Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A1/A2,σci1/σci2 and σtm1/σtm2 and an increase in B1/B2,γ1/γ2. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σs. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

Variational Reconstruction and Simulation Experiments of Sea Surface Wind Field for Ocean Data Buoy

The sea surface wind field is an important physical parameter in oceanography and meteorology.With the continuous refinement of numerical weather prediction,air-sea interface materials,energy exchange,and other studies,three-dimensional(3D)wind field distribution at local locations on the sea surface must be measured accurately.The current in-situ observation of sea surface wind parameters is mainly achieved through the installation of wind sensors on ocean data buoys.However,the results obtained from this single-point measurement method cannot reflect wind field distribution in a vertical direction above the sea surface.Thus,the present paper proposes a theoretical framework for the optimal inversion of the 3D wind field structure variation in the area where the buoy is located.The variation analysis method is first used to reconstruct the wind field distribution at different heights of the buoy,after which theoretical analysis verification and numerical simulation experiments are conducted.The results indicate that the use of variational methods to reconstruct 3D wind fields is significantly effective in eliminating disturbance errors in observations,which also verifies the correctness of the theoretical analysis of this method.The findings of this article can provide a reference for the layout optimization design of wind measuring instruments in buoy observation systems and also provide theoretical guidance for the design of new observation buoys in the future.

Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.

Impacts of XBT,TAO,Altimetry and ARGO Observations on the Tropical Pacific Ocean Data Assimilation

This study aims at assessing the relative impacts of four major components of the tropical Pacific Ocean observing system on assimilation of temperature and salinity fields. Observations were collected over a period between January 2001 through June 2003 including temperature data from the expendable bathythermographs （XBT）, thermistor data from the Tropical Ocean Global Atmosphere Tropical Atmosphere-Ocean （TOGA-TAO） mooring array, sea level anomalies from the Topex/Poseidon and Jason-1 altimetry （T/P-J）, and temperature and salinity profiles from the Array for Real-time Geostrophic Oceanography （ARGO） floats. An efficient three-dimensional variational analysis-based method was introduced to assimilate the above data into the tropical-Pacific circulation model. To evaluate the impact of the individual component of the observing system, four observation system experiments were carried out. The experiment that assimilated all four components of the observing system was taken as the reference. The other three experiments were implemented by withholding one of the four components. Results show that the spatial distribution of the data influences its relative contribution. XBT observations produce the most distinguished effects on temperature analyses in the off-equatorial region due to the large amount of measurements and high quality. Similarly, the impact of TAO is dominant in the equatorial region due to the focus of the spatial distribution. The Topex/Poseidon-Jason-1 can be highly complementary where the XBT and TAO observations are sparse. The contribution of XBT or TAO on the assimilated salinity is made by the model dynamics because no salinity observations from them are assimilated. Therefore, T/P-J, as a main source for providing salinity data, has been shown to have greater impacts than either XBT or TAO on the salinity analysis. Although ARGO includes the subsurface observations, the relatively smaller number of observation makes it have the smallest contribution to the assimilation system.

Effect of 2-m Temperature Data Assimilation in the CMA-MESO 3DVAR System

Assimilation of surface observations including 2-m temperature(T_(2m))in numerical weather prediction(NWP)models remains a challenging problem owing to differences between the elevation of model terrain and that of actual observation stations.NWP results can be improved only if surface observations are assimilated appropriately.In this study,a T_(2m)data assimilation scheme that carefully considers misrepresentation of model and station terrain was established by using the three-dimensional variational data assimilation(3DVAR)system of the China Meteorological Administration mesoscale model(CMA-MESO).The corresponding forward observation operator,tangent linear operator,and adjoint operator for the T_(2m)observations under three terrain mismatch treatments were developed.The T_(2m)data were assimilated in the same method as that adopted for temperature sounding data with additional representative errors,when station terrain was 100 m higher than model terrain;otherwise,the T_(2m)data were assimilated by using the surface similarity theory assimilation operator.Furthermore,if station terrain was lower than model terrain,additional representative errors were stipulated and corrected.Test of a rainfall case showed that the observation innovation and analysis residuals both exhibited Gaussian distribution and that the analysis increment was reasonable.Moreover,it was found that on completion of the data assimilation cycle,T_(2m)data assimilation obviously influenced the temperature,wind,and relative humidity fields throughout the troposphere,with the greatest impact evident in the lower layers,and that both the area and the intensity of rainfall were better forecasted,especially for the first 12hours.Long-term continuous experiments for 2–28 February and 5–20 July 2020,further verified that T_(2m)data assimilation reduced deviations not only in T_(2m)but also in 10-m wind forecasts.More importantly,the precipitation equitable threat scores were improved over the two experimental periods.In summary,this study confirmed that the T_(2m)data assimilation scheme that we implemented in the kilometer-scale CMA-MESO 3DVAR system is effective.