113 年 國立成功大學土木工程系碩士班乙組《基礎工程》

Fig. 1 shows a mat foundation. Please answer the following questions (45%)

Mat size: BxL = 8m x 8m
Q = 36,000 kN
Groundwater table at 5m depth.
Sand layer 1 (above groundwater table): thickness = 5m, $\gamma = 16 \, \text{kN/m}^3$, $\phi' = 30^\circ$.
Sand layer 2 (below groundwater table): thickness = 6m, $\gamma = 18 \, \text{kN/m}^3$, $\phi' = 30^\circ$.
Clay layer: thickness = 4m, $e_0 = 0.6$, $\sigma'_c = 200 \, \text{kPa}$, $\gamma = 17 \, \text{kN/m}^3$.
Incompressible layer below clay.

Bearing capacity factors (for Terzaghi's theory)

Fig. 2: Contours of $\Delta\sigma / q_0$ ($\Delta\sigma$: vertical stress increase) below the center line of a squared loaded area.

(1) Determine the average net pressure on soil caused by the mat foundation (5%).
(2) Use Terzaghi's bearing capacity theory (the factors given in the table below Fig. 1) to determine the net ultimate bearing capacity of this mat (only considering the contribution of sand layer; NOTE the groundwater table!) and also calculate the factor of safety based on the answer of (1) (15%).
(3) Assuming the mat can be regarded as a uniformly loaded squared area, suggest a minimum depth of boring based on Fig. 2 (the approximate depths corresponding to $\Delta\sigma/q_0$ values of 0.05, 0.1, and 0.02 noted in Fig. 2 may be used) and also briefly explain the reason (5%).
(4) Again, regarding the mat as a uniformly loaded squared area, estimate the vertical stress increase caused by the mat foundation below its center at the middle of clay layer based on the Fig. 2 (5%).
(5) Following (4), estimate the consolidation settlement of the clay layer under the center of the mat ($C_c = 0.3$ and $C_s = 0.1$; using the stress increase at the middle of the clay layer as the average) (15%).

For the gravity retaining wall (concrete = 24 kN/m³) as shown in Fig 3, give the following data.
Wall dimensions: H = 5 m, D = 1 m, $x_1 = x_4 = x_5 = 0.5 \, \text{m}$, $x_2 = x_3 = x_6 = 1 \, \text{m}$.
Soil properties:
$\gamma_1 = 16 \, \text{kN/m}^3$, $\phi'_1 = 30^\circ$, $c'_1 = 0$.
$\gamma_2 = 17 \, \text{kN/m}^3$, $\phi'_2 = 20^\circ$, $c'_2 = 30 \, \text{kN/m}^2$.
At the interface of the soil and the base: friction angle $\delta' = (1/2)\phi'_2$; adhesion $c'_a = (1/2)c'_2$.

Answer the following questions (45%).

(1) Calculate the Rankine active force per unit length of the wall (with the simplified assumption for design). (10%)
(2) Following (1), Calculate the corresponding overturning moment about the toe. (5%)
(3) Following (2), Calculate the factor of safety against overturning (neglect the passive force in front of the wall). (10%)
(4) Following (1), calculate the factor of safety against sliding (neglect the passive force in front of the wall). (10%)
(5) Is the wall safe (considering both overturning and sliding)? If not, give one suggestion for improvement. (10%).

Fig. 3
🖼️【此處有附圖，請對照原卷】

Fig. 4 shows the axial force distribution with depth of a pile, which represents its load transfer mechanism. As its ultimate load-carrying capacity $Q_u$ was reached by a vertical compression load test, the axial force distribution curve is curve (B). The diameter and length of the pile are 0.6 m and 20 m, respectively. Answer the following questions (10%).

(1) Determine the average unit friction resistance (per area) at the depth range of 0~10 m? (5%)
(2) If the factors of safety for the frictional resistance of the pile skin and the load-carrying capacity of the pile point are 2.5 and 4, respectively, determine the allowable load-carrying capacity of this pile. (5%)

Fig. 4
🖼️【此處有附圖，請對照原卷】