The distribution of deformation bands and their mode of occurrence are key aspects of reservoir appraisal for oil and gas exploration. These structures are mainly formed in high-porosity granular media and affect the petrophysical properties of the whole rock, such as the porosity and permeability, and can act as a barrier to fluid flow [1
The type of deformation bands is known to be related to the stress magnitude evolution [3
] and in particular, to the Q/P ratio, where Q is the differential stress (Q = σ1
) and P is the effective mean stress (here taken as a biaxial parameter, P = (σ1
)/3). In a Q-P plot (Figure 1
), a direct analysis can be made between the stress path and the failure envelopes, whose sizes can vary, depending on the porosity or the grain radius of the rock [13
]. Interestingly, the type of deformation bands can also be related to the band orientation where the stress path intersects the failure envelope; for low Q/P values (0.35 < Q/P < 0.7), the bands are perpendicular or sub-perpendicular to the maximum stress direction and are called Pure Compaction Bands (PCBs) [15
]. For higher Q/P values (>0.7), the bands are oblique to the maximum stress direction, with a lower α angle (Figure 1
B): Such structures are called Shear Enhanced Compaction Bands (SECBs) and can be observed with conjugated orientations [15
]. The conjugated angle (2α Figure 1
B) can change within the SECB domain [16
] and may present a shear component that offsets preexistent structures. The Q/P threshold value separating the two types of bands (i.e., PCBs and SECBs) is not fixed and can depend on the nature of the materials. In the following, we will take a value of Q/P = 0.7 (Figure 1
), which is consistent with the average observation provided by geomechanical experiments conducted on different sandstones [14
In some cases, deformation bands can occur at shallow depths, in unconsolidated to poorly lithified sediments (e.g., [2
]). Most of these shallow band occurrences are explained by the large grain size and porosity of the host rocks, or by the kinematics of the general tectonic setting and the related stress evolution.
Recently, Robert et al. [24
] analyzed cataclastic bands in the calcarenite facies of the Aren formation, formed under a compressive regime and in front of a thrust in the Tremp basin situated in the southern central Pyrenees. The Meso-Cenozoic Tremp basin was formed during the late Cretaceous and Cenozoic. The basin is limited at its northern border by the Sant-Corneli-Boixols fold and thrust belt, which developed during the Pyrenean orogeny [31
]. The Sant-Corneli-Boixols is a fault-propagation fold that emerged above a detachment located within the Triassic evaporites, resulting from an inversion of lower Cretaceous basins [32
]. In front of the fold, syn-tectonic growth-strata developed from the late upper Cretaceous (Campanian) to Paleocene [39
], in which the deformation bands in the Aren formation (Maastrichtian) have been analyzed [24
This article aims to verify the hypothesis proposed by Robert et al. [24
] of a shallow occurrence of these bands, involving both the material properties in each facies and the fold and thrust kinematics, based on geological evidence and confirmed by a magnetic fabric study.
Geomechanical experiments directly conducted on the Aren formation could have been a way to proceed in order to estimate the P* value and an ad hoc failure envelope for the materials involved. Unfortunately, the original porosity of this calcarenite was completely filled with cement, which means the mechanical properties are nowadays very different from those prevailing at the time of the deformation bands’ occurrence, proposed to be directly linked with the Boixols thrust activity. The other method is to precisely estimate the stress path, taking into account the horizontal tectonic shortening during the burial of the formation. This was partly done by Robert et al. [24
] in a 1D approach, without considering either the fold geometry or its kinematic, i.e., we have imposed on a simple lithological column, with a constant density, a horizontal tectonic shortening component in order to reverse the tectonic regime. With this method, the authors proposed a depth that is supposed to be relatively shallow, approximately less than 500 m [24
]. They also proposed associated yield envelopes compatible with the field observations and burial history, with low values (<30 MPa) for the critical pressure P* (intersection between the envelope and the P axis on a Q-P plot) [24
]. Therefore, in this article, we propose to follow the stress evolution more precisely with 2D numerical modelling of the Sant-Corneli-Boixols fold by comparing it with the proposed yield envelopes [24
Many numerical modelling studies on the stress regime evolution and whether the distribution is linked, or not, with a thrust or fold at the basin scale, have been conducted [41
]. Other studies have been made to constrain the distribution of fractures and/or faults to compare the data with field observations, in particular, those related to fold growth [40
]. However, none of these studies have really focused on deformation bands’ occurrence. Finally, only a few studies have dealt with modelling the stress evolution with a finite element during the shortening of a folding layer to show the distribution of deformation and stress [51
], also adding some heterogeneity in different layers of the prototypes [54
In this study, we focused on the stress evolution in front of a growing fold and thrust in direct connection with the thrust activation by using the Limit Analysis Method (LAM). Previously, various studies have already been completed by applying the LAM, but were focused on mechanical conditions to localize and activate faults or thrusts [55
] and not to understand the spatial distribution of the stress field.
The simulation of a fault propagation fold was undertaken to test the hypothesis of shallow deformation bands, as described in front of the Boixols thrust, in the Tremp basin, Spain [24
]. The numerical results mechanically constrain the stress evolution for the fault propagation, allowing us to compare the data with the theoretical stress paths presented in our previous study [24
]. Consequently, this methodology will allow us to predict the occurrence of different types of bands, their distribution, and the chronology within the fold. Although this study is only based on 2D modelling, the aim is to focus on the stress magnitude and evolution through burial and compression. The models, however, do not take into account the problematic issue of the 3D nature of the stress regime, as implied by the formation of deformation bands under a strike-slip regime.
This study complements the previous work by Robert et al. [24
]. This study presents a macro- and micro-analysis of the deformation bands during Boixols thrust and fold growth in order to test the hypothesis of a shallow occurrence of these bands (Tremp basin, Spain) [24
]. Numerical simulations were made using the LAM with OptumG2 software in order to follow the stress evolution and to predict the band distribution through 2D cross sections with an imposed fault-propagation fold kinematic.
Our simulations show that the thrust is guiding the high values of stress, which implies relatively high values of the Q/P ratio (between 0.7 and 1.2) at the back of the fold and ahead of the thrust tip. Below the thrust and far away, in front of the deformed area, this ratio is decreasing to lower values, although close to 0.7.
The stress results were used to determine the deformation bands’ distribution during the fold evolution and the relative burial of syn-tectonic layers that we added to the models. Low values of the Q/P ratios will potentially form Pure Compaction Bands, whereas Shear Enhanced Compaction Bands will occur for higher values of this ratio (higher than 0.7).
We compared these results with known values of mechanical properties of siliciclastic rocks to predict the actual band distribution observed by Robert et al. [24
] and to explain a shallow occurrence of these deformation bands. Using ad hoc yield envelopes proposed for the calcarenite, the first deformation bands would occur at a depth of approximately 450 m, which was the depth proposed in our previous work [24
Finally, we suggested that the calcarenite mechanical properties do not follow the same trend as sandstones and carbonates with respect to the relationship between critical pressure, porosity, and grain size. We propose, in a diagram that relates P* to porosity times grain size [13
], that the calcarenite follows an intermediate trend, with an estimated slope of −0.68, similar to the results obtained for carbonate rocks, although with a slight shift towards higher values of P*. This still needs to be confirmed by geomechanical experiments on similar facies of high-porosity rocks with a heterogeneous composition.
The protocol we used in this study can be reused for other geological settings, or for different types of rock, to predict the damage state of a reservoir from the knowledge of the kinematic and the rock facies. Here, we chose to check the hypothesis for strike-slip structures, but other studies can be conducted on the thrust fault regime to increase the accuracy for the 2D issue.