CZ2008422A3 - Method of trigonometric measurement of vertical shifts during static loading tests of building objects - Google Patents

Abstract

Trigonometric Measurement of Vertical Shifts Applied to Static Load Tests of Building Buildings Using Total Station, Intentional Target, and Transient Position, which must lie outside the fall zone. Before the measurement, the building object is glued with a vertically intentional target formed by an axial cross with at least two concentric circles. The measurement shall be carried out in at least three load conditions, ie without load, self-loading and unloading. Two or more meric stages are repeated in each load condition. The zenith angles are always measured in both positions of the telescope on the intersection of the circles of the deliberate target with its vertical axis. The oblique length is determined only in the first stage. The measured zenith angles are reduced to the center of the deliberate target. Reductions of the modified zenith angles are compared in the individual stages and load conditions, and their changes are obtained, which are used to calculate the vertical displacements determined relative to the transient position. Finally, the null hypothesis is tested to determine if the vertical shift is statistically significant.

Description

Method of trigonometric measurement of vertical displacements during static load tests of building objects

Technical field

The present invention relates to a method of trigonometric measurement of vertical displacements which are carried out in static load tests of buildings, in particular bridges.

BACKGROUND OF THE INVENTION

Trigonometric method is one of the possible geodetic methods for determination of vertical displacements of building objects - its principle is given eg in Hauf, M. et al .: Geodesy. Praha, SNTL 1982. A known method of this type consists in repeatedly measuring zenith angles, which are angles in the vertical plane between the vertical and the intent to the observed point, provided that the position of the known distance from the observed points is constant throughout the measurement. Static loading tests are most often a precise re-alignment of zenith angles from a fixed position lying outside the deformation zone at a known distance from the observed points. The observed points shall be appropriately signaled to allow accurate, preferably multiple, targeting at each measurement stage, repeating at approximately five-minute intervals, at each load case, without load, in the design load cases and after unloading.

Zenite angles were previously measured by one of the second theodolites with an optical micrometer designed for engineering measurements of highest precision. Measurements were made in 1 to 3 groups with dual targeting and dual coincidence in each row without the possibility of registering measurements to the instrument's electronic memory and subsequent automated calculation processing. The deliberate target with a circular target mark was in various contrasting designs, eg a yellow circle in a red box. Determining the required lengths was a big problem. Horizontal lengths were measured separately, usually prior to measuring zenith angles, either directly after the observation point was measured through the measuring zone, or by measuring the parallactic angle to the 2 m • · base bar or trigonometrically using a general base whose length was again determined by base batten. This outdated measurement procedure was very time consuming, especially when it was necessary to show vertical displacements of less than 1 mm.

SUMMARY OF THE INVENTION

The above-mentioned disadvantages are eliminated by the method of trigonometric measurement of vertical displacements during static load tests of building objects by means of a precise total station with a biaxial electronic compensator and a deliberate target according to the present solution. The essence of this new solution is the following procedure. The total station shall be placed as a suitable intermediate position, which is chosen outside the drop zone and whose position is fixed throughout the measurement. The vertical displacements are determined relative to this position by first horizontally adjusting the total station on a firmly pressed tripod, with its vertical axis assuming the vertical position. Before the measurement at the selected point of each observation point, an intentional target consisting of an axial cross with at least two concentric circles is vertically attached to the measured building object. Now the measurement is carried out in at least three load cases, without load of the measured building object, then in at least one load case and always after unloading. Measurements performed in all load cases are completely analogous and in each load case are carried out in at least two measurement stages. In addition, during the first measurement stage, the aiming target is centered and the inclined length between the center of the aiming target and the intermediate station is measured with an electronic rangefinder. This oblique length is reduced to a horizontal length. Furthermore, the zenith angles are measured at each stage. Initially, the telescope is measured at the intersection of the concentric circles of the aiming target with its vertical axis, progressively from the upper intersection to the lower intersection. Then the telescope is interlaced to the second position and zenith angles are again measured at said intersections, but in reverse order from the lower intersection to the upper intersection. All measured values of zenith angles are continuously registered in the total station memory. Subsequently, each zenith angle is reduced to the center of the aiming target, wherein the reduction found for the intersection above the center is added to the measured zenith angles and the reduction found for the intersection below the center is subtracted from the measured zenith angles. The arithmetic mean is calculated from the reduced zenith angles at each stage and the empirical standard is determined.

• · deviation of the result of each measurement stage. Subsequently, the thus obtained zenith angles are compared in individual stages and load cases, thereby obtaining their changes, which occurred due to the vertical shift of Ah. The vertical displacements Ah of the observed point are determined from the distance of two points lying on one vertical. For each vertical displacement Ah, the standard deviation of the displacement is also calculated, and then the null hypothesis H _o is tested: LH ~ 0. This test determines whether these displacements actually occurred or whether the observed vertical displacement Ah results from random measurement errors with unchanged building position. If the vertical displacement is found to be satisfactory due to its standard deviation of the relation ΔΑ <σ _Μ , the null hypothesis cannot be rejected and the movement of the structure is not proved by measurement. With the mutual relation <Δ / ι <2σ _ω , the validity of this hypothesis can be doubted and the movement of the structure can be admitted and if the relation Δ / ι> 2σ _ω is valid, the value A /? statistically significant and indicates a vertical shift.

The aiming target is preferably a reflecting target and then the length measurement is performed with a conventional infrared rangefinder. A non-reflective intentional target can also be used but then a laser rangefinder must be used to measure the length.

In a preferred embodiment, the measurement of the length between the center of the aiming target and the intermediate station is controlled at the beginning of each load case in both positions of the telescope.

It is also advantageous for the entire cycle of measurement of vertical displacements of building objects to be repeated several times in succession at different designed load cases in such a way that for each subsequent cycle the last load stages after unloading the measured building object become starting stages for the next measurement cycle.

The reduction of the measured zenith angles to the first to fourth intersection at the center of the target can be performed according to the formula z = z ± t5 _z , where

rsinz 2 r sin ² z

- arctg --------------------- (d _H / sin) + rcosz 2d _H Trsin2z where cíh = t / _s sin z, d ₅ is the oblique length and duje reduced horizontal length, with the upper sign for the upper intersection and the lower for the lower intersection.

The determination of the vertical displacements is preferably carried out according to the simplified formula Δ ^ (ί _Η - ^ τ- = ^ - (1 + cotg ^of 2) = hz, where £ = - (1 + cotg of ² z) is all stages for psin zpp of the individual observation point on the transitional position constant.

The accuracy of vertical displacement characteristics can be estimated by variance or variance

where the standard deviation of the difference in zenith angles σ _Δί = σ _ζ 72 and σ _? is the standard deviation of the measured zenith angle.

The advantage of this innovation of trigonometric method using total station is its speed and efficiency. The surveyor may immediately transmit the relevant results of the individual stages, which can be considered objective, immediately after the end of the load case to the test laboratory managing the static load tests. The achieved accuracy of the experimental measurements, characterized by the standard deviation, ranges from 0.2 to 0.1 mm. There was no significant dependence of the achieved accuracy on the horizontal length of the project in the range of 20 to 60 m, nor on the inclination of the project in the range of 90 to 110 gon. Due to the variability of building structures with time and temperature, it is better to increase the number of measurement stages than the number of individual measurements to more concentric circles, which are further processed in time and better reflect the continuous changes of vertical displacements in time.

BRIEF DESCRIPTION OF THE DRAWINGS

9 t · 9 · · · t t t

In the accompanying drawing, one example of a reflective reticle with two concentric circles is shown in FIG. Giant. 2 illustrates the derivation of the vertical offset calculation formula. Fig. 3 is a diagram for determining the reduction of the measured zenith angle, and Fig. 4 shows a sighting target with values for a particular measurement.

DETAILED DESCRIPTION OF THE INVENTION

In today's surveying practice, the use of second-theodolites with optical micrometers, ie devices without electronics and software, has virtually ceased. The present new strategy for solving vertical displacements by the trigonometric method therefore assumes that a very accurate total station is used for the measurement. The total station is an electronic theodolite with built-in electronic rangefinder, comprehensive software and measurement registration. These instruments accelerate the measurement process itself, which is beneficial in the case of static load tests of buildings, where the results of individual measurements depend on time. But to measure effectively with these instruments requires, besides geodesy knowledge, computer and information literacy.

The new method of trigonometric measurement of vertical displacements in building load tests, such as bridges, can be described by the following steps.

First, the total station is placed as a suitable intermediate position, which is selected outside the drop zone and whose position is fixed throughout the measurement. Vertical shifts are determined relative to this opinion by the following procedure. First, the total station is horizontal on a firmly pressed tripod, where the vertical axis of the total station assumes the vertical position. Before the actual measurement, a deliberate target formed by an axial cross is applied vertically to the measured building object at each selected point of the observed point. In this case, it is a reflective target having two concentric circles, but a deliberate non-reflective target and a plurality of circles can also be used. If a reflective aiming target is used, the following infrared rangefinder measurement is performed, if a non-reflective aiming target is used, a laser rangefinder is used. Now the measurement is carried out in at least three load cases, ie without load of the measured building object, then in at least one load case and always after unloading. The measurements carried out are completely analogous in all load cases and are carried out in at least two measurement stages in each load case. In addition, in the first measurement stage, the center of the aiming target, in the present example of the reflective target, is targeted, and in this example the inclined length between the center of the aiming target and the intermediate station is measured by an electronic rangefinder. The inclined length thus measured is now reduced to a horizontal length. Furthermore, zenith angles are measured at two stages of the telescope at each stage. At first, the telescope is measured at the intersection points of the concentric circles of the target target with its vertical axis, successively from the top intersection to the bottom intersection, in this example from the first intersection 1 to the second intersection 2, the third intersection 3 to the fourth intersection. the telescope is interlaced to the second position and zenith angles are again measured at said intersections, but in reverse order from the lower fourth intersection 4 to the upper first intersection L All such measured zenith angles are continuously registered in the total station memory. Each detected zenith angle is then reduced to the center of the aiming target, i.e. the reduction found for the intersections above the center, i.e. in the example for the first intersection 1 and the second intersection 2, is added to the measured zenith angles and here for the third intersection 3 and the fourth intersection 4, it is subtracted from the measured zenith angles. Their arithmetic mean is calculated from the reduced zenith angles in the individual stages and the empirical standard deviation of the result of the individual measuring stage and consequently the load case is determined.

Subsequently, the obtained zenith angles are compared in individual stages and thus their changes, which occurred due to vertical displacement, are obtained. Vertical displacements Δ /? The point of observation is calculated according to the formula used to calculate the distance of two points lying on one perpendicular. The standard deviation of the displacement σ _ω is also calculated for each vertical displacement. In practice, vertical displacements depend on the movement of the building. Therefore, it is necessary to test the null hypothesis (Hq: ΔΗ = 0) to make sure that the displacements actually occurred, or that the calculated change kh results only from random measurement errors when the building position remains unchanged.

At ΔΑ <σ _{Μ the} null hypothesis cannot be rejected and the movement of the structure is not proved by measurement,

At σ _ω <ΔΑ <2σ _ω , the validity of this hypothesis can be doubted and the movement of the structure can be admitted

At ΔΑ> 2σ _ω , kh is statistically significant. The null hypothesis is rejected and there is practically a vertical shift,

It is advisable to check the length between the center of the target and the intermediate position at the beginning of each load case in both positions of the telescope. Similarly, for several different designed load cases, it is advisable to repeat the entire cycle of measurement of vertical displacements of buildings several times immediately after each other so that for each subsequent cycle the last stages of the load case after the measured construction object are unloaded become the starting stages for the next measurement cycle.

For the sake of clarity, the procedure for determining the values in determining vertical displacements during static load tests of building objects is given below.

The vertical shift causes a change in the zenith angle, which is measured at each stage. In the basic load case, the angle z 'is measured in at least two stages, in the next stage, i.e., in the respective load case, the angle z'. The change in zenith angle that occurs due to vertical displacement is, Δζ = ζ'-ζ [gon]. The vertical offset & h is calculated using the formula used to calculate the distance of two points lying on one vertical. Its derivation is evident from Fig. 2. It is assumed based on experience to date, that during the whole measurement there was no change of the position of the position P and thus the horizontal distance d _H ·,,, _L , sin from cos z-cos from sm z, sinAz

ΔΛ = d _H (cotgz-cotgz) = d _H ------ _: ----— ----- = ---- 7 - 7, smzsinz smzsmz where 4 _h is the horizontal length.

(1) in «

The inclined length d _s is measured by an electronic rangefinder, which is further reduced to the horizontal length c. The length is better controlled at the beginning of each load case - in both positions of the telescope to the center of the reflective target.

Since the angle δ z can be expected to be small, it is expressed in mgon, then it holds. Áz

51ΠΔΖ «- ·,

P then

-Λ'- (2) psinzsinz where p = - · 10 ⁵ = 63 662 mgon.

π

Formula (2) is further simplified if z is z, then

αA = i / _h - = d _H - (1 + cotg ² z) = fcAz, (3) psin where quantity dd k = - = - (1 + cotg ² z) is for all stages of the single psin zp

observed point on the opinion constant.

The variance, or variance, of the calculated vertical displacement (1) is σ ² * = (Δλ / dH) ² σ ² ϋ + d ² ((1 + cotg ² z) ² + (1 + cotg ² z ') ² ) (σ _? / p) ¹ , where cr _D is the standard deviation and mean error of the measured length, respectively, and σ, is the standard deviation of the measured zenith angle.

φ

Φ

Φ »

The first term that expresses the influence of the accuracy of the measured length is negligible.

Practically only the second term is used, which expresses the influence of the accuracy of the measured zenith angles and in addition z »z ', then the resulting variance is« · ··

D ♦ · * φ «· * (d Y ~ - (1 + cotg ² of)

VP J

_σ Δ1 -σ ν Υ2.

(4)

The zenith angles are measured on the reflective aiming target on the foil, for example, a Leica target of 20x20 mm, which according to the manufacturer is intended for a range of 2 to 40 m, or 40x40 mm for a range of 20 to 100 m, can be selected. or 60x60 mm for a range of 60 to 180 m. In the realized measurement, four target points corresponding to the first point of intersection 1, the second point of intersection 2, the third point of intersection 3 and the fourth point of intersection 4 were used. these points are followed by vertical displacements. The measurement of zenith angles takes place in two positions of the telescope, since it is then possible to determine the instrument index error and check the measurement, always with double targeting, aiming alternately from above and below according to the general scheme A * - Β ¹ , B - A ¹¹ measurement order. According to this scheme, at the first position of the telescope, it is first measured sequentially to the target points given by the first to fourth intersections of 1,2, 3,4. Then the telescope is placed in the second position and the measurement is repeated on the same target points, but in reverse order, ie 4, 3, 2, 1. The measurements are registered in the instrument's electronic memory or on the memory card.

As already mentioned, zenith angles are measured on a reflective aiming target having a total of four target points. Another solution is to reduce the measured zenith angles to the center S of the target.

Referring to FIG. 4, rsinz 2rsin ^{2 of} ₁ = arctg = - _; - (J _H / sinz) + rcosz ŽdjjTrsinŽz (-) ... bodyl, 2 (+)., Points 3,4 '(5) where r is the radius of the respective circle, the diameters of the two circles, fig. and the values of 14.953 mm and 29.938 mm were determined in the example.

• · ·

The reduced zenith angle is ž = z ± B ₁ . The reduction (5) is calculated for each target point,

For the first intersection 1 and the second intersection 2, the value is added, for the third intersection 3 and the fourth intersection 4,

For further processing, the diameter ζ _χ = Σζ / 4 is calculated from the reduced zenith angles. The empirical standard deviation of the resulting zenith angle or the obtained diameter, respectively, is determined according to the formula where the corrections v = z _A - z, n - 4, Empirical standard deviation σ _; - = 2σ ^ of one measurement of the zenith angle in our case is twice as large as it is a multiple of the square root of the number of measurements than the standard deviation of the mean,

In practice, vertical displacements depend on the movement of the building. It is therefore necessary to test the null hypothesis to determine whether these shifts actually occurred.

Let ΔΗ be the true value of the vertical shift and hh is the vertical shift calculated from repeated measurements of zenith angles. We assume that the determined values of Ah have a normal distribution of kh-NibH,.

The null hypothesis Ho: ΔΗ = 0 is formulated, compared to the alternative hypothesis Hy ΔΗ a0. If PokudΑ. > q The null hypothesis is rejected. To the detriment of Him, those cases where hodnota / ι is far from hodně will testify. According to Anděl, J .: Mathematical Statistics. Prague, SNTL 1985, where a general derivation is given, the number q is calculated from the condition that the probability of type 1 error is equal to a (test level)

Generally, the distribution function holds Φ (~ χ) = 1 -Φ (χ). Hence, with respect to (6), we can write a = p (| Ah |> q) =? (| Δ / ι | /> q l.

(6) α = 2 (1-Φ ( ₉ / σ _ω )).

(7) •

• ·

The critical value of the distribution N (0,1) is the number u (a), which exceeds the random variable with the probability a = 1-Φ ( _Μ (α)). Then with respect to (7), u (a / 2) = -L a

For a = 0.05 is u (al2) = 1.96, and therefore? = 1.96σ _ω . The null hypothesis Hq is rejected at the level a if | ΔΑ | ζ1,96σ _ω . In practice, the vertical movement of a building is determined by Bohm, J. - Radouch, V. - Hampacher, M .: Theory of Errors and Compensation Calculus. Prague, Geodetic and Cartographic Enterprise 1988:

1. At ΔΑ <σ _{ω the} null hypothesis ΔΗ = 0 cannot be rejected and the movement of the structure is not proved by measurement,

2. With σ _ω <Δ / i <2σ _ω , the validity of this hypothesis can be doubted and the movement of the structure can be admitted,

3. When \ h> 2σ _ω is the value of Δ /? statistically significant. We reject the null hypothesis ΔΗ = 0 and are practically convinced of the movement of the building.

Measurements in two positions of the telescope can be grouped into two units within a series according to the proposed measurement scheme. This procedure allows better control of zenith angle measurements than measurements at one telescope position. It is sufficient to calculate the projected vertical displacements of measurements in one telescope position, but the time savings of measurement work are not large enough to recommend this procedure. The processing of measurement results is possible with the use of computer technology immediately after the end of the respective load case, when preliminary results are obtained, with additional analysis of the results, which is stated in the report on the course of the load test.

Claims (8)

PATENT CLAIMS 1. Method of trigonometric measurement of vertical displacements in static load tests of building objects by means of an accurate total station, a dual electronic compensator and a sighting target, characterized in that the total station is positioned as a suitable intermediate position, selected outside the drop zone and fixed and vertical displacements are determined relative to this position by first horizontal total station stationing on firmly pressed tripod, where its vertical axis assumes the vertical position and the measured building object is glued vertically to the measured building object at the selected point of each observed point target consisting of an axial cross with at least two concentric circles, after which the measurement is carried out in at least three load cases, without loading of the measured building object, in at least one load case, and always after unloading, when the measurements carried out in all load cases are completely analogous and in each load case are carried out in at least two measurement stages, while in the first measurement stage, in addition to the center of the aiming target and measured by the electronic rangefinder and a transitional position that is reduced to horizontal length and zenith angles measured at each stage, first in the first position of the telescope to the intersections of the concentric circles of the target target with its vertical axis, gradually from the upper intersection to the lower intersection, zenith angles are again measured at said intersections, but in reverse order from the lower intersection to the upper intersection, and all zenith angles measured in this way are continuously registered in the memory of the total station, then each zenith angle is reduced to the center of the aiming target, where the reduction found for the intersection above the center is added to the measured zenith angles and the reduction found for the intersection below the center is subtracted from the measured zenith angles and the arithmetic mean is calculated the empirical standard deviation of the result of the individual measurement stage, then the thus obtained zenith angles in the individual stages and load cases are compared, thereby obtaining their variations due to the vertical displacement, whereby the vertical displacements Ah of the observed point are determined For each vertical displacement, the standard deviation of the displacement is also calculated, and the null hypothesis Hy is tested. 0 = 0, in order to determine whether the displacements actually occurred or that the observed vertical displacement Δ /? follows only the random measurement errors in an unchanged position of the building, where in you can not reject the null hypothesis and the movement of construction is not measurements demonstrated when _σ ω <ΔΑ _<2σ ω be the validity of this hypothesis question and move buildings may be accepted and when ΔΑ> _2σ ω the value ΔΛ is statistically significant and indicates a vertical shift. The measuring method of claim 1, wherein the aiming target is a reflective target and the length measurement is performed with a conventional infrared rangefinder. 3. The measurement method of claim 1, wherein the aiming target is non-reflective and the length measurement is performed by a laser rangefinder. Measurement method according to claim 1 and claim 2 or 3, characterized in that the measurement of the length between the center of the target target and the intermediate station is controlled at the beginning of each load case in both binocular positions. Measurement method according to any one of claims 1 to 4, characterized in that the entire cycle of measurement of vertical displacements of building objects is repeated at different projected load cases several times immediately after each other, with for each subsequent cycle the last load stages after the measured load. the building object become the initial stages for the next cycle of measurement, Measurement method according to any one of claims 1 to 5, characterized in that the reduction of the measured zenith angles to the first to fourth intersections (1,2,3,4) to the center of the target is performed according to the formula = = z ± 5 _X , where 6. = arctg ----- ^rs - ^nz - = - ² - ^r . ^sin /. _t kd _e sj _n z, d _s is the oblique length (d _H / sinzjTrcosz 2ί / _Η ΤΓδίη2ζ and du is the reduced horizontal length, with the upper sign for the upper intersection (1, 2) and the lower for the lower intersection (3,4) . Measurement method according to any one of claims 1 to 6, characterized in that the determination of vertical displacements is carried out according to a simplified formula Ú 2 Δ 2 ú? 5h d ~ _u ~~ ---- T d _H - (l + cot ² z) = AUZ wherein variable £ = - ^ (1 + cot ² a) is of j9sín ρ p for all stages of a single point on the observed transition constant opinion. Measurement method according to any one of claims 1 to 7, characterized in that the estimation of the vertical displacement accuracy characteristics is performed by variance or variance = where the standard deviation of the difference in zenith angles σ ^ -σ-βϊ and σ _ί is the standard deviation of the measured zenith angle.