Three triaxial tests, Mohr circles, φ

Step 1: Principal stresses at failure ($\sigma_1 = \sigma_3 + \sigma_d$)

Step 2: Mohr circles and envelope. Draw each circle with its centre on the $\sigma$-axis and radius as in the table, then draw the common tangent.

 tau
  |            ___..--''''-.
  |        ,-''   ___...--'' `.
  |     ,-'  _.--'' .--''  .   \
  |   ,'  .-'  __,-'  _.-'  \   \
  |  / .'.-' ,-'  _.-'   phi  |  |
  +--+---------------------------+-- sigma
    0   300  400  500   1175 1560 1960

The tangent passes (almost) through the origin, so $c \approx 0$ (a cohesionless soil).

Step 3: Angle of internal friction

$$\sin\phi = \frac{\sigma_1-\sigma_3}{\sigma_1+\sigma_3}$$ $$\begin{aligned} \text{Test 1: } \sin\phi &= \frac{875}{1475} = 0.593 \;\Rightarrow\; \phi = 36.4^\circ \\ \text{Test 2: } \sin\phi &= \frac{1160}{1960} = 0.592 \;\Rightarrow\; \phi = 36.3^\circ \\ \text{Test 3: } \sin\phi &= \frac{1460}{2460} = 0.594 \;\Rightarrow\; \phi = 36.4^\circ \end{aligned}$$

Answer: $c \approx 0$ and $\phi \approx 36.4^\circ$ (about $36^\circ$).