Investigating the kinematics of the unstable slope of Barberà de la Conca (Catalonia, Spain) and the effects on the exposed facilities by GBSAR and multi-source conventional monitoring

Abstract

The paper presents a multi-source approach tailored for the analysis of ground movements affecting the village of Barberà de la Conca (Tarragona, Catalonia, Spain), where cracks on the ground and damage of different severity to structures and infrastructure was recorded. For this purpose, monitoring of ground displacements performed by topographic survey, geotechnical monitoring and remote sensing techniques (ground-based synthetic aperture radar, GBSAR) are combined with multi-temporal damage surveys and monitoring of cracks (crackmeters) to get an insight into the kinematics of the urban slope. The obtained results highlight the correspondence between the monitoring data and the effects on the exposed facilities induced by ground displacements, which seem to occur predominantly in the horizontal plane with diverging directions (northward and southward) from the main ground fracture crossing the centre of the village. The case study stands as a further contribution to fostering this kind of integrated approaches that via cross-validations can improve data reliability as well as enrich datasets for slope instability recognition and analysis, which are crucial to plan risk mitigation works.

Appendix

Hereafter, the projection of 3D topographic displacement data along the GBSAR line of sight (LOS) is briefly described. The reader can refer to Fig. 6c.

Considering east (E), north (N) and height (H) of GBSAR position (POS) coordinates:

$$ {POS}_{\left(E,N,\kern0.5em H\right) GBSAR}=\left\{{E}_{POS},{N}_{POS},{H}_{POS}\right\} $$

(1)

and east (E), north (N) and height (H) of the i-th topographic point (P) coordinates:

$$ {P}_{\left(E,N,H\right) topographic}=\left\{{E}_P,{N}_P,{H}_P\right\} $$

(2)

obtained as difference, in each direction, between the final and initial position of the considered topographic point [E_P = E_{P, f} − E_{P, i}; N_P = N_{P, f} − N_{P, i}; H_P = H_{P, f} − H_{P, i}], the projection of displacement vector of the topographic point ${\overline{S}}_P=\left\{{S}_E,{S}_N,{S}_H\right\}$ along the GBSAR LOS direction ${\overline{S}}_{P\_ LOS}$, can be evaluated according to Eq. 3

$$ {\overline{S}}_{P\_ LOS}={\overline{s}}_P\times {\overline{LOS}}_{vers}=\left({S}_E\times {E}_{vers}\right)+\left({S}_N\times {N}_{vers}\right)+\left({S}_H\times {H}_{vers}\right) $$

(3)

where the east (E), north (N) and high (H) component of Line of Sight versor ${\overline{LOS}}_{vers}=\left\{{E}_{vers},{N}_{vers},{H}_{vers}\right\}$ are derived using the Line of Sight versor equation (Eq.4):

$$ {\overline{LOS}}_{VERS}=\frac{\overline{LOS}}{\left\Vert \overline{LOS}\right\Vert }=\frac{\left\{{E}_{LOS},{N}_{LOS},{H}_{LOS}\right\}}{\sqrt{{E_{LOS}}^2+{N_{LOS}}^2+{H_{LOS}}^2}} $$

(4)

in which the Line of Sight vector components $\overline{LOS}=\left\{{E}_{LOS},{N}_{LOS},{H}_{LOS}\right\}$ are evaluated using the Line of Sight equation (Eq.5):

$$ \overline{LOS}=\left({E}_P-{E}_{POS}\right)\ast \hat{i}+\left({N}_P-{N}_{POS}\right)\ast \hat{j}+\left({H}_P-{H}_{POS}\right)\ast \hat{k} $$

(5)