Equivalent Surface Tractions Research Articles

Three-Dimensional Site Response Analysis of Clay Soil Considering the Effects of Soil Behavior and Type

To understand changes in bedrock motion at the ground surface, frequency effects, and spatial distribution within the soil, it is important to look at how a site responds to earthquakes. This is important for soil–structure interaction in structural and geotechnical earthquake engineering. This study deals with the effect of classifying clays according to shear wave velocity (stiff/medium/soft) and nonlinearity in behavior (linear/nonlinear) on the analysis of the site response. A 3D soil model with a combination of free fields and quiet boundaries and advanced constitutive models for soil to obtain accurate results was used to conduct this study. A strong TABAS earthquake was used to excite the compliant base of the model after converting the velocity record of TABAS to an equivalent surface traction force using a horizontal force–time history proportional to the velocity–time history. This study reveals that the site response analysis is affected by the type of clay soil and the soil material behavior, with soft clay soil causing higher PGV and PGV values in the linear case and lower values in the nonlinear case due to soil yielding, which causes soil response attenuation. This results in extremely conservative and expensive building designs when linear soil behavior is adopted. On the other hand, the applied earthquake exhibits greater attenuation at longer frequencies and greater amplification at mid and short frequencies. However, at frequencies near the applied earthquake frequency, neither attenuation nor amplification occurs. Furthermore, nonlinear soil behavior is crucial for soil evaluation and foundation design due to higher octahedral shear strain and settlement values, especially in softer soils, resulting from extensive plastic deformation.

Fast Approximate Quantification of Endovascular Stent Graft Displacement Forces in the Bovine Aortic Arch Variant

Purpose: Displacement forces ( DF s) identify hostile landing zones for stent graft deployment in thoracic endovascular aortic repair (TEVAR). However, their use in TEVAR planning is hampered by the need for time-expensive computational fluid dynamics (CFD). We propose a novel fast-approximate computation of DF s merely exploiting aortic arch anatomy, as derived from the computed tomography (CT) and a measure of central aortic pressure. Materials and Methods: We tested the fast-approximate approach against CFD gold-standard in 34 subjects with the “bovine” aortic arch variant. For each dataset, a 3-dimensional (3D) model of the aortic arch lumen was reconstructed from computed tomography angiography and CFD then employed to compute DF s within the aortic proximal landing zones. To quantify fast-approximate DF s, the wall shear stress contribution to the DF was neglected and blood pressure space-distribution was averaged on the entire aortic wall to reliably approximate the patient-specific central blood pressure. Also, DF values were normalized on the corresponding proximal landing zone area to obtain the equivalent surface traction ( EST ). Results: Fast-approximate approach consistently reflected (r2=0.99, p<0.0001) the DF pattern obtained by CFD, with a −1.1% and 0.7° bias in DF s magnitude and orientation, respectively. The normalized EST progressively increased (p<0.0001) from zone 0 to zone 3 regardless of the type of arch, with proximal landing zone 3 showing significantly greater forces than zone 2 (p<0.0001). Upon DF normalization to the corresponding aortic surface, fast-approximate EST was decoupled in blood pressure and a dimensionless shape vector (S) reflecting aortic arch morphology. S showed a zone-specific pattern of orientation and proved a valid biomechanical blueprint of DF impact on the thoracic aortic wall. Conclusion: Requiring only a few seconds and quantifying clinically relevant biomechanical parameters of proximal landing zones for arch TEVAR, our method suits the real preoperative decision-making process. It paves the way toward analyzing large population of patients and hence to define threshold values for a future patient-specific preoperative TEVAR planning.

Computational Fluid Dynamics Modeling of Proximal Landing Zones for Thoracic Endovascular Aortic Repair in the Bovine Arch Variant

To assess the endograft displacement forces (DF), which quantify the forces exerted by the pulsatile blood flow on the vessel wall and transmitted on the terminal fixation site of the endograft after its deployment in proximal landing zones (PLZs) of the bovine aortic arch variant. Thirty healthy aortic computed tomographic angiographies of subjects with bovine arch configuration (10 per type of arch, I-III) were selected for the purpose of the study. A 3-dimensional model of the aortic arch lumen was reconstructed. Computational fluid dynamics modeling was then used to compute DF magnitude and orientation (i.e., x, y, and z axes) in PLZs of each case. DF values were normalized to the corresponding aortic wall area to estimate equivalent surface traction (EST). DF were highest in zone 0, consistently with the greater surface area. DF in zone 3 were much greater than in zone 2 because of a 3-fold greater upward component (z axis) (P<0.001), being therefore mainly oriented orthogonally to the aortic blood flow and to the vessel longitudinal axis in that zone. EST progressively increased from zone 0 toward more distal PLZs, with EST in zone 3 being much greater than that in zone 2 (P<0.001). The same pattern was observed after stratification by type of arch. The bovine arch is associated with a consistent fluid dynamic pattern, which identifies in zone 3 an unfavorable biomechanical environment for endograft deployment.

Impact of Aortic Tortuosity on Displacement Forces in Descending Thoracic Aortic Aneurysms

As elastin fibres in the aorta deteriorate with age, the descending thoracic aorta (DTA) becomes longer and more tortuous. In patients with DTA aneurysms, this increased tortuosity may result in a hostile haemodynamic environment for thoracic endovascular aortic repair (TEVAR). The objective of this study was to analyse how increased tortuosity affects haemodynamic displacement forces (DFs) in different segments of the DTA in patients with DTA aneurysms (DTAAs). Thirty patients with DTAAs were selected to form three equal groups based on the maximum tortuosity of their DTA: low < 30°, moderate 30°-60°, and high > 60°. Computational fluid dynamics simulations were performed to calculate DFs in all patients. Image based segmentations were carried out to create patient specific models of the aortic geometry. When physiological simulation results were obtained, the haemodynamic DFs on the aortic wall were calculated in four segments of the DTA (zones 4A - D). To enable comparison of DFs in different segments, the DF was normalised by the aortic wall surface area, the equivalent surface traction (EST). The mean age was 73 years, with 67% male. In zone 4C, where most tortuosity occurs, the EST in patients with high tortuosity was more than three times higher, than those with low tortuosity (low, 743N/m2; moderate, 956N/m2; high, 2294N/m2; p=.004). These differences could be attributed to the higher sideways components of the DF vectors, which were more than two times greater in patients with high tortuosity than in patients with low or moderate tortuosity (low, 5.01N; moderate, 5.50N; high, 13.21N; p=.009). High tortuosity results in increased displacement forces in the distal segments of the DTA. These forces should be taken into account when planning for TEVAR, as potentially they increase the risk of stent graft related complications, such as migration and endoleak.

The Modified Arch Landing Areas Nomenclature identifies hostile zones for endograft deployment: a confirmatory biomechanical study in patients treated by thoracic endovascular aortic repair†.

Our goal was to confirm whether the Modified Arch Landing Areas Nomenclature (MALAN) for thoracic endovascular aortic repair, in which each landing area is described by indicating both the proximal landing zone (PLZ) and the type of arch (e.g. 0/I), identifies unfavourable landing zones for endograft deployment in diseased aortas. Preoperative computed tomography angiography scans of 10 patients scheduled for thoracic endovascular aortic repair for aneurysm or penetrating ulcer of the arch and with a potential hostile PLZ were reviewed. Five had proximal deployment planned in MALAN area 3/III and 5, in MALAN area 2/III. The angulation of each PLZ was calculated. Computational fluid dynamics modelling was used to compute magnitude and orientation of pulsatile displacement forces in each PLZ. Normalized values based on PLZ areas (i.e. equivalent surface traction) were calculated. Results were compared to those obtained in healthy controls stratified by the MALAN. Angulation was severe (>60°) in MALAN areas 3/III and 2/III, which was consistent with the findings obtained in healthy controls. Increased magnitude (P = 0.021) and unfavourable orientation (i.e. orthogonal to the longitudinal aortic axis) of equivalent surface traction (P = 0.011) was also found in these areas compared to the adjacent ones, following the same pattern seen in the controls. Adverse events related to proximal endograft performance were reported in 3/10 cases. This study confirms in diseased aortas initial proof-of-concept findings on the predictive value of the MALAN to identify landing areas with a geometric and haemodynamic environment hostile for thoracic endovascular aortic repair. These adverse biomechanical features may entail an increased risk of dismal endograft performance.

The Modified Arch Landing Areas Nomenclature (MALAN) Improves Prediction of Stent Graft Displacement Forces: Proof of Concept by Computational Fluid Dynamics Modelling

To assess whether the Modified Arch Landing Areas Nomenclature (MALAN), which merges Ishimaru's map with the Aortic Arch Classification, predicts the magnitude of displacement forces and their orientation in proximal landing zones for TEVAR. Computational fluid dynamic (CFD) modelling was employed to prove the hypothesis. Healthy aorta CT angiography scans were selected based on aortic arch geometry to reflect Types I to III arches equally (each n=5). CFDs were used to compute pulsatile displacement forces along the Ishimaru's landing zones in each aorta including their three dimensional orientation along the upward component and sideways component. Values were normalised to the corresponding aortic wall area to calculate equivalent surface traction (EST). In Types I and II arches, EST did not change across proximal landing zones (p=.297 and p=.054, respectively), whereas in Type III, EST increased towards more distal landing zones (p=.019). Comparison of EST between adjacent zones, however, showed that EST was greater in 3/II than in 2/II (p=.016), and in 3/III than in 2/III (p=.016). Notably, these differences were related to the upward component, that was four times greater in 3/II compared with 2/II (p<.001), and five times greater in 3/III compared with 2/III (p<.001). CFD modelling suggests that MALAN improves discrimination of expected displacement forces in proximal landing zones for TEVAR, which might influence clinical outcomes. The clinical relevance of the finding, however, remains to be validated in a dedicated post-operative outcome analysis of patients treated by TEVAR of the arch.

Three-dimensional models of elastostatic deformation in heterogeneous media, with applications to the Eastern California Shear Zone

SUMMARY We present a semi-analytic iterative procedure for evaluating the 3-D deformation due to faults in an arbitrarily heterogeneous elastic half-space. Spatially variable elastic properties are modelled with equivalent body forces and equivalent surface traction in a ‘homogenized’ elastic medium. The displacement field is obtained in the Fourier domain using a semi-analytic Green function. We apply this model to investigate the response of 3-D compliant zones (CZ) around major crustal faults to coseismic stressing by nearby earthquakes. We constrain the two elastic moduli, as well as the geometry of the fault zones by comparing the model predictions to Synthetic Aperture Radar inferferometric (InSAR) data. Our results confirm that the CZ models for the Rodman, Calico and Pinto Mountain faults in the Eastern California Shear Zone (ECSZ) can explain the coseismic InSAR data from both the Landers and the Hector Mine earthquakes. For the Pinto Mountain fault zone, InSAR data suggest a 50 per cent reduction in effective shear modulus and no significant change in Poisson's ratio compared to the ambient crust. The large wavelength of coseismic line-of-sight displacements around the Pinto Mountain fault requires a fairly wide (∼1.9 km) CZ extending to a depth of at least 9 km. Best fit for the Calico CZ, north of Galway Dry Lake, is obtained for a 4 km deep structure, with a 60 per cent reduction in shear modulus, with no change in Poisson's ratio. We find that the required effective rigidity of the Calico fault zone south of Galway Dry Lake is not as low as that of the northern segment, suggesting along-strike variations of effective elastic moduli within the same fault zone. The ECSZ InSAR data is best explained by CZ models with reduction in both shear and bulk moduli. These observations suggest pervasive and widespread damage around active crustal faults.

The Stress Field Produced by Localized Plastic Slip at a Free Surface

Uniform plastic slip is assumed to occur in a cubic region embedded at the free surface of a semi-infinite elastic solid. The slip plane and slip direction are both inclined at 45 deg to the free surface and to two opposite interior faces of the cube. The stress field produced by the slip is the same as that produced by equivalent uniform tractions acting on the faces of the cube. Closed-form solutions are obtained for all stress components by employing Papkovitch functions to calculate the effects of the equivalent surface tractions. Calculated numerical results for the distribution of stress components are shown graphically. Certain stress components are found to be discontinuous across the boundary surface of the region of plastic slip.