ANSWERS TO “TEST YOUR KNOWLEDGE” ON PAGE 34 Answers:

1. The answer is choice “a” or “Tambora, 1815.” It is considered as the largest eruption in historic time. The year 1816 was “the year without a summer.”.

2. The answer is choice “a” or “Hornfels.”

Hornfels is a fine-grained, non-foliated metamorphic rock produced by contact metamorphism; baked by the heat from a nearby magmatic body. Hornfels may be pelitic developing from the contact metamorphism of mudstone, clay-rich and silt rich strata, but may also develop from originally carbonate-rich and mafic lithologies.

In contrast, granite gneiss is foliated and the product of the high-grade regional metamorphism of granitic rocks, etc. Slate is also foliated and constitutes the product of low-grade regional metamorphism of argillaceous strata. 3. The answer is choice “a” or the “biharmonic equation.”

In mathematics, the biharmonic equation is a fourth-order partial differential equation which is used in areas of continuum mechanics, includ- ing linear elasticity theory and in the solution of Stokes flow (creeping flow/viscous flow). It is written as

= 0 44444422422422 = 0

biharmonic equation also satisfies the compatibility equation (strain) and is rewritten as:

44444422 = 0

By varying boundary conditions, the equation becomes useful in fault modeling (e.g., Hafner solutions, etc.) by determining major and minor principal stress trajectories and related, predictable fault geometries.

Choice “b” or Laplace’s equation is: 2 = 0

The symbol () is referred to as the Laplace operator or Laplacian, where:

Thus, 2222222 Laplace’s equation is then: 2222222 = 0

Note that is a scalar function.

The general theory of solutions to Laplace’s equation is known as “potential theory.” The solutions of Laplace’s equation are the “harmonic functions.” Laplace’s equation is useful in working with electric, gravitational, and fluid potentials and, in reference to heat conduction, Laplace’s equation becomes the steady-state heat equation.

Choice “c” or Boyle’s equation or Boyle’s Law refers to the properties of gases. It states that the absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies, as longs as the temperature and the amount of gas remain unchanged within a closed system. It is commonly written as:

P1V1 = P2V2

4. The answer is choice “c” or [LI = 3.1; this is a “quick clay”]. LI = (Wn – PL) / (LL – PL)

LI = (Wn – PL) / PI

(1) (2)

The denominator in (2) is the plasticity index (PI). Substituting the numerical values given in our problem: LI = (32 – 15.8) / 5.2 = 3.1

(3)

The “sensitivity” of a clay is related to its liquidity index. A dramatic loss of strength should be expected in flocculated clays where the natural water content is considerably greater than the liquid limit. This is typical of “quick clays” where the fabric can suddenly collapse from a flocculated into a dispersed arrangement, raising pore pressures, overcoming strength and leading to failure.

5. The answer is choice “a” or “The northeast corner of the township.” This is true in the US. In Canada, the numbering is reversed and starts in the southeast corner of the township. (Answer by David M. Abbott, CPG-04570).

36 TPG • Jul.Aug.Sep 2018 www.aipg.org

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1. The answer is choice “a” or “Tambora, 1815.” It is considered as the largest eruption in historic time. The year 1816 was “the year without a summer.”.

2. The answer is choice “a” or “Hornfels.”

Hornfels is a fine-grained, non-foliated metamorphic rock produced by contact metamorphism; baked by the heat from a nearby magmatic body. Hornfels may be pelitic developing from the contact metamorphism of mudstone, clay-rich and silt rich strata, but may also develop from originally carbonate-rich and mafic lithologies.

In contrast, granite gneiss is foliated and the product of the high-grade regional metamorphism of granitic rocks, etc. Slate is also foliated and constitutes the product of low-grade regional metamorphism of argillaceous strata. 3. The answer is choice “a” or the “biharmonic equation.”

In mathematics, the biharmonic equation is a fourth-order partial differential equation which is used in areas of continuum mechanics, includ- ing linear elasticity theory and in the solution of Stokes flow (creeping flow/viscous flow). It is written as

= 0 44444422422422 = 0

biharmonic equation also satisfies the compatibility equation (strain) and is rewritten as:

44444422 = 0

By varying boundary conditions, the equation becomes useful in fault modeling (e.g., Hafner solutions, etc.) by determining major and minor principal stress trajectories and related, predictable fault geometries.

Choice “b” or Laplace’s equation is: 2 = 0

The symbol () is referred to as the Laplace operator or Laplacian, where:

Thus, 2222222 Laplace’s equation is then: 2222222 = 0

Note that is a scalar function.

The general theory of solutions to Laplace’s equation is known as “potential theory.” The solutions of Laplace’s equation are the “harmonic functions.” Laplace’s equation is useful in working with electric, gravitational, and fluid potentials and, in reference to heat conduction, Laplace’s equation becomes the steady-state heat equation.

Choice “c” or Boyle’s equation or Boyle’s Law refers to the properties of gases. It states that the absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies, as longs as the temperature and the amount of gas remain unchanged within a closed system. It is commonly written as:

P1V1 = P2V2

4. The answer is choice “c” or [LI = 3.1; this is a “quick clay”]. LI = (Wn – PL) / (LL – PL)

LI = (Wn – PL) / PI

(1) (2)

The denominator in (2) is the plasticity index (PI). Substituting the numerical values given in our problem: LI = (32 – 15.8) / 5.2 = 3.1

(3)

The “sensitivity” of a clay is related to its liquidity index. A dramatic loss of strength should be expected in flocculated clays where the natural water content is considerably greater than the liquid limit. This is typical of “quick clays” where the fabric can suddenly collapse from a flocculated into a dispersed arrangement, raising pore pressures, overcoming strength and leading to failure.

5. The answer is choice “a” or “The northeast corner of the township.” This is true in the US. In Canada, the numbering is reversed and starts in the southeast corner of the township. (Answer by David M. Abbott, CPG-04570).

36 TPG • Jul.Aug.Sep 2018 www.aipg.org

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