Stress modelling of magma storage zones and its implications for rapid kimberlitic magma ascent

Rapid ascent of low viscous kimberlitic magmas is reflected from the presence of meta-stable diamond phenocrysts. Existing models suggest that high velocity magma ascent takes place as a mechanical coupling interaction between the CO2-rich volatile phase originating from the magma and the hydraulic fracture (Type-I). However, for such fracturing to occur at a depth of ~200 km, the system need to have a huge tensile stress to overcome the lithostatic pressure (~60 Kb) and the tensile strength of the rocks (0.4 - 0.5 Kb). The objective of the present work is to present a mechanical model and show the specific conditions in which the magma storage zone (MSZ) can build up such large tensile stresses to cause fracturing for magma ascent. Finite Element (FE) method was employed to map the stress field in the mantle rock around a magma chamber. MSZ was modeled as a semi-elliptical zone at bottom of the model of 150 km depth and 300 km width. Two types of FE modelling was performed considering two factors: (1) density contrast (Δρ) between magma and ambient mantle, and (2) shape (Ar: ratio of vertical and horizontal dimensions) of the MSZ. Figure 1 show the Δρ contrasts required for tensile fracturing to occur at the MSZ tip for different values of their Ar. Results reveal a distinct zone of maximum tensile stresses in the neighborhood of the MSZ, suggesting the potential locations of tensile fracturing. It shows that the tensile stress magnitude decreases exponentially away from the MSZ top vertically. The results illustrate a nonlinear relation of stress with increasing Δρ (Figure 1). We show that for models with Ar >1 there is a localization of tensile stress at the MSZ tip, and for the models with Ar << 1 it diffuse along the boundary (Figure 2). We also show that for a particular Δρ, tensile stress increases for increasing Ar. The results indicate that MSZ with large Ar are more potential for tensile fracturing to occur at their vertices. Considering the tensile strength of mantle in the order of 0.5 Kb, this study presents the conditions of tensile rupturing for kimberlite magma ascent in an Ar versus Δρ space. Figure 1. Variations of effective maximum tensile stress with density contrast Δρ for different shapes of MSZ. Figure 2: Patterns of tensile stress localization in the neighbourhood of MSZ with varying shapes. (a) Ar = 2 and (b) Ar = 0.9.