Minerals and Rocks: Worked Applications

A specimen has bulk volume $150\ \text{cm}^3$ and independently measured solid volume $135\ \text{cm}^3$. Find its porosity and void ratio.

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A porous rock specimen has $n=28\%$ and bulk volume $1.00\ \text{m}^3$. Find its void volume, solid volume and void ratio.

A specimen has $e=0.60$ and $V_v=30\ \text{cm}^3$. Find solid volume, bulk volume and porosity.

A dry specimen weighs $1.3\ \text{kN}$, has bulk volume $0.050\ \text{m}^3$ and porosity $2\%$. With $\gamma_w=9.81\ \text{kN/m}^3$, find dry bulk unit weight and grain specific gravity.

Use a fixed bulk volume $200\ \text{cm}^3$, porosity $25\%$, pore saturation $60\%$ and $G_s=2.65$. With $\rho_w=1.000\ \text{g/cm}^3$, find the phase volumes, mass water content and bulk unit weight. Take $\gamma_w=9.81\ \text{kN/m}^3$ and neglect air mass.

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A specimen has measured bulk volume $120\ \text{cm}^3$, dry mass $270\ \text{g}$ and independently known $G_s=2.70$. A specified procedure fills all pores accessible to that procedure; after external surface water is removed, its mass is $285\ \text{g}$. Assume $\rho_w=1.000\ \text{g/cm}^3$, no solid loss and no reaction.

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A specified slake-durability test starts with $500\ \text{g}$ of dry specimen material. The net dry retained masses are $460\ \text{g}$ after the first cycle and $410\ \text{g}$ after the second. Container tare has been removed. Calculate the two-cycle retained-mass index used in the lesson.

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Under controlled scratch comparisons, an unknown makes a genuine scratch on a calcite reference ($H=3$), while an apatite reference ($H=5$) scratches the unknown. What hardness information and mineral identification are supported?

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A mapped granite weathers. Transport and sorting produce loose, predominantly quartz sand with nominal grains around $0.5\ \text{mm}$. The sediment is cemented, then later recrystallizes in the solid state into an interlocking, quartz-rich rock. Identify the supplied stages and distinguish metamorphism from melting.

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A core test reports intact UCS $80\ \text{MPa}$ at its stated moisture condition. Field logging identifies joints, but their persistence, condition, water pressures and relationship to the proposed works are not yet resolved. Can the UCS be used as a unique rock-mass strength or foundation capacity?

Petrography identifies chalcedony and strained quartz in a candidate aggregate. A draft report calls both “amorphous silica” and concludes that damaging ASR is certain. Correct the description and the acceptance reasoning.

A proposed shale fill source has dry intact UCS $60\ \text{MPa}$, porosity $8\%$ and a reported two-cycle slake-durability index of $42\%$ under the specified procedure. Does the dry strength or porosity prove suitability for the embankment?