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Theory and Practice of Safety Settlement Observation of Buildings of No-Benchmark
DOI: 10.12677/GST.2023.114048, PDF, HTML, XML, 下载: 141  浏览: 191

Abstract: This paper introduces a method of no-benchmark in building safety observation theory and practice to observe differential settlement, and its safety is judged by the uneven settlement value. This method solves the difficult problem of benchmark layout in building safety observation practice and improves the efficiency and convenience of operation.

1. 引言

2. 沉降观测的基准与平差模型

$\left\{\begin{array}{l}V=A\stackrel{⌢}{X}-L\\ {V}^{\text{T}}PV=\mathrm{min}\\ {\stackrel{⌢}{X}}^{\text{T}}{P}_{X}\stackrel{⌢}{X}=\mathrm{min},\text{\hspace{0.17em}}或\text{\hspace{0.17em}}{G}^{\text{T}}{P}_{X}\stackrel{⌢}{X}=0\end{array}$ (1)

(1)式中，第1式为误差方程，第2式为最小二乘条件，第3式为最小范数条件。GT为基准条件方程系数，Px为未知数的权，它代表点位的稳定程度。对式(1)求解得

$\stackrel{⌢}{X}={\left({A}^{\text{T}}PA+{P}_{X}G{G}^{\text{T}}{P}_{X}\right)}^{-1}{A}^{\text{T}}PL$ (2)

$\left\{\begin{array}{l}{Q}_{X}={Q}_{P}\left({A}^{\text{T}}PA\right){Q}_{P}\\ {Q}_{P}={\left({A}^{\text{T}}PA+{P}_{X}G{G}^{\text{T}}{P}_{X}\right)}^{-1}\end{array}$ (3)

3. 绝对沉降量与安全性

Figure 1. Sketch map of sedimentation observation with benchmark

4. 无基准点安全性沉降观测

Figure 2. Sketch map of absolute and relative subsidence

Figure 3. Sedimentation observation of no-benchmark

$\underset{i=1}{\overset{n}{\sum }}{d}_{i}^{j}=0$ (4)

${d}_{i}^{j}={\left({d}_{i}^{j}\right)}^{\prime }-{d}_{\mathrm{max}}^{j}$ (5)

${\Delta }_{i}=\underset{j=1}{\overset{N}{\sum }}{d}_{i}^{j}$ (6)

5. 实验验证

Figure 4. Example of sedimentation observation

Table 1. Observed data

Table 2. Absolute settlement and relative settlement of fixed reference

Table 3. No-Benchmark relative settlement

6. 结论

NOTES

*第一作者。

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