updated docs pages

Author: patrickboateng

docs/formulas/allowable-bearing-capacity.md

@@ -0,0 +1,21 @@
+# Bowles Allowable Bearing Capacity
+
+## Bowles Bearing Capacity for pad foundation
+
+$
+q_a(kPa) = 19.16(N_1)_{55} f_d\left(\dfrac{S}{25.4}\right),
+\ B \ \le \ 1.2m
+$
+
+$
+q_a(kPa) = 11.98(N_1)_{55}\left(\dfrac{3.28B + 1}{3.28B} \right)^2
+f_d \left(\dfrac{S}{25.4}\right), \ B \ \gt 1.2m
+$
+
+$f_d = 1 + 0.33 \cdot \dfrac{D_f}{B} \le 1.33$
+
+## Bowles Bearing Capacity for mat foundation
+
+$q_a(kPa) = 11.98(N_1)_{55}f_d\left(\dfrac{S}{25.4}\right)$
+
+$f_d = 1 + 0.33 \cdot \dfrac{D_f}{B} \le 1.33$

docs/formulas/allowable-bearing-capacity/bowles.md

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+# Allowable Bearing Capacity Formulas
+
+## Description of symbols used in bearing capacity equations
+
+| Symbol | Unit | Description                       |
+|--------|------|-----------------------------------|
+| $q_a$  | kPa  | Allowable bearing capacity        |
+| $N$    | –    | Corrected SPT N-value             |
+| $f_d$  | –    | Depth factor                      |
+| $c_w$  | –    | Water correction factor           |
+| $S$    | mm   | Tolerable settlement              |
+| $B$    | m    | Width of foundation footing       |
+| $D_f$  | m    | Depth of foundation footing       |
+| $D_w$  | m    | Depth of water below ground level |

docs/formulas/allowable-bearing-capacity/index.md

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+# Meyerhof Allowable Bearing Capacity
+
+## Meyerhof Bearing Capacity for pad foundation
+
+$
+q_a(kPa) = 12N f_d\left(\dfrac{S}{25.4}\right), \ B \ \le 1.2m
+$
+
+$
+q_a(kPa) = 8N\left(\dfrac{3.28B + 1}{3.28B} \right)^2 f_d\left(
+\dfrac{S}{25.4}\right), \ B \ \gt 1.2m
+$
+
+$f_d = 1 + 0.33 \cdot \dfrac{D_f}{B} \le 1.33$
+
+## Meyerhof Bearing Capacity for mat foundation
+
+$q_a(kPa) = 8 N f_d\left(\dfrac{S}{25.4}\right)$
+
+$f_d = 1 + 0.33 \cdot \dfrac{D_f}{B} \le 1.33$

docs/formulas/allowable-bearing-capacity/meyerhof.md

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+# Terzaghi Allowable Bearing Capacity
+
+## Terzaghi Bearing Capacity for pad foundation
+
+$
+q_a(kPa) = 12N \dfrac{1}{c_w f_d}\left(\dfrac{S}{25.4}\right),
+\ B \ \le 1.2m
+$
+
+$
+q_a(kPa) = 8N\left(\dfrac{3.28B + 1}{3.28B} \right)^2\dfrac{1}
+{c_w f_d}\left(\dfrac{S}{25.4}\right), \ B \ \gt 1.2m
+$
+
+$f_d = 1 + 0.25 \cdot \dfrac{D_f}{B} \le 1.25$
+
+$c_w = 2 - \dfrac{D_w}{2B} \le 2, D_w \gt D_f$
+
+$c_w = 2 - \dfrac{D_f}{2B} \le 2, D_w \le D_f$
+
+## Terzaghi Bearing Capacity for mat foundation
+
+$q_a(kPa) = 8N\dfrac{1}{c_w f_d}\left(\dfrac{S}{25.4}\right)$
+
+$f_d = 1 + 0.25 \cdot \dfrac{D_f}{B} \le 1.25$
+
+$c_w = 2 - \dfrac{D_w}{2B} \le 2, D_w \gt D_f$
+
+$c_w = 2 - \dfrac{D_f}{2B} \le 2, D_w \le D_f$

docs/formulas/allowable-bearing-capacity/terzaghi.md

@@ -4,6 +4,6 @@ This documentation section provides explanations of the geotechnical formulas
 used in `geolysis`. Each explanation includes the formula, its variables, and
 a brief description of its application.
 
-- [Allowable Bearing Capacity](allowable-bearing-capacity.md)
-- [Ultimate Bearing Capacity](ultimate-bearing-capacity.md)
-- [Standard Penetration Test (SPT)](spt.md)
+- [Allowable Bearing Capacity](allowable-bearing-capacity/index.md)
+- [Ultimate Bearing Capacity](ultimate-bearing-capacity/index.md)
+- [Standard Penetration Test (SPT)](spt/index.md)

docs/formulas/index.md

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+# Dilatancy Corrections
+
+## Corrections
+
+$(N_1)_{60 \, (CORR)} = 15 + \dfrac{1}{2}((N_1)_{60} - 15) \, , \, (N_1)_{60} \gt 15$
+
+$(N_1)_{60 \, (CORR)} = (N_1)_{60} \, , \, (N_1)_{60} \le 15$
+

docs/formulas/spt.md

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+# SPT Formulas
+
+## Description of symbols used in SPT Corrections
+
+| Symbol                 | Description                                        |
+|------------------------|----------------------------------------------------|
+| $(N_1)_{60}$           | SPT blow count corrected for overburden pressure   |
+| $(N_1)_{60 \, (CORR)}$ | SPT blow count corrected for dilatancy             |
+| $N_{60}$               | SPT blow count corrected for 60% hammer efficiency |
+| $C_N$                  | Overburden pressure correction factor              |
+| $\sigma_o$             | Effective overburden pressure at the test depth    |

docs/formulas/spt/dilatancy-corrections.md

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+# Overburden Pressure Corrections
+
+$(N_1)_{60} = C_N \cdot N_{60}$
+
+$C_N \le 2$
+
+!!! note
+
+    `60` is used in this case to represent `60%` hammer
+     efficiency and can be any percentage of hammer efficiency
+     e.g. $N_{55}$ for `55%` hammer efficiency.
+
+## Gibbs & Holtz (1957)
+
+$C_N = \dfrac{350}{\sigma_o + 70} \, \sigma_o \le 280kN/m^2$
+
+!!! note
+
+    $\frac{N_c}{N_{60}}$ should lie between 0.45 and 2.0, if
+    $\frac{N_c}{N_{60}}$ is greater than 2.0, :math:`N_c` should be
+    divided by 2.0 to obtain the design value used in finding the
+    bearing capacity of the soil.
+
+## Peck and Bazaraa (1969)
+
+$
+C_N = \dfrac{4}{1 + 0.0418 \cdot \sigma_o}, \,
+\sigma_o \lt 71.8kN/m^2
+$
+
+$
+C_N = \dfrac{4}{3.25 + 0.0104 \cdot \sigma_o},
+\, \sigma_o \gt 71.8kN/m^2
+$
+
+$C_N = 1 \, , \, \sigma_o = 71.8kN/m^2$
+
+## Peck et al. (1974)
+
+$C_N = 0.77 \log \left(\dfrac{2000}{\sigma_o} \right)$
+
+## Liao & Whitman (1986)
+
+$C_N = \sqrt{\dfrac{100}{\sigma_o}}$
+
+## Skemton (1986)
+
+$C_N = \dfrac{2}{1 + 0.01044 \cdot \sigma_o}$