What Is a Planimeter?

Apparatus for measuring the strength and deformation characteristics of soil samples under plane strain stress. Principal stress is applied in two directions of the rectangular parallelepiped sample, and the third direction (usually the two ends of the sample length) uses a fixed rigid plate to limit deformation in this direction. A pressure box can be installed in the middle of the rigid plate to measure the pressure change in this direction. In order to simulate the in-situ stress state, the sample is first consolidated by K0, and then the test is performed according to the conventional triaxial compression test procedure. The medium principal stress needs to be determined during the test. With this instrument, two compressive stress paths and two elongation stress paths can be tested. ^[1]

Many soil mechanics problems are plane strain states, such as earth dams, tunnels, and retaining walls. However, the force state of various geotechnical test instruments is very different from this. Therefore, from the perspective of simulating the stress state of actual engineering problems, it is necessary to develop a plane strain gauge, usually referred to as a plane strain gauge for short.

In the early 1960s, Cambridge University and Imperial College successively developed different types of plane strain gauges. Due to the limitation of the level of electronic instruments at that time, most of the measurement methods were relatively simple. Until the late 1960s, the United States and Japan successively introduced the basic form of the British plane strain gauge, and installed various sensors for electrical measurement. In 1971, the Massachusetts Institute of Technology made a relatively complete plane strain gauge. In the mid-1970s, Japan's Gutten Co., Ltd. improved on the basis of the MIT plane strain gauge and made a multifunctional triaxial instrument, which became the official commodity supply market.

China's research on constitutive relations of soil and the development of corresponding instruments are relatively early. As early as the mid-1960s, the Wuhan Institute of Rock and Soil Mechanics of the Chinese Academy of Sciences absorbed the results of Cambridge University in the UK and developed a True triaxial instrument. This true triaxial instrument can, in principle, achieve shearing in a plane strain state. This instrument is continuously being debugged and improved. At the end of the 1970s, Tsinghua University and the Northwest Institute of Water Resources Science each imported a multi-functional triaxial instrument from Japan's Gu Teng Society, and they are debugging and conducting some experimental research work. In 1981, the Beijing Academy of Hydraulic Engineering modified the conventional triaxial pressure chamber. Two steel plates were added to the triaxial pressure chamber to achieve the shearing of the plane strain state. It is called a simple plane strain gauge, but this kind of instrument Measurement of the medium principal stress ₂ has not yet been performed.

In addition, Zhejiang University, Wuhan Institute of Water Resources and Electric Power, etc. are also conducting research in this area. ^[2]

The plane strain gauge has the following components:

Plane strain pressure chamber
Principal stress stabilization and back pressure volume change control system
Gearbox and worm gear system for strain-controlled main stress loading
Rolling diaphragm pressure cylinder for stress controlled main stress loading

1. Calibration of the stress on the end faces of the sample without interference:

During the test, three pairs of principal stresses are required not to interfere with each other.

The calibration method is: use a plexiglass block as a simulation sample. After the instrument is completely installed, a large principal stress _{1 is} applied step by step. At this time, the measurement system for the medium principal stress ₁ and the small principal stress ₃ can always maintain zero. This shows that the instrument's large principal stress will not interfere with the middle principal stress and the small principal stress. Conversely, the large and medium principal stress measurement systems are adjusted to zero. In the process of increasing the small principal stresses, the large and middle principal stress measurement systems can also always maintain the zero position, indicating that the small principal stresses will not Disturb to large and medium principal stresses. The medium principal stress is the pressure on the fixed end face due to the action of ₁ and ₃ , and it will not interfere with ₁ and ₃ .

2. Calibration of main stress in small earth pressure box measurement:

The small earth pressure box is properly embedded in the fixed end plate, and the fixed end plate and the earth pressure box are placed in a calibration tank for classification and pressure to perform calibration. The calibration curve is obtained. After three calibrations, all the measurement points are on the same straight line Above, it shows that this kind of earth pressure box has good linearity and repeatability.

Then, use a plexiglass plate as a simulated sample. After the instrument is completely installed, apply pressure between the sample and the rubber film from the sample pore pressure measurement hole (the pressure of the pressure bag on the small principal stress surface at this time). Keep it slightly higher than the pressure in the pore pressure system). At this time, the applied pressure and the pressure reflected by the earth pressure box can still fall well on the calibration curve of the earth pressure box. In addition, strain-controlled shear rate calibration and calibration of the main stress regulator system are also required. The calibration method is the same as the conventional static triaxial. ^[2]

Main functions of plane strain gauge

1. Carry out the shear strength test of soil samples under the plane strain state, and study the influence of different stress states on the shear strength index.

2. Carry out research on the stress-strain relationship of soils under plane strain conditions, and evaluate the applicability of mathematical models (such as Duncan model) often used to calculate the stress-strain characteristics of soils under plane strain conditions.

3. Realize the control of two pairs of principal stress combinations at the same time on the plane strain gauge, and carry out research on the effect of stress path on shear strength.

4. Using the obtained stress-strain-strength-time relationship (that is, the SST relationship), the constitutive relationship of the soil in the plane strain state is studied in the octahedral stress space.