This paper develops a dual-indicator discrete method (DDM) for evaluating the system reliability performance of long soil subgrade slopes. First, they are segmented into many slope sections using the random finite element method, to ensure each section statistically contains one potential local instability. Then, the $$k$$
k
-out-of-$$n$$
n
system model is used to describe the relationship between the total number of sections $$n$$
n
, the acceptable number of failure sections $$m$$
m
, the reliability of sections $$R_{{{\text{sec}}}}$$
R
sec
, and the system reliability $$R_{{{\text{sys}}}}$$
R
sys
. Finally, $$m$$
m
and $$R_{{{\text{sys}}}}$$
R
sys
are jointly used to assess the system reliability performance. For cases lacking spatial data of soil properties, a simplified DDM is provided in which long subgrade slopes are segmented by the empirical value of section length and $$R_{{{\text{sec}}}}$$
R
sec
is substituted by that of cross-sections taken from them. The results show that (1) DDM can provide the probability that the actual number of local instabilities does not exceed a desired threshold. (2) $$R_{{{\text{sys}}}}$$
R
sys
decreases with increasing $$n$$
n
or decreasing $$R_{{{\text{sec}}}}$$
R
sec
; that is, it is likely to encounter more local instabilities for longer or weaker subgrade slopes. $$n$$
n
is negatively related to the horizontal scale of fluctuation of soil properties and positively related to the total length of subgrade slopes $$L$$
L
. (3) When $$L$$
L
is sufficiently large, there is a considerable opportunity to meet local instabilities even if $$R_{{{\text{sec}}}}$$
R
sec
is large enough.
In order to find out the shrinkage law of cement stabilized macadam material under specific conditions, this paper studied the expansion and shrinkage properties of cement stabilized macadam material under two environmental conditions, five kinds of cement dosage conditions, suspended compacted type and skeleton compaced type based on the multi-dimensional expansion and shrinkage tester. Through the test comparison, it is confirmed that the water loss rate of cement stabilized macadam material increases with the increase of cement dosage, showing a general change rule of rising first and then stabilizing. The average increase of the total water loss rate of suspended compacted cement stabilized macadam at room temperature was greater than that of the skeleton compacted cement stabilized macadam. The dry shrinkage strain also follows the above trend. Either at room temperature or under the conditions of dry shrinkage box, the water loss rate of suspended compacted cemeny stabilized macadam is higher than that of skeleton compacted cement stabilized macadam , which can be up to 3.23% higher. By comparing the temperature shrinkage coefficient under the high and low temperature environment, the temperature coefficient of the skeleton compacted cement stabilized macadam is smaller than that of the suspended compacted cement stabilized macadam. The temperature shrinkage coefficient of the suspended compacted cement stabilized macadam increases by 5.56% on average for each 0.5% increase of the cement dosage, and the temperature shrinkage coefficient of the skeleton compacted cement stabilized macadam increases by 6.33% on average. Through the comparative analysis of tests, it can be found that the anti-reflection crack ability of the skeleton compacted cement stabilized macadam material is better, and the fine aggregate content should be strictly controlled in the construction.
In this paper, we consider a coupled system of mixed hyperbolic-parabolic type, which describes Biot's consolidation model in poro-elasticity. We study an inverse problem of determining five spatially varying coefficients in the model, i.e. two Lamé coefficients, the secondary consolidation effects and two densities, by three measurements of displacement in an arbitrary subboundary and temperature in an arbitrary neighborhood of the boundary over a time interval. By assuming that, in a neighborhood of the boundary of the spatial domain, the densities, secondary consolidation effects and the Lamé coefficients are known, we prove a logarithmic stability estimate for the inverse problem.
High-temperature gas will cause stress and deformation of the rotor during the operation of the twin-screw compressor, which will affect the structural performance of the screw rotor. Based on the CFD/CSD coupling solution technology, the method of thermal solid numerical analysis is developed. The fluid control equations are time-averaged differential equations, and the turbulence model is a two-equation Realizable -model. The thermal deformation and thermal stress of the rotor are obtained by solving the structural static equilibrium equation. The reliability of the proposed method is verified by solving the thermal deformation of the L-shaped large-diameter buried pipeline. Finally, the thermal deformation and thermal stress of the rotor under different exhaust pressures and different speeds are mainly studied. Through simulation analysis, the variation law of rotor deformation, stress and modal under different temperature fields of the compressor is obtained, which can provide a certain theoretical reference for the compressor structural design and optimization.
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