Characteristics of horizontal ground motion measures along principal directions

Ground motion records are often used to develop ground motion prediction equations （GMPEs） for a randomly oriented horizontal component, and to assess the principal directions of ground motions based on the Arias intensity tensor or the orientation of the major response axis. The former is needed for seismic hazard assessment, whereas the latter can be important for assessing structural responses under multi-directional excitations. However, a comprehensive investigation of the pseudo-spectral acceleration （PSA） and of GMPEs conditioned on different axes is currently lacking. This study investigates the principal directions of strong ground motions and their relation to the orientation of the major response axis, statistics of the PSA along the principal directions on the horizontal plane, and correlation of the PSA along the principal directions on the horizontal plane. For these, three sets of strong ground motion records, including intraplate California earthquakes, inslab Mexican earthquakes, and interface Mexican earthquakes, are used. The results indicate that one of the principal directions could be considered as quasi-vertical. By focusing on seismic excitations on the horizontal plane, the statistics of the angles between the major response axis and the major principal axis are obtained; GMPEs along the principal axes are provided and compared with those obtained for a randomly oriented horizontal component; and statistical analysis of residuals associated with GMPEs along the principal directions is carried out.

Implications for identification of principal stress directions from acoustic emission characteristics of granite under biaxial compression experiments

The rock fracture characteristics and principal stress directions are crucial for prevention of geological disasters.In this study,we carried out biaxial compression tests on cubic granite samples of 100 mm in side length with different intermediate principal stress gradients in combination with acoustic emission(AE)technique.Results show that the fracture characteristics of granite samples change from‘sudden and aggregated’to‘continuous and dispersed’with the increase of the intermediate principal stress.The effect of increasing intermediate principal stress on AE amplitude is not significant,but it increases the proportions of high-frequency AE signals and shear cracks,which in turn increases the possibility of unstable rock failure.The difference of stress in different directions causes the anisotropy of rock fracture and thus leads to the obvious anisotropic characteristics of wave velocity variations.The anisotropy of wave velocity variations with stress difference is probable to identify the principal stress directions.The AE characteristics and the anisotropy of wave velocity variations of granite under two-dimensional stress are not only beneficial complements for rock fracture characteristic and principal stress direction identification,but also can provide a new analysis method for stability monitoring in practical rock engineering.

Three-dimensional stress variation characteristics in deep hard rock of CJPL-Ⅱ project based on in-situ monitoring

In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.

Implications for rock instability precursors and principal stress direction from rock acoustic experiments

The characteristics of rock instability precursors and the principal stress direction are very crucial for the prevention of geological disasters.This study investigated the qualitative relationship between rock instability precursors and principal stress direction through wave velocity in rock acoustic emission(AE)experiments.Results show that the wave velocity variation exhibits obvious anisotropic characteristics in 0%–20%and 60%–90%of peak strength due to the differences of stress-induced microcrack types.The amplitude of wave velocity variation is related to the azimuth and position of wave propagation path,which indicates that the principal stress direction can be identified by the anisotropic characteristics of wave velocity variations.Furthermore,the experiments also demonstrate that the AE event rate and wave velocity show quiet and stable variations in the elastic stage of rock samples,while they present a trend of active and unstable variations in the plastic stage.It implies that both the AE event rate and wave velocity are effective monitoring parameters for rock instability.The anisotropic characteristics of the wave velocity variation and AE event rate are beneficial complements for identifying the rock instability precursors and determining the principal stress direction,which provides a new analysis method for stability monitoring in practical rock engineering.

Influence of maximum principal stress direction on the failure process and characteristics of D-shaped tunnels

To investigate the failure process and characteristics of D-shaped tunnels under different maximum principal stress directions θ, true-triaxial tests were conducted on cubic sandstone samples with a through D-shaped hole. The test results show that the failure process can be divided into 4 periods:calm, buckling deformation, gradual buckling and exfoliation of rock fragment, and formation of a Vshaped notch. With an increase in θ from 0° to 90°, the size of the rock fragments first decreases and then increases, whereas the fractal dimension of the rock fragments first increases and then decreases. Meanwhile, the failure position at the left side shifts from the sidewall to the corner and finally to the floor, whereas the failure position at the right side moves from the sidewall to the spandrel and finally to the roof, which is consistent with the failure position in underground engineering. In addition, the initial vertical failure stress first decreases and then increases. By comparing the results,the failure severities at different maximum principal stress directions can be ranked from high to low in the following order: 90°>60°>30°>45°>0°.

Cyclic behavior of reinforced sand under principal stress rotation

Although the cyclic rotation of the principal stress direction is important,its effect on the deformation behavior and dynamic properties of the reinforced soil has not been reported to date.Tests carried out on large-scale hollow cylinder samples reveal that the cyclic rotation of the principal stress direction results in significant variations of strain components(ε,ε,εand γ) with periodic characteristics despite the deviatoric stress being constant during tests.This oscillation can be related to the corresponding variations in the stress components and the anisotropic fabric that rotate continuously along the principal stress direction.Sand under rotation appears to develop a plastic strain.Similar trends are observed for reinforced sand,but the shear interaction,the interlocking between particles and reinforcement layer,and the confinement result in significant reductions in the induced strains and associated irrecoverable plastic strains.Most of the strains occur in the first cycle,and as the number of cycles increases,the presence of strains becomes very small,which is almost insignificant.This indicates that the soil has reached anisotropic critical state(ACS),where a stable structure is formed after continuous orientation,realignment and rearrangement of the particles accompanied with increasing cyclic rotation.Rotation in the range of 60°-135° produces more induced strains even in the presence of the reinforcement,when compared with other ranges.This relates to the extension mode of the test in this range in which σ>σand to the relative approach between the mobilized plane and the weakest horizontal plane.Reinforcement results in an increase in shear modulus while it appears to have no effect on the damping ratio.Continuous cycles of rotation result in an increase in shear modulus and lower damping ratio due to the densification that causes a decrease in shear strain and less dissipation of energy.

Pore Water Pressure Buildup Under Cyclic Rotation of Principal Stress and Stability Evaluation of Seabed Deposit

The cyclic rotation of principal stress direction with a constant amplitude is the characteristics of cyclic stress in seabed deposit induced by travelling waves. Presented in the paper are the results obtained from tests simulating the cyclic stress characteristics, with emphasis laid on the buildup of pore water pressure in soil samples. Regression analysis of test data shows that the pore water pressure can be expressed as the function of the number of cycles of cyclic loading, or as the function of generalized shear strain. Using the results thus obtained, the possibility of failure of seabed deposit under cyclic loading induced by travelling waves can be evaluated. The comparison with the results of conventional cyclic torsional shear tests shows that neglect of the effect of the cyclic rotation of the principal stress direction will result in considerable over-estimation of the stability of seabed deposit.

Stress Path Analysis of Deep-Sea Sediments Under the Compression-Shear Coupling Load of Crawler Collectors

The mechanical properties of deep-sea sediments during the driving process of crawler collectors are essential factors in the design of mining systems.In this study,a crawler load is divided into a normal compression load and a horizontal shear load.Then,the internal stress state of sedimentary soil is examined through a theoretical calculation and finite element numerical simulation.Finally,the driving of crawlers is simulated by changing the relative spatial position between the load and stress unit,obtaining the stress path of the soil unit.Based on the calculation results,the effect of the horizontal shear load on the soil stress response is analyzed at different depths,and the spatial variation law of the soil stress path is examined.The results demonstrate that the horizontal shear load has a significant effect on the rotation of the principal stress,and the reverse rotation of the principal stress axis becomes obvious with the increase in the burial depth.The stress path curve of the soil is different at various depths.The spatial variation rule of the stress path of the shallow soil is complex,whereas the stress path curve of the deep soil tends to shrink as the depth increases.The stress path of the corresponding depth should be selected according to the actual research purpose and applied to the laboratory test.

Real-time Visual Odometry Estimation Based on Principal Direction Detection on Ceiling Vision

In this paper,we present a novel algorithm for odometry estimation based on ceiling vision.The main contribution of this algorithm is the introduction of principal direction detection that can greatly reduce error accumulation problem in most visual odometry estimation approaches.The principal direction is defned based on the fact that our ceiling is flled with artifcial vertical and horizontal lines which can be used as reference for the current robot s heading direction.The proposed approach can be operated in real-time and it performs well even with camera s disturbance.A moving low-cost RGB-D camera（Kinect）,mounted on a robot,is used to continuously acquire point clouds.Iterative closest point（ICP） is the common way to estimate the current camera position by registering the currently captured point cloud to the previous one.However,its performance sufers from data association problem or it requires pre-alignment information.The performance of the proposed principal direction detection approach does not rely on data association knowledge.Using this method,two point clouds are properly pre-aligned.Hence,we can use ICP to fne-tune the transformation parameters and minimize registration error.Experimental results demonstrate the performance and stability of the proposed system under disturbance in real-time.Several indoor tests are carried out to show that the proposed visual odometry estimation method can help to signifcantly improve the accuracy of simultaneous localization and mapping（SLAM）.

CURVATURE COMPUTATIONS OF 2-MANIFOLDS IN IR^k

In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k > 3.

Experimental Study on the Effect of Cyclic Preloading on the Resistance to Liquefaction of Saturated Loose Sand under Wave Loading

By using the soil static and dynamic universal triaxial and torsional shear apparatus, a series of combined cyclic shear tests are performed to simulate the rotation in the principal stress direction induced by ocean wave. The tests include the cyclic preloading tests and liquefaction tests in the second loading on saturated loose sand with a relative density of 30%. The all tests are consolidated under isotropic condition. The effect of the cyclic preloading on the resistance to liquefaction of saturated loose sands under the condition of continuous rotation in the principal stress direction is investigated. Experimental data indicate that the void ratio of saturated sands has a negligible reduction after cyclic preloading. With the increase of the intensity of cyclic preloading (in the amplitude and in the number of cycles), the resistance to liquefaction in the second loading is increased continuously under the condition that the liquefaction does not occur during the cyclic preloading. The reason is that the construction of more stable structure due to the uniformity of the void and the better interlocking of the particles when the cyclic preloading is applied to the saturated sand.

Partial Dynamic Dimension Reduction for Conditional Mean in Regression

In many regression analysis,the authors are interested in regression mean of response variate given predictors,not its the conditional distribution.This paper is concerned with dimension reduction of predictors in sense of mean function of response conditioning on predictors.The authors introduce the notion of partial dynamic central mean dimension reduction subspace,different from central mean dimension reduction subspace,it has varying subspace in the domain of predictors,and its structural dimensionality may not be the same point by point.The authors study the property of partial dynamic central mean dimension reduction subspace,and develop estimated methods called dynamic ordinary least squares and dynamic principal Hessian directions,which are extension of ordinary least squares and principal Hessian directions based on central mean dimension reduction subspace.The kernel estimate methods for dynamic ordinary least squares and dynamic Principal Hessian Directions are employed,and large sample properties of estimators are given under the regular conditions.Simulations and real data analysis demonstrate that they are effective.