The low masonry structure is the most commonly applied building type in rural China. It is possible to install small-diameter, low cost, and easily constructed laminated rubber bearing (LRB) components. Isolation technology has broad application prospects in rural buildings. We developed a small-diameter LRB in this study wherein the isolation layer is set above the floor for easy installation and replacement. We built and tested 4 walls to observe the effects of different LRB thicknesses; we assessed test respective phenomena and seismic parameters accordingly. We ran another test on five small-diameter LRB components with varying horizontal stiffness, different forms of shear strain-equivalent horizontal stiffness, and postyield stiffness while changing the fitting formula for the second shape coefficient to give small-diameter LRB design providing gist.
The isolation structure system serves to protect structural and nonstructural components in the building in which it is installed [
In this study, we conducted an experiment consisting of four 1/2-ratio pseudodynamic seismic tests on masonry wall structures. We used one piece of a masonry wall with no isolation bearing (SRB) and three with different LRB specifications, completing 4 groups of masonry building bearing wall models to the seismic performance test. The equivalent horizontal stiffness, postyield stiffness, and damping ratio [
Masonry wall specimens: (a) MLQT-1; (b) MLQT-4.
The bearing wall test loading device is shown in Figure
Bearing wall experiment loading device: (a) photo; (b) drawing.
We also conducted an experiment to test various LRB mechanical parameters based on the “isolated rubber bears experimental method” [
Experimental bar specifications.
Bar model | Rubber shear elasticity modulus (MPa) | Effective diameter (mm) | Number of layers | Rubber layer thickness (mm) | Thin steel plate thickness (mm) | Thin steel plate number | Lead core diameter (mm) | Cover steel plate thickness (mm) | Bear overall height (mm) | Second shape coefficient = dia/total thickness of the rubber layer |
---|---|---|---|---|---|---|---|---|---|---|
GZ1 | 0.39 | 110 | 12 | 1.8 | 2 | 11 | 12 | 10 | 63.6 | 5.1 |
GZ2 | 0.39 | 110 | 12 | 2.5 | 2 | 11 | 13 | 10 | 72 | 3.7 |
GZ3 | 0.39 | 110 | 10 | 3.5 | 2 | 9 | 14 | 10 | 73 | 3.1 |
GZ4 | 0.39 | 110 | 12 | 1.9 | 2 | 11 | 10 | 10 | 64.8 | 4.8 |
GZ5 | 0.55 | 110 | 12 | 1.8 | 2 | 11 | 12 | 10 | 63.6 | 5.1 |
We conducted the horizontal stiffness experiment on these LRB specimens at the Guangzhou University Engineering Seismic Research Center on a 1000 t electro-hydraulic servo press and shear tester with the horizontal dynamic loading equipment shown in Figure
Testing LRB and equipment: (a) dynamic loading equipment; (b) LRB.
We conducted five small-diameter LRB horizontal stiffness tests to observe the effects of different LRB horizontal shear strains and second shape coefficients [
The small-diameter LRB mechanical property parameters for rural dwellings provided a reference for our LRB test specimen design. The horizontal isolation layer increases the fundamental horizontal period of the structure significantly; this layer is what isolates the structural system from strong seismic disturbances in the ground. Structural deformation is concentrated in the isolation layer [
We adopted pseudodynamic loading conditions for the purposes of this test. A horizontal simulating was applied to the top of the wall [
The following assumption [
The superstructure was fitted here with the LRB and considered as a rigid body. Displacement on one side moves along a similar trapezoid (first mode) as the oscillating displacement increases in equal proportion at the same height. The double bilinear isolation system can be simplified using this model [
The equivalent seismic response in the bilinear [
Assuming that seismic shear force [
The superstructure seismic force distribution is rectangular along its height when the base is isolated:
The superstructure is equivalent to a particle, as is the isolated layer [
The equivalent stiffness is
The period is
The first model participation coefficient is
We calculated the horizontal equivalent stiffness and equivalent viscous damping ratio in the isolated layer using an oscillation equation’s plural damping theory. The natural vibration period of a rural masonry structure is short, so the appropriate horizontal damping coefficient is 1.2 [
The horizontal direction seismic reduction coefficient is expressed as
The LRB horizontal displacement under strong seismic conditions can be calculated as follows:
We used a linear stiffness and damping equivalent calculation method to assess LRB mechanical properties. The linear stiffness is secant in this case:
We analyzed the LRB damping force separately according to a unidirectional damping resilience-displacement relation:
Plugging the formulas (
The linear elastic unit [
There are three main types of the double linear model: the ideal elastic-plastic model, linear strengthen elastic-plastic model, and negative stiffness property elastic-plastic model [
We took the double linear model property LRB for equivalent linear model simulation. The equivalent stiffness and equivalent stiction damping ratio in this case is
We assessed the LRB equivalent stiffness and equivalent stiction damping ratio under different horizontal displacement conditions. The double linear model force parameter conversion formula is
The LRB surface was modeled here using a Prager mobile induration model [
The yield center mobile increases as follows:
A triple linear model can be adopted upon extensive deformation in the structure (i.e., stiffness hardening). The resilience-displacement relationship [
The stiction damping model [
The force-displacement relation [
Our model is a combination of double and triple linear models, wherein we consider five LRB equivalent damping ratios with a total damping ratio of 10~20% and a high damping ratio of 15~20% shown in Table
LRB horizontal stiffness calculation results.
Bearing number | GZ1-0.5 | GZ2-0.5 | GZ3-0.5 | GZ4-0.5 | GZ5-0.5 |
---|---|---|---|---|---|
Equivalent horizontal stiffness (N/mm) | 278.47 | 177.12 | 156.13 | 211.73 | 328.51 |
Equivalent damping ratio (%) | 10.6 | 17.25 | 19.24 | 19.07 | 12.52 |
Postyield stiffness (N/mm) | 236 | 140 | 205 | 156 | 270 |
Yield stress | 945 | 1160 | 1390 | 1420 | 1280 |
Supporter third hysteretic data: (a) 100% shear strain hysteretic loop; (b) 250% shear strain hysteretic loop.
Our specimen MLQT-1 is an uninstalled LRB wall. The corresponding relation between earthquake intensity and peak acceleration of seismic waves was imposed under 70, 100, 300, and 400 gal El Centro wave excitation models. We found no obvious cracks until reaching displacement of 9.6 mm and horizontal force of +137.879 kN, at which point the corresponding peak acceleration of seismic waves was 300 gal. We continued reverse loading until finding oblique cracks in the wall as shown in Figure
MLQT-1 collapse state.
MLQT-2 was equipped with a 50 mm LRB masonry specimen and input with a damping ratio of 0.15 and 70, 100, 300, 400, and 510 gal El Centro wave excitation models [
MLQT-2: (a) LRB limit of displacement state; (b) LRB broken state.
As shown in Figure
Specimen MLQT-3 was equipped with a 57 mm LRB masonry specimen designed to be resistant to seismic waves of 400 gal peak acceleration. Once the peak acceleration reached 400 gal, the maximum displacement was 14.2 mm, i.e., below the allowable limit of 22.5 mm. The contact between the LRB and steel plate separated only slightly, which did not affect the continuation of the experiment. The maximum displacement was observed upon reaching 620 gal, at 26.4 mm, which does exceed the allowable limit. The specimen was considered to be broken at this time. The LRB internal steel plate was broken and fully exposed upon reaching 800 gal (Figure
MLQT-3: (a) LRB limit of displacement state; (b) LRB broken state.
MLQT-4 was equipped with a 90 mm LRB masonry specimen and designed to resist the peak acceleration of an 800 gal seismic wave [
MLQT-4: (a) LRB limit of displacement state; (b) LRB broken state.
As shown in Figure
We found that MLQT-1 280–400 gal showed a maximum displacement difference of −3 mm by −4 minus −1 mm, −7 minus −4 mm; the value changed suddenly and dramatically by the end of the test and diagonal cracks appeared through the wall. MLQT-2 reached a maximum displacement exceeding the allowable limit at 300 gal, as listed in Table
MLQT-1\MLQT-2 displacement.
Specimen number | Peak acceleration (gal) | Maximum displacement (mm) |
---|---|---|
140 | −1.879 | |
200 | −4.280 | |
280 | −7.251 | |
400 | 8.779 | |
200 | 9.990 | |
300 | 13.610 | |
400 | 16.657 | |
510 | 21.497 |
The MLQT-3 allowable displacement is 22.5 mm [
MLQT-3\MLQT-4 displacement.
Specimen number | Peak acceleration (gal) | Maximum displacement |
---|---|---|
400 | 14.231 mm (allowable disp 22.50 mm) | |
620 | ||
800 | ||
1000 | 50.943 mm (allowable disp 60.05 mm) | |
1240 | ||
1400 |
MLQT-1, from 35 to 70 gal, applied acceleration increase of 100%, and then max base shear increased by 130%. For an increased acceleration of 40%, from 70 to 100 gal, the max base shear increased by 34% (Table
Maximum shear with peak acceleration (MLQT-1).
Specimen number | Peak acceleration (gal) | Max base shear (kN) |
---|---|---|
MLQT-1 | 35 | 13.49 |
70 | −31.149 | |
100 | −41.830 | |
140 | −58.136 | |
200 | −98.837 | |
280 | 115.429 | |
400 | −131.231 |
Maximum shear with peak acceleration (MLQT-2).
Specimen number | Peak acceleration (gal) | Max base shear |
---|---|---|
MLQT-2 | 70 | 11.677 |
100 | 16.006 | |
200 | 34.855 | |
300 | 55.546 | |
400 | 72.753 | |
510 | 98.816 |
MLQT-2, at 70 to 100 gal, increased in applied acceleration by 40%, and max base shear increased by 37.04%. From 100 to 200 gal, acceleration increased by 50%, and max shear increased by 117.40%. From 200 to 300 gal, acceleration increased by 50%, and max shear increased by 59.36%. From 300 to 400 gal, acceleration increased by 30%, and max shear increased by 30.94%. From 400 to 510 gal, acceleration increased by 26%, and max shear increased by 35.82%. The numerical percentage variations are listed in Table
MLQT-3, from 100 to 200 gal, increased in applied acceleration by 50% [
Maximum shear with peak acceleration (MLQT-3).
Specimen number | Peak acceleration (gal) | Max base shear |
---|---|---|
MLQT-3 | 100 | 9.791 |
200 | 14.097 | |
280 | 17.660 | |
400 | 24.073 | |
620 | 40.825 | |
800 | 44.778 |
MLQT-4, from 70 to 140 gal, increased in applied acceleration by 100% and in max base shear by 50%. From 140 to 200 gal, acceleration increased by 40%, and max base shear increased by 30%. From 200 to 280 gal, acceleration increased by 40%, and max base shear increased by 75%. From 280 to 400 gal, acceleration increased by 40%, and max base shear increased by 10%. From 620 to 800 gal, acceleration increased by 30%, and max base shear increased by 20%. From 800 to 1,000 gal, acceleration increased by 25%, and max base shear increased by 10%. From 1,000 to 1,024 gal, acceleration increased by 20%, and max base shear increased by 10%. From 1,240 to 1,400 gal, acceleration increased by 13%, and max base shear increased by 3%. The numerical percentage variations are listed in Table
Maximum shear with peak acceleration (MLQT-4).
Specimen number | Peak acceleration (gal) | Max base shear (kN) |
---|---|---|
MLQT-4 | 70 | 2.045 |
140 | 3.019 | |
200 | 4.000 | |
280 | 7.000 | |
400 | 7.909 | |
620 | 11.206 | |
800 | 13.825 | |
1000 | 15.207 | |
1240 | 16.556 | |
1400 | 17.021 |
We drew a hysteretic curve under the action of various earthquake intensities according to the test data presented above [
MLQT-4 (800 gal) hysteretic curve: (a) hysteresis curve of 90 mm LRB wall; (b) maximum hysteresis loop area.
Upon reaching the yield load, MLQT-1 displacement growth accelerated though the hysteretic curve continued to present an inverse S shape. The load applied in the opposite direction decreased the wall’s stiffness due to the slip effect and yet-unclosed fractures [
When the LRB started working in the MLQT-2 specimen, the area of the hysteresis ring was approximately full [
The MLQT-3 hysteretic curve presented an inverse S trend in the negative direction (Figure
Specimens MLQT-3 hysteretic curve: (a) 100 gal; (b) 280 gal; (c) 400 gal; (d) 620 gal.
As per the MLQT-4 hysteretic curve, as shown in Figure
MLQT-4 hysteretic curve: (a) 70 gal; (b) 100 gal; (c) 200 gal; (d) 280 gal; (e) 400 gal; (f) 620 gal; (g) 800 gal; (h) 1000 gal; (i) 1240 gal.
Equivalent horizontal stiffness [
The relationship between isolation layers with each LRB equivalent horizontal stiffness is expressed as
We determined each LRB’s equivalent horizontal stiffness from MLQT-2, MLQT-3, and MLQT-4 for comparison against the design values. As shown in Figure
Equivalent horizontal stiffness: (a) MLQT-2; (b) MLQT-3; (c) MLQT-4.
We noted in our experiment that the lower connection plate of the LRB tended to separate from the rubber layer. This reduced the area of the connection between the rubber bottom and steel plate, causing a slight increase in vertical stress and slightly improving LRB horizontal stiffness. In MLQT-2 and MLQT-3, we found that the LRB components were broken due to the separation of the steel plate and rubber layer. The corresponding peak acceleration postyield stiffness and equivalent viscous damping ratio curve are further evidence of this phenomenon and further indicate that damage to the bearing affected the sample’s mechanical properties. The LRB must be repaired properly after an “intense” earthquake occurs.
We obtained hysteretic curves with different levels of simulated seismic intensity according to the experimental data. We then analyzed the LRB equivalent horizontal stiffness, postyield stiffness, and equivalent viscous damping ratio mechanical properties [
The postyield stiffness of the structural isolation layer is calculated as follows:
We calculated the LRB postyield stiffness for MLQT-2-4 for comparison with the design values as shown in Figure
Postyield stiffness: (a) MLQT-2; (b) MLQT-3; (c) MLQT-4.
The MLQT-4 postyield stiffness curve appears to be consistent with the relevant theory, as the elastic deformation range of the LRB is large. After the LRB yields, the stiffness rapidly increases where the contact area between the rubber layer and the connecting plate is stripped away. Compared to other LRB components, this is more obvious in the lower LRB (which has less rubber).
The equivalent viscous damping ratio is a key parameter determining the equivalent period based on displacement in a seismic design [
The equivalent viscous damping ratio of each LRB can be calculated as
Each LRB’s equivalent viscous damping ratio was obtained from MLQT-2-4 and compared with the 250% LRB shear deformation horizontal property as shown in Figure
Equivalent viscous damping ratio: (a) MLQT-2; (b) MLQT-3; (c) MLQT-4.
As shown in Figure
We conducted a horizontal stiffness experiment on five types of small LRB to explore various horizontal shearing strains and second shape coefficients as they affect the equivalent horizontal stiffness, yield stiffness, and hysteretic properties of the structure. We gave each shearing strain fitting formula an equivalent horizontal stiffness and yield stiffness while varying the second shape coefficient [
Residential buildings generally contain circle rubber bearings, the vertical stiffness and bearing capacity of which are related to the single rubber effective pressure area and free sides of the superficial area (first shape coefficient). Their stability is related to the inner rubber layer diameter divided by the total thickness of the inner rubber (second shape coefficient).
The LRB has the same steady vertical bearing capacity as other bearing components, in addition to favorable isolation, self-resetting, damping energy dissipation properties, and a large damping ratio (±25%). The LRB resilience model, which is commonly utilized in urban sky-rises, is a double linear model that has a much larger natural rubber bearing and high damping rubber bearing damping ratio; it is ineffective for rural dwelling isolation components. We used technical methods in this study to decrease the LRB damping ratio and observe the isolation effects in small- and medium-intensity earthquakes. We focused on the horizontal property design indicators of postyield stiffness, yield force, equivalent stiffness, and equivalent damping ratio.
We adopted inverse calculation methods for our LRB designs and built the seismic response spectrum method into our parameter calculations [
The maximum shear coefficient can be calculated as follows:
We obtained an LRB horizontal displacement-load-related curve from our experimental data adopting a sine wave of 0.5 Hz and shear strain of 100% third hysteresis. We calculated the experimental LRB equivalent horizontal stiffness
We calculated the equivalent horizontal stiffness related to shear strain from the experimental LRB hysteresis curve as shown in Figure
Relative equivalent horizontal stiffness with shear strain.
Figure
Relative postyield stiffness with shear strain.
The second shape coefficient (
Relative equivalent horizontal stiffness with the second shape coefficient.
Formulas (
As shown in Figure
We also calculated the experimental LRB postyield stiffness
Postyield stiffness related to the second shape coefficient.
Under the same vertical pressure action, the postyield stiffness
We next drew a pressure displacement-pressure curve to explore the vertical contraction stiffness after three loading cycles as shown in Table
Pressure stiffness Kv calculation results.
Bearing | 1# | 2# | 3# | 4# | 5# | |||||
---|---|---|---|---|---|---|---|---|---|---|
Number vertical | 1-1 | 1-2 | 2-1 | 2-2 | 3-1 | 3-2 | 4-1 | 4-2 | 5-1 | 5-2 |
Stiffness | 47.91 | 57.22 | 42.04 | 42.04 | 29.86 | 29.01 | 38.87 | 36.79 | 62.42 | 71.03 |
Figure
As shown in Figure
1# bearing third hysteretic loop comparison: (a) 0.5 Hz loading frequency; (b) 0.1 Hz loading frequency.
We separately input a 0.5 Hz sine wave to the five experimental LRB components and imposed maximum displacement loading of 50%, 100%, and 250%. There was no apparent difference among the LRBs in this case, so we redrew the LRB GZD-0.5 hysteretic curve for comparison as shown in Figure
GZ5-0.5 hysteretic curves with varying shear strain.
When the shear strain was 50% or 100%, the LRB hysteretic curves were rhomboid and every loop could be divided into four stages according to the loading process. We observed linear regularity among the horizontal loading and displacement indicators in this case. When the shear strain was 250%, the hysteretic curve formed an inverse S in a positive direction. The LRB stiffness degenerated to a certain extent as the inner rubber of the bearing slid along the steel plate. The area of the hysteretic curve increased as the shear strain increased, as the supporter degraded the energy resistance.
The LRB isolation effects can be balanced according to the horizontal seismic coefficient and horizontal displacement. Seismic fortification intensity is generally 6–8 degrees (0.20 g); in rural areas, the horizontal seismic coefficient should be less than 0.4. The isolation structure’s horizontal displacement should be less than 0.55 times the bearing’s effective diameter or 3-fold greater than the inner rubber’s total thickness [
We used a typical rural masonry dwelling to design our finite element calculation model and shaking table test model. The model is a two-layer single-bay brick masonry house with a reduced-scale (1 : 2) size of 2.25 m × 1.95 m × 3.3 m and a wall thickness of 120 mm. The four corners of the “house” were given four identical LRBs. The door was a one-layer 450 mm wide opening with sliding supporters (LRBs) on either side; the upper part of the slider was connected to the structure while the lower part slid freely along the pedestal plane.
We used finite element software SAP2000 to construct the isolated structure model. LRBs 1–4# were, respectively, imposed as model supporters and El Centro waves were input separately in
We analyzed the above model’s horizontal seismic coefficient and maximum horizontal displacement to determine the experimental LRB postyield stiffness and equivalent horizontal stiffness, as shown in Figures
Seismic coefficient related to postyield stiffness.
Horizontal displacement related to postyield stiffness.
Seismic coefficient related to equivalent horizontal stiffness.
Horizontal displacement related to equivalent horizontal stiffness.
The model seismic coefficient showed an increasing and nearly linear trend with LRB postyield addition. The coefficients were similar in
Formulas (
The model horizontal displacement decreased as the supporter postyield stiffness increased in a nearly linear relation [
As shown in Figures
LRB postyield stiffness should be 149.7–167.8 N/mm and equivalent horizontal stiffness should be 193.9–218.65 N/mm when the horizontal displacement is less than 60.5 mm and the seismic coefficient is below 0.4 requirements, so we selected the 4# LRB accordingly to conduct our shaking table test.
The isolated masonry structure horizontal seismic coefficient can be determined by multistorey masonry calculation. A smaller seismic coefficient indicates stronger seismic resistance but also generally reflects greater horizontal displacement in the LRB. The horizontal displacement thus must be restricted within a certain value; in this case, the isolation structure’s horizontal seismic coefficient should be less than 0.4.
We constructed a test bearing based on actual rural dwelling design and material requirements and then subjected it to a shaking table test. After inputting an 8.5 degree (300 gal peak acceleration) El Centro wave, we observed the deformation concentration in the isolation layer; the upper structure was altered but did not present any apparent cracks. When the seismic wave peak acceleration reached 800 gal, the structure remained intact and its maximum horizontal displacement value was permissible. To this effect, the proposed LRB is safe and feasible.
In an earthquake, the isolation layer presents horizontal displacement which creates a displacement in the upper structure. The seismic structure’s top storey may show greater displacement under certain earthquake conditions even when the isolation layer’s displacement is relatively small. The support will be destroyed when the isolation layer’s horizontal displacement exceeds the LRB limit; in this case, the entire upper structure may fail. We assert that support displacement should not exceed a minimum effective diameter of 0.55- or 3-fold greater than the inner rubber’s total thickness. The effective LRB diameters in this experiment were 110 mm, in which case the horizontal displacement limit is 60.5 mm.
We simulated an earthquake wave acting on this model in SAP2000. Again, five LRBs were modeled with 8.5 fortification intensity and a 0.3 g structure base displacement average value. As shown in Table
LRB base displacement and seismic coefficient results.
Supporter number | Base displacement (mm) | Seismic coefficient |
---|---|---|
1# | 50.412 | 0.507 |
2# | 72.261 | 0.265 |
3# | 64.6 | 0.382 |
4# | 56.11 | 0.373 |
5# | 44.227 | 0.544 |
We conducted an experiment to test the seismic performance and mechanical failure of several LRB structural specimens in this study, each with different parameters and excited by seismic waves of varying intensity. Our conclusions can be summarized as follows. The 50 mm thick LRB specimen MLQT-2 was ineffective as its rubber layer is too thin (3 × 1.2 mm). The 57 mm thick LRB specimen MLQT-3 LRB exceeds the limit displacement for strong-intensity seismic waves. LRB specimen MLQT-4, which is 90 mm thick, can withstand middle-intensity seismic waves. The LRB exceeds the limit displacement for strong-intensity seismic waves in this case, but the LRB and structure were unbroken by the end of the test (though any stronger seismic waves would cause the LRB to break) MLQT-4 was shown to withstand stronger peak acceleration seismic waves than other specimens due to its effective masonry performance and mortar strength. Changes in LRB thickness changes do not appear to affect bearing capacity but do change the position of the centroid. We recommend that the superstructure be designed according to extant standards and that the sliding bearing isolator support be placed in the appropriate position according to the stresses acting on the structure We wrote a seismic coefficient fitting formula that reflects the regular changes in small-diameter LRB horizontal displacement according to our shaking table test results. This formula may serve as a workable reference for practical LRB designs The structure’s horizontal seismic coefficient and horizontal displacement have a fittable relation with the LRB’s horizontal stiffness (provided that said stiffness falls within a reasonable range in the shaking table test) Various shear strains produce different forms of LRB equivalent horizontal stiffness and postyield indicators according to the second shape coefficient. When this coefficient is less than 4.8, the LRB equivalent horizontal stiffness changes in a stable manner and the curve of the two indicators can be accurately fitted. Restricting the second shape coefficient below 4.8 can assist in reducing the cost and material waste of the structure’s fabrication We analyzed the LRB horizontal stiffness with the structure model seismic coefficient and horizontal displacement relation to establish a curve-fitting formula. We input our shaking table test results to find that a small-diameter LRB remits ideal seismic resistance in typical, rural low masonry structures
The raw/processed data required to reproduce these findings cannot be shared at this time, as they are also being utilized in an ongoing study.
The work described in this article is part of the author’s own Ph.D. academic dissertation, “Low isolated masonry structures antiseismic property experimental study and its application.”
The author declares no conflicts of interest.
This work was funded by the Twelve Five National Science Supporting Plan Foundation of China (Grant no. 2014BAL06B04).