More complex numerical models explore how such cavity sources may eventually develop into anelastic processes and subsidence32. Geomechanical models of the subsidence process have been developed to compare the InSAR subsidence along a 2D transect crossing the surface projection of salt cavities M30 and M31 (Figs. 1a and 3a), which are located inside the residential area of Pinheiro. Two independent injection pressure scenarios (S1 and S2) were used to test the different geomechanical stages of the cavity evolution, surrounding crack propagation, stress development, and induced surface displacement that occur under different initial conditions. The first scenario (S1) considers a higher cavity pressure compared to the surrounding soil and simulates mining conditions. The working pressure usually stabilizes the salt cavities during dissolution mining. The second scenario (S2) considers a hypothetical lower cavity pressure, caused by depressurization and aim to simulate inactive mining conditions 25.
In this study, we investigated the ongoing geological instabilities in Maceió by integrating multi-temporal InSAR analysis with source modelling using elastic inversion and the distinct element method. The main outcomes from our results are that the subsidence in Maceió (1) started to gradually evolve almost two decades ago with slow acceleration at the beginning and faster acceleration in the last 4 years; (2) reached a maximum cumulative value close to the lagoon coast of approximately 2 m at the end of 2020; (3) is attributable to a depth source between 600 to 1000 m that coincides with the salt cavity locations; (4) both active/pressurized and inactive/depressurized salt mining conditions led to mechanical instability of the cavities with local upward migration and likely partial to total cavity collapses; and (5) developed from the deforming cavities cracks propagated upward towards the shallower layers.
We performed 2D distinct element modelling (DEM) with PFC2D V5 software from Itasca. The DEM simulates the material as an assemblage of discrete and rigid particles of different radii and geomechanical parameters36. The particles are bonded together using the so-called soft-contact approach, which allows them to rotate and overlap at contact points, simulating mechanical interaction. For a proper representation of the matrix between grains, the parallel-bond scheme was used, which allows the simulation of shear and tensile crack formation and block rotations37. Based on the available stratigraphic information, we set up the configuration of the material layers and properties (supplementary Fig. S4). Detailed parameters of the simulated geologic materials and parameters as well as geometries are given in supplementary Tables S2 and S3. We installed the two cavities by deleting the particles at a specific depth and according to the size detected by the sonar measurements. The two cavities had centre point depths of 1010 m and 1070 m and sizes of approximately 14,100 m3 and 31,400 m3 for M30 and M31, respectively. Instantaneous particle deletion was followed by the setting of temporarily high bond strengths to avoid dynamic effects. To simulate the geomechanical behaviour of the subsurface, two independent scenarios, pressurized conditions (S1) and depressurized conditions (S2), were used. For S1, a pressure of 2.758 MPa, equivalent to the reported salt-mining pressure in this area, was initially injected into the cavity walls, which was simulated as explicit radial forces onto the inner rim particles. The modelling was redone with different initial conditions, including a lower pressure of 1.5 MPa and reproducing possible mining depressurized/inactive conditions. Different aspects should be considered in terms of uncertainty. First, it is important to highlight that the geomechanical model that was performed is a 2D model along a transect. The disk-shaped particles contain a third particle dimension of size one, which is added for correct calculations. Therefore, it might overestimate the instability due to missing bonds in the third dimension, and it is not possible to compare the volume changes directly with those retrieved in the 3D geophysical source inversion. Second, the model resolution (model size vs. particle radii) and bulk rock parameter calibration contain another uncertainty in particle-based simulations37. However, extensive experience with similar simulation setups has recently been achieved, and particle scale parameters have been adjusted by applying findings from available simulated compression and tension tests32,38 on material samples used in this study (consolidated rock, unconsolidated rock, and halite).
Third, DEM models have an intrinsic uncertainty due to random particle packing, a feature also observable in natural geologic depositional environments. Therefore, a repetition of four models per scenario was performed with different random particle assemblies. The resulting error margin in the subsidence calculation for the total collapse of both cavities (scenario S2) is plotted in supplementary Fig. S4b. The error is low at the margins of the 2D transect and higher with values up to approximately 50 cm in the part most affected by deformation. Due to the discontinuous nature of the model, each random assembly produces also different structures in the subsurface and at the surface. An even larger number of model generations would decrease the error. We restricted the detailed stress and crack analysis to a representative model for each scenario and have shown that the subsidence determined by InSAR is within the range of the simulated subsidence, even close to the mean of all assemblies. 1e1e36bf2d