c = i_q
else:
g_c = i_q - (1 - i_q) / (5.14 * np.tan(sl.phi_r))
g_q = (1.0 - np.tan(slope)) ** 2
g_g = g_q
# tilted base factors
if sl.phi_r == 0:
b_c = g_c
else:
b_c = 1 - 2 * base_tilt / (5.14 * np.tan(sl.phi_r))
b_q = (1.0 - base_tilt * np.tan(sl.phi_r)) ** 2
b_g = b_q
# stress at footing base:
if gwl == 0:
q_d = sl.unit_eff_weight * fd.depth
unit_weight = sl.unit_bouy_weight
elif gwl > 0 and gwl < fd.depth:
q_d = (sl.unit_dry_weight * gwl) + (sl.unit_bouy_weight * (fd.depth - gwl))
unit_weight = sl.unit_bouy_weight
elif gwl >= fd.depth and gwl <= fd.depth + fd_width:
sl.average_unit_bouy_weight = sl.unit_bouy_weight + (
((gwl - fd.depth) / fd_width) * (sl.unit_dry_weight - sl.unit_bouy_weight))
q_d = sl.unit_dry_weight * fd.depth
unit_weight = sl.average_unit_bouy_weight
elif gwl > fd.depth + fd_width:
q_d = sl.unit_dry_weight * fd.depth
unit_weight = sl.unit_dry_weight
if verbose:
log("Nc: ", fd.nc_factor)
log("N_qV: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("d_c: ", d_c)
log("d_q: ", d_q)
log("d_g: ", d_g)
log("i_c: ", i_c)
log("i_q: ", i_q)
log("i_g: ", i_g)
log("g_c: ", g_c)
log("g_q: ", g_q)
log("g_g: ", g_g)
log("b_c: ", b_c)
log("b_q: ", b_q)
log("b_g: ", b_g)
log("q_d: ", q_d)
# Capacity
fd.q_ult = (sl.cohesion * fd.nc_factor * s_c * d_c * i_c * g_c * b_c +
q_d * fd.nq_factor * s_q * d_q * i_q * g_q * b_q +
0.5 * fd_width * unit_weight *
fd.ng_factor * s_g * d_g * i_g * g_g * b_g)
if verbose:
log("qult: ", fd.q_ult)
return fd.q_ult
def capacity_salgado_2008(sl, fd, h_l=0, h_b=0, vertical_load=1, verbose=0, **kwargs):
"""
Calculates the capacity according to
The Engineering of Foundations textbook by Salgado
ISBN: 0072500581
The method combines load factors from Bolton (1979) and shape factors from Brinch-Hansen (1970)
:param sl: Soil object
:param fd: Foundation object
:param h_l: Horizontal load parallel to length
:param h_b: Horizontal load parallel to width
:param vertical_load: Vertical load
:param verbose: verbosity
:return: ultimate bearing stress
"""
# Need to make adjustments if sand has DR<40% or
# clay has liquidity indices greater than 0.7
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
h_eff_b = kwargs.get("h_eff_b", 0)
h_eff_l = kwargs.get("h_eff_l", 0)
ip_axis_2d = kwargs.get('ip_axis_2d', None)
# TODO: implement phi as fn of sigma_m
temp_fd_length = fd.length
temp_fd_width = fd.width
if ip_axis_2d is not None:
if ip_axis_2d == 'width':
temp_fd_length = temp_fd_width * 100
elif ip_axis_2d == 'length':
temp_fd_width = temp_fd_length * 100
else:
raise ValueError(f"ip_axis_2d must be either 'width' or 'length', not {ip_axis_2d}")
v_l = kwargs.get("loc_v_l", temp_fd_length / 2) # given in fd coordinates
v_b = kwargs.get("loc_v_b", temp_fd_width / 2)
if temp_fd_length > temp_fd_width: # TODO: deal with plane strain
fd_length = temp_fd_length
fd_width = temp_fd_width
loc_v_l = v_l
loc_v_b = v_b
loc_h_b = h_b
loc_h_l = h_l
else:
fd_length = temp_fd_width
fd_width = temp_fd_length
loc_v_l = v_b
loc_v_b = v_l
loc_h_b = h_l
loc_h_l = h_b
ecc_b = loc_h_b * h_eff_b / vertical_load
ecc_l = loc_h_l * h_eff_l / vertical_load
width_eff = min(fd_width, 2 * (loc_v_b + ecc_b), 2 * (fd_width - loc_v_b - ecc_b))
length_eff = min(fd_length, 2 * (loc_v_l + ecc_l), 2 * (fd_length - loc_v_l - ecc_l))
# check para 3.4.1
if width_eff / 2 < fd_width / 6:
DesignError("failed on eccentricity")
# LOAD FACTORS:
fd.nq_factor = np.exp(np.pi * np.tan(sl.phi_r)) * (1 + np.sin(sl.phi_r)) / (1 - np.sin(sl.phi_r))
fd.ng_factor = 1.5 * (fd.nq_factor - 1) * np.tan(sl.phi_r)
# fd.ng_factor = (fd.nq_factor - 1) * np.tan(1.32 * sl.phi_r)
if sl.phi_r == 0:
fd.nc_factor = 5.14
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
# shape factors:
s_q = 1 + (width_eff / length_eff) * np.sin(sl.phi_r)
s_g = max(1 - 0.4 * width_eff / length_eff, 0.6)
s_c = 1.0
# depth factors:
d_over_b = min(1, fd.depth / width_eff) # limit to 1
d_q = 1 + 2 * np.tan(sl.phi_r) * (1 - np.sin(sl.phi_r)) ** 2 * d_over_b
d_g = 1.0
d_c = 1.0
# stress at footing base:
q_d = sl.unit_dry_weight * fd.depth
if verbose:
log("width_eff: ", width_eff)
log("length_eff: ", length_eff)
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("d_c: ", d_c)
log("d_q: ", d_q)
log("d_g: ", d_g)
log("q_d: ", q_d)
# Capacity
fd.q_ult = (sl.cohesion * fd.nc_factor * s_c * d_c +
q_d * fd.nq_factor * s_q * d_q +
0.5 * width_eff * sl.unit_dry_weight *
fd.ng_factor * s_g * d_g)
if verbose:
log("qult: ", fd.q_ult)
return fd.q_ult
def capacity_nzs_vm4_2011(sl, fd, h_l=0, h_b=0, vertical_load=1, slope=0, verbose=0, **kwargs):
"""
calculates the capacity according to
Appendix B verification method 4 of the NZ building code
:param sl: Soil object
:param fd: Foundation object
:param h_l: Horizontal load parallel to length
:param h_b: Horizontal load parallel to width
:param vertical_load: Vertical load
:param slope: ground slope
:param verbose: verbosity
:return: ultimate bearing stress
"""
# Need to make adjustments if sand has DR<40% or
# clay has liquidity indices greater than 0.7
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
horizontal_load = np.sqrt(h_l ** 2 + h_b ** 2)
v_l = kwargs.get("loc_v_l", fd.length / 2) # given in fd coordinates
v_b = kwargs.get("loc_v_b", fd.width / 2)
h_eff_b = kwargs.get("h_eff_b", 0)
h_eff_l = kwargs.get("h_eff_l", 0)
if fd.length > fd.width: # TODO: deal with plane strain
fd_length = fd.length
fd_width = fd.width
loc_v_l = v_l
loc_v_b = v_b
loc_h_b = h_b
loc_h_l = h_l
else:
fd_length = fd.width
fd_width = fd.length
loc_v_l = v_b
loc_v_b = v_l
loc_h_b = h_l
loc_h_l = h_b
ecc_b = loc_h_b * h_eff_b / vertical_load
ecc_l = loc_h_l * h_eff_l / vertical_load
width_eff = min(fd_width, 2 *
(loc_v_b + ecc_b), 2 * (fd_width - loc_v_b - ecc_b))
length_eff = min(fd_length, 2 *
(loc_v_l + ecc_l), 2 * (fd_length - loc_v_l - ecc_l))
area_foundation = length_eff * width_eff
# check para 3.4.1
if width_eff / 2 < fd_width / 6:
raise DesignError("failed on eccentricity")
# LOAD FACTORS:
fd.nq_factor = ((np.tan(np.pi / 4 + sl.phi_r / 2)) ** 2 * np.exp(np.pi * np.tan(sl.phi_r)))
if sl.phi_r == 0:
fd.nc_factor = 5.14
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
fd.ng_factor = 2.0 * (fd.nq_factor - 1) * np.tan(sl.phi_r)
# shape factors:
s_c = 1.0 + fd.nq_factor / fd.nc_factor * width_eff / length_eff
s_q = 1 + width_eff / length_eff * np.tan(sl.phi_r)
s_g = max(1.0 - 0.4 * width_eff / length_eff, 0.6) # add limit of 0.6 based on Vesics
# depth factors:
if fd.depth / width_eff > 1:
k = np.arctan(fd.depth / width_eff)
else:
k = fd.depth / width_eff
if sl.phi_r == 0:
d_c = 1 + 0.4 * k
d_q = 1.0
else:
d_q = (1 + 2 * np.tan(sl.phi_r) *
(1 - np.sin(sl.phi_r)) ** 2 * k)
d_c = d_q - (1 - d_q) / (fd.nq_factor * np.tan(sl.phi_r))
d_g = 1.0
# load inclination factors:
if sl.phi_r == 0:
i_c = 0.5 * (1 + np.sqrt(1 - horizontal_load / (area_foundation * sl.cohesion)))
i_q = 1.0
i_g = 1.0
else:
if h_b == 0:
i_q = 1 - horizontal_load / (vertical_load + area_foundation * sl.cohesion /
np.tan(sl.phi_r))
i_g = i_q
elif h_b > 0 and h_l == 0:
i_q = ((1 - 0.7 * horizontal_load / (vertical_load + area_foundation * sl.cohesion /
np.tan(sl.phi_r))) ** 3)
i_g = ((1 - horizontal_load / (vertical_load + area_foundation * sl.cohesion /
np.tan(sl.phi_r))) ** 3)
else:
raise DesignError("not setup for bi-directional loading")
i_c = (i_q * fd.nq_factor - 1) / (fd.nq_factor - 1)
# ground slope factors:
g_c = 1 - slope * (1.0 - fd.depth / (2 * width_eff)) / 150
g_q = (1 - np.tan(slope * (1 - fd.depth / (2 * width_eff)))) ** 2
g_g = g_q
# stress at footing base:
q_d = sl.unit_dry_weight * fd.depth
if verbose:
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("H: ", horizontal_load)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("d_c: ", d_c)
log("d_q: ", d_q)
log("d_g: ", d_g)
log("i_c: ", i_c)
log("i_q: ", i_q)
log("i_g: ", i_g)
log("g_c: ", g_c)
log("g_q: ", g_q)
log("g_g: ", g_g)
# Capacity
fd.q_ult = (sl.cohesion * fd.nc_factor * s_c * d_c * i_c * g_c +
q_d * fd.nq_factor * s_q * d_q * i_q * g_q +
0.5 * width_eff * sl.unit_dry_weight *
fd.ng_factor * s_g * d_g * i_g * g_g)
if verbose:
log("q_ult: ", fd.q_ult)
return fd.q_ult
def capacity_meyerhof_1963(sl, fd, gwl=1e6, h_l=0, h_b=0, vertical_load=1, axis_inf=None, verbose=0, **kwargs):
"""
Calculates the foundation capacity according Meyerhoff (1963)
http://www.engs-comp.com/meyerhof/index.shtml
:param sl: Soil object
:param fd: Foundation object
:param h_l: Horizontal load parallel to length
:param h_b: Horizontal load parallel to width
:param vertical_load: Vertical load
:param verbose: verbosity
:return: ultimate bearing stress
"""
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
horizontal_load = np.sqrt(h_l ** 2 + h_b ** 2)
if axis_inf is None:
if fd.length > fd.width:
fd_length = fd.length
fd_width = fd.width
else:
fd_length = fd.width
fd_width = fd.length
elif axis_inf == 'width':
fd_width = fd.length
fd_length = None
elif axis_inf == 'length':
fd_width = fd.width
fd_length = None
else:
raise ValueError(f'axis_inf must be either: None, "width", or "length" not {axis_inf}')
fd.nq_factor = ((np.tan(np.pi / 4 + sl.phi_r / 2)) ** 2 *
np.exp(np.pi * np.tan(sl.phi_r)))
if sl.phi_r == 0:
fd.nc_factor = 5.14
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
fd.ng_factor = (fd.nq_factor - 1) * np.tan(1.4 * sl.phi_r)
if verbose:
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
kp = (np.tan(np.pi / 4 + sl.phi_r / 2)) ** 2
# shape factors
if fd_length is None:
s_c = 1
s_q = 1
else:
s_c = 1 + 0.2 * kp * fd_width / fd_length
if sl.phi > 10:
s_q = 1.0 + 0.1 * kp * fd_width / fd_length
else:
s_q = 1.0
s_g = s_q
# depth factors
d_c = 1 + 0.2 * np.sqrt(kp) * fd.depth / fd_width
if sl.phi > 10:
d_q = 1 + 0.1 * np.sqrt(kp) * fd.depth / fd_width
else:
d_q = 1.0
d_g = d_q
# inclination factors:
theta_load = np.arctan(horizontal_load / vertical_load)
i_c = (1 - theta_load / (np.pi * 0.5)) ** 2
i_q = i_c
if sl.phi > 0:
i_g = (1 - theta_load / sl.phi_r) ** 2
else:
i_g = 0
# stress at footing base:
if gwl == 0:
q_d = sl.unit_bouy_weight * fd.depth
unit_weight = sl.unit_bouy_weight
elif gwl > 0 and gwl < fd.depth:
q_d = (sl.unit_dry_weight * gwl) + (sl.unit_bouy_weight * (fd.depth - gwl))
unit_weight = sl.unit_bouy_weight
elif gwl >= fd.depth and gwl <= fd.depth + fd_width:
sl.average_unit_bouy_weight = sl.unit_bouy_weight + (
((gwl - fd.depth) / fd_width) * (sl.unit_dry_weight - sl.unit_bouy_weight))
q_d = sl.unit_dry_weight * fd.depth
unit_weight = sl.average_unit_bouy_weight
elif gwl > fd.depth + fd_width:
q_d = sl.unit_dry_weight * fd.depth
unit_weight = sl.unit_dry_weight
if verbose:
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("d_c: ", d_c)
log("d_q: ", d_q)
log("d_g: ", d_g)
log("i_c: ", i_c)
log("i_q: ", i_q)
log("i_g: ", i_g)
log("q_d: ", q_d)
# Capacity
fd.q_ult = (sl.cohesion * fd.nc_factor * s_c * d_c * i_c +
q_d * fd.nq_factor * s_q * d_q * i_q +
0.5 * fd_width * unit_weight *
fd.ng_factor * s_g * d_g * i_g)
return fd.q_ult
def capacity_hansen_1970(sl, fd, h_l=0, h_b=0, vertical_load=1, slope=0, base_tilt=0, verbose=0, **kwargs):
"""
Calculates the foundation capacity according Hansen (1970)
Ref: http://bestengineeringprojects.com/civil-projects/
hansens-bearing-capacity-theory/
:param sl: Soil object
:param fd: Foundation object
:param h_l: Horizontal load parallel to length
:param h_b: Horizontal load parallel to width
:param vertical_load: Vertical load
:param slope: ground slope
:param base_tilt: The slope of the underside of the foundation
:param verbose: verbosity
:return: ultimate bearing stress
"""
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
if fd.length > fd.width: # TODO: deal with plane strain
fd_length = fd.length
fd_width = fd.width
else:
fd_length = fd.width
fd_width = fd.length
area_foundation = fd_length * fd_width
horizontal_load = np.sqrt(h_l ** 2 + h_b ** 2)
c_a = 0.6 - 1.0 * sl.cohesion
fd.nq_factor = ((np.tan(np.pi / 4 + sl.phi_r / 2)) ** 2 * np.exp(np.pi * np.tan(sl.phi_r)))
if sl.phi_r == 0:
fd.nc_factor = 5.14
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
fd.ng_factor = 1.5 * (fd.nq_factor - 1) * np.tan(sl.phi_r)
# shape factors
if sl.phi_r == 0:
s_c = 0.2 * fd_width / fd_length
else:
s_c = 1.0 + fd.nq_factor / fd.nc_factor * fd_width / fd_length
s_q = 1.0 + fd_width / fd_length * np.sin(sl.phi_r)
s_g = 1.0 - 0.4 * fd_width / fd_length
# depth factors:
if fd.depth / fd_width > 1:
k = np.arctan(fd.depth / fd_width)
else:
k = fd.depth / fd_width
d_c = 1 + 0.4 * k
if sl.phi == 0:
d_c = 0.4 * k
d_q = 1 + 2 * np.tan(sl.phi_r) * (1 - np.sin(sl.phi_r)) ** 2 * k
d_g = 1.0
# incline load factors:
if sl.phi_r == 0:
i_q = 1.0
i_c = 0.5 - 0.5 * np.sqrt(1 - horizontal_load / area_foundation * c_a)
i_g = 1.0
else:
i_q = ((1.0 - 0.5 * horizontal_load /
(vertical_load + area_foundation * c_a / np.tan(sl.phi_r))) ** 5)
i_c = i_q - (1 - i_q) / (fd.nq_factor - 1)
i_g = ((1 - (0.7 * horizontal_load) /
(vertical_load + area_foundation * c_a / np.tan(sl.phi_r))) ** 5)
# slope factors:
if sl.phi_r == 0:
g_c = (slope / np.pi * 180) / 147
else:
g_c = 1.0 - (slope / np.pi * 180) / 147
g_q = 1 - 0.5 * np.tan(slope) ** 5
g_g = g_q
# base tilt factors:
if sl.phi_r == 0:
b_c = (base_tilt / np.pi * 180) / 147
else:
b_c = 1.0 - (base_tilt / np.pi * 180) / 147
b_q = (np.exp(-0.0349 * (base_tilt / np.pi * 180) * np.tan(sl.phi_r)))
b_g = (np.exp(-0.0471 * (base_tilt / np.pi * 180) * np.tan(sl.phi_r)))
if verbose:
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("d_c: ", d_c)
log("d_q: ", d_q)
log("d_g: ", d_g)
log("i_c: ", i_c)
log("i_q: ", i_q)
log("i_g: ", i_g)
log("g_c: ", g_c)
log("g_q: ", g_q)
log("g_g: ", g_g)
log("b_c: ", b_c)
log("b_q: ", b_q)
log("b_g: ", b_g)
# stress at footing base:
q_d = sl.unit_dry_weight * fd.depth
# Capacity
if sl.phi_r == 0:
fd.q_ult = (sl.cohesion * fd.nc_factor *
(1 + s_c + d_c - i_c - g_c - b_c) + q_d)
else:
fd.q_ult = (sl.cohesion * fd.nc_factor *
s_c * d_c * i_c * g_c * b_c +
q_d * fd.nq_factor * s_q * d_q * i_q * g_q * b_q +
0.5 * fd_width * sl.unit_dry_weight *
fd.ng_factor * s_g * d_g * i_g * g_g * b_g)
def capacity_terzaghi_1943(sl, fd, round_footing=False, verbose=0, **kwargs):
"""
Calculates the foundation capacity according Terzaghi (1943)
Ref: http://geo.cv.nctu.edu.tw/foundation/
download/BearingCapacityOfFoundations.pdf
:param sl: Soil object
:param fd: Foundation object
:param round_footing: if True, then foundation is round
:param verbose: verbosity
:return: ultimate bearing stress
Note: the shape factor of 1.3 is used for aspect ratio > 6
"""
if not kwargs.get("disable_requires", False):
models.check_required(sl, ["phi_r", "cohesion", "unit_dry_weight"])
models.check_required(fd, ["length", "width", "depth"])
if fd.length > fd.width: # TODO: deal with plane strain
fd_length = fd.length
fd_width = fd.width
else:
fd_length = fd.width
fd_width = fd.length
a02 = ((np.exp(np.pi * (0.75 - sl.phi / 360) * np.tan(sl.phi_r))) ** 2)
a0_check = (np.exp((270 - sl.phi) / 180 * np.pi * np.tan(sl.phi_r)))
if (a02 - a0_check) / a02 > 0.001:
raise DesignError
fd.nq_factor = (a02 / (2 * (np.cos((45 + sl.phi / 2) * np.pi / 180)) ** 2))
fd.ng_factor = (2 * (fd.nq_factor + 1) * np.tan(sl.phi_r) / (1 + 0.4 * np.sin(4 * sl.phi_r)))
if sl.phi_r == 0:
fd.nc_factor = 5.7
else:
fd.nc_factor = (fd.nq_factor - 1) / np.tan(sl.phi_r)
# shape factors:
if round_footing:
s_c = 1.3
s_g = 0.6
elif fd_length / fd_width < 5:
s_c = 1.3
s_g = 0.8
else:
s_c = 1.0
s_g = 1.0
s_q = 1.0
# stress at footing base:
q_d = sl.unit_dry_weight * fd.depth
# Capacity
fd.q_ult = (sl.cohesion * fd.nc_factor * s_c + q_d * fd.nq_factor * s_q + 0.5 * fd_width *
sl.unit_dry_weight * fd.ng_factor * s_g)
if verbose:
log("Nc: ", fd.nc_factor)
log("Nq: ", fd.nq_factor)
log("Ng: ", fd.ng_factor)
log("s_c: ", s_c)
log("s_q: ", s_q)
log("s_g: ", s_g)
log("qult: ", fd.q_ult)
return fd.q_ult