Scales of columnar jointing in igneous rocks: field measurements and controlling factors

Abstract

Columnar jointing is a common feature of solidified lavas, sills and dikes, but the factors controlling the characteristic stoutness of columns remain debated, and quantitative field observations are few in number. In this paper, we provide quantitative measurements on sizing of columnar joint sets and our assessment of the principal factors controlling it. We focus on (1) chemistry, as it is the major determinant of the physical (mechanical and thermal) properties of the lava, and (2) geology, as it influences the style of emplacement and lava geometry, setting boundary conditions for the cooling process and the rate of heat loss. In our analysis, we cover lavas with a broad range of chemical compositions (from basanite to phonolite, for six of which we provide new geochemical analyses) and of geological settings. Our field measurements cover 50 columnar jointing sites in three countries. We provide reliable, manually digitized data on the size of individual columns and focus the mathematical analysis on their geometry (23,889 data on side length, of which 17,312 are from full column sections and 3,033 data on cross-sectional area and order of polygonality). The geometrical observations show that the variation in characteristic size of columns between different sites exceeds one order of magnitude (side length ranging from 8 to 338 cm) and that the column-bounding polygons’ average order is less than 6. The network of fractures is found to be longer than required by a minimum-energy hexagonal configuration, indicating a non-equilibrium, geologically quick process. In terms of the development and characteristic sizing of columnar joint sets, our observations suggest that columns are the result of an interplay between the geological setting of emplacement and magma chemistry. When the geological setting constrains the geometry of the emplaced body, it exerts a stronger control on characteristic column stoutness. At unconstrained geometries (e.g. unconfined lava flows), chemistry plays the major role, resulting in stouter columns in felsic lavas and slenderer columns in mafic lavas.

Appendix: Comparable cooling regimes for intrusive and extrusive cases: an equivalent thickness ratio

With the objective of comparing the thickness of a simple intrusive (dyke) and extrusive (flow) igneous body having the same cooling regime, we make the following assumptions:

• We place ourselves in a 1D problem along the y-axis (parallel to the temperature gradient).

• Host rock and magma have the same thermal diffusivity κ that does not vary with temperature T.

• The host rock temperature is initially set at 0°C (no preheating of the rock by previous lava).

• There is no latent heat of crystallisation due to solidification.

• The magma is suddenly emplaced at temperature T ₀, both in the intrusive and the extrusive case.

For an intrusion of thickness d _i located between −d _i/2 < y < d _i/2 and cooling to both sides (country rock in |y| > d _i/2), the temperature evolution as a function of depth y and time t is given by Carslaw and Jaeger (1959, p. 54):

$$ T\left( {y,t} \right) = \frac{1}{2}{T_0}\left[ {{\text{erf}}\left( {\frac{{\frac{{{d_{\text{i}}}}}{2} - y}}{{2\sqrt {{\kappa t}} }}} \right) + {\text{erf}}\left( {\frac{{\frac{{{d_{\text{i}}}}}{2} + y}}{{2\sqrt {{\kappa t}} }}} \right)} \right] $$

(4)

In the extrusive case, the upper surface of the magma is maintained at 0°C (infinite heat transfer to the air). The lava flow of thickness d _e is located in the region 0 < y < d _e and cools to the host rock located y > d _e. With these boundary conditions, the temperature evolution is given by Carslaw and Jaeger (1959, p. 62):

$$ T\left( {y,t} \right) = \frac{1}{2}{T_0}\left[ {2{\text{erf}}\left( {\frac{y}{{2\sqrt {{\kappa t}} }}} \right) - {\text{erf}}\left( {\frac{{y - {d_{\text{e}}}}}{{2\sqrt {{\kappa t}} }}} \right) - {\text{erf}}\left( {\frac{{y + {d_{\text{e}}}}}{{2\sqrt {{\kappa t}} }}} \right)} \right] $$

(5)

With a change of variable from t to τ = κ · t/d ² and the notation y* = y/d (where d is, respectively, d _i and d _e for the above cases), the above equations can be written as

$$ {\Theta_{\text{i}}}\left( {{y^{ \star }},\tau } \right) = \frac{{T\left( {\frac{y}{{{d_{\text{i}}}}},\tau } \right)}}{{{T_0}}} = \frac{1}{2}\left[ {{\text{erf}}\left( {\frac{{\frac{1}{2} - {y^{ \star }}}}{{2{\tau^{{\frac{1}{2}}}}}}} \right) + {\text{erf}}\left( {\frac{{\frac{1}{2} + {y^{ \star }}}}{{2{\tau^{{\frac{1}{2}}}}}}} \right)} \right] $$

(6)

and

$$ {\Theta_{\text{e}}}\left( {{y^{ \star }},\tau } \right) = \frac{{T\left( {\frac{y}{{{d_{\text{e}}}}},\tau } \right)}}{{{T_0}}} = \frac{1}{2}\left[ {{\text{2erf}}\left( {\frac{{{y^{ \star }}}}{{2{\tau^{{\frac{1}{2}}}}}}} \right) - {\text{erf}}\left( {\frac{{{y^{ \star }} - 1}}{{2{\tau^{{\frac{1}{2}}}}}}} \right) - {\text{erf}}\left( {\frac{{{y^{ \star }} + 1}}{{2{\tau^{{\frac{1}{2}}}}}}} \right)} \right] $$

(7)

We then define the remaining heat as the ratio between mean temperature of the emplaced lava body and the initial temperature T ₀. This leads for the intrusive case to

$$ {E_{\text{i}}}\left( \tau \right) = \int_{{ - 0.5}}^{{0.5}} {{\Theta_{\text{i}}}\left( {{y^{ \star }},\tau } \right){\rm d} {y^{ \star }}} $$

(8)

and for the extrusive case to

$$ {E_{\text{e}}}\left( \tau \right) = \int_0^1 {{\Theta_{\text{e}}}\left( {{y^{ \star }},\tau } \right){\rm d} {y^{ \star }}} $$

(9)

We numerically integrate Eqs. 8 and 9 and investigate for a given percentage of remaining heat ∈ the ratio of extrusive thickness d _e to intrusive thickness d _i for which the cooling rate is the same in both magmas bodies at time t:

$$ {E_{\text{i}}}\left( {{\tau_{\text{i}}}} \right) = \in = {E_{\text{e}}}\left( {{\tau_{\text{e}}}} \right), $$

(10)

$$ {E_{\text{i}}}\left( {t\frac{\kappa }{{{d_{\text{i}}}{{\left( { \in, t} \right)}^2}}}} \right) = {E_{\text{e}}}\left( {t\frac{\kappa }{{{d_{\text{e}}}{{\left( { \in, t} \right)}^2}}}} \right) $$

(11)

The result is shown in Fig. 12. We can first see that an extrusion is always required to be thicker than an intrusion cooling at the same rate, whatever the amount of remaining heat in the lava, because a lava flow always cools faster than an intrusive magma body. Second, the smaller the remaining heat in the lava, the higher extrusive/intrusive thickness ratio is required (the more rapid the cooling of a flow compared to a dyke).

Fig. 12

Thickness ratio of igneous bodies having the same cooling rate, as a function of the remaining heat within the body. See text for details

As the temperature at emplacement T ₀ is near or below the liquidus (in the order of 1,000–1,200°C) and jointing occurs near the glass transition temperature T _G (in the order of 650–950°C with the rock compositions in this paper and using the model by Giordano et al. (2008)), the remaining heat exceeds 50% at that emplacement when jointing takes place. Therefore, when comparing extrusive and intrusive bodies having the same cooling rate, a realistic number with which one should divide the thickness of a dyke (sill) to compare it to that of a free flow is 1.5.