Damage characteristics and dynamic stress response of aging masonry structures for blast-induced ground motion were performed using high-order local modal analysis method. A complete investigation of damage types and locations of aging masonry buildings due to tunnel blasting vibration were performed by on-site survey. A typical 2-storey aging masonry building located above a tunnel was selected for dynamic response analysis. The experimental dynamic characteristics of the structure were determined by using the operational modal analysis (OMA) method. Finite element models for the masonry structures were updated by modifying material parameters based on OMA results. The first five natural frequencies of the updated finite element models ranged from 8.80–24.99 Hz, and the first five modes were global modes. The sixth to twentieth natural frequencies ranged from 26.10–36.34 Hz, and the sixth to twentieth modes were local modes whose deformation was greater than the global deformation. Since the principal frequencies of the tunnel blast vibration were mostly higher than the natural global modes’ frequencies and were much closer to the natural frequencies of local members, local members experienced more intensive vibrations compared to the main body structure. The principal compressive stress (PCS) and principal tensile stress (PTS) of local members were several times greater than that of the main body structure. Therefore, local members of the masonry building suffered most from the tunnel blasting vibration. Corners due to stress concentration, the contact area between brick and concrete, local members, and precast floor seams are prone to damage during tunnel blasting. With the vibration velocity increasing, the PCS and PTS of local members gradually increase. But, the PTS ratio of local members decreases with the increase of peak particle velocities. The dynamic response analysis result and the damage locations using high-order local modal analysis method are in accordance with the damage found at the site.
Nowadays, with the remarkable progress of railways, highways, and subways, there is an increasing number of shallow buried tunnels being built beneath buildings in old urban districts. Damage to aging buildings due to weakened seismic capacity is common during tunnel drilling and blasting. Frequent vibration induced by tunnel blasting further exacerbates damage to the building and may cause serious failure of the building. Multiple damage analyses of buildings near tunnel blasting projects were conducted. Results showed that some local non-load-bearing members of structures such as corners of stress concentration, brick and concrete contact areas, precast floor seams, and infilled walls experienced cracking. However, cracking in load-bearing components, such as beams, slabs, columns, and shear walls, was not found. High-frequency tunnel blasting induced damage characteristics are clearly different from damage induced by natural seismic ground motion.
Recently, much effort has been spent on estimating the dynamic response and damage to frame and masonry structures relative to blasting-induced ground motion. The structural damage of a typical low-to high-rise RC frames is performed using a shaking table on a 1 : 5-scale frame model. Conventional damage assessment methods adopted in seismic analysis are not applicable for high-frequency ground motion [
Safety assessments of structures subjected to near-field blast-induced ground excitations were firstly performed using OMA. A reinforced concrete building, a masonry building, a reinforced concrete highway bridge, and a masonry arch bridge were selected for safety evaluation. The OMA method can determine experimental dynamic characteristics of structures under near-field blast-induced ground excitations [
The method of indirect vibration monitoring and safety control standard of the deep underground pipeline was proposed [
In this study, a damage assessment of local members of a building near a tunnel excavation is performed using the OMA method. Vibration characteristics are measured during blasting around the building. A complete investigation of damage types and locations of aging masonry buildings is performed by an on-site survey. The initial model of the selected 2-storey masonry structure is constructed, and the analytical frequencies and mode shapes are attained using the ANSYS finite element program. Experimental dynamic characteristics (natural frequencies, mode shapes, and damping ratios) of the structure are determined via the OMA method. Analytical and experimental mode characteristics are compared, and finite element models of the masonry structures are updated by modifying material parameters. Global and local building modes are analyzed using the updated finite element models. The interaction between external blast vibrations, structure global modes, and local modes are analyzed. The dynamic response of local members of masonry structures under blast-induced ground excitations is examined using the updated finite element models. The stresses on various local components in masonry structures in different conditions are studied, and the damage mechanism and location for each masonry structure is obtained.
The New Hongyan Tunnel in the Chengdu-Chongqing High-Speed Railway has a length of 6690 m and is located in the city of Chongqing. The shallow portion of the tunnel is situated at the entrance/exit to the high-speed railway. Tunnel depth varies from 10 to 50 m, approximately. The overlying soils are Quaternary gravel, soil, silt, and clay. The bedrock is composed of alternating mudstone and sandstone layers. 29% of the surrounding rock is grade V and 71% of the surrounding rock is grade IV. Houses are very dense around the tunnel; 2- and 3-storey aging brick houses account for most of the structures. Brick houses were built in the 1970s or 1980s. Aging masonry structures are approximately between 16 m and 40 m away from the tunnel vault crown. Because brick houses are weak and poor, the vibration induced by tunnel blasting poses a serious threat to the safety of the houses.
Peak particular velocity (PPV) and dominant frequency (DF) are measured during blasting around the buildings on hard soil to evaluate the effects of blasting on the buildings. Masonry buildings above the tunnel are approximately between 16 m and 40 m away from the tunnel vault.
In this study, UBOX-5016 is used for recording vibrations produced in the tunnel. Blasting vibration characteristics are measured by vibration sensors with a biaxial speedometer (vertical and longitudinal). Vibration sensors are located on hard ground in the direction of blasting (Figure
Photograph showing the UBOX-5016 instrument and vibration sensors.
A total fifty measurements were taken from the tunnel during a 3-month period. Only nine measurements are considered in this study. The tunnel depth, distance away from the blasting center, PPV, and DF of the nine measurements are presented in Table
Vibration characteristics of the blasting.
Blasting number | Detonator type | Tunnel depth (m) | Distance away from blasting center (m) |
|
|
|
|
---|---|---|---|---|---|---|---|
1 | Nonelectric | 17.9 | 30.7 | 2.974 | 70.80 | 0.761 | 20.75 |
2 | Nonelectric | 18.2 | 32.6 | 2.227 | 76.90 | 0.807 | 21.97 |
3 | Electronic | 17.5 | 29.2 | 1.940 | 46.99 | 0.651 | 11.60 |
4 | Electronic | 37.6 | 43.1 | 1.395 | 92.77 | 0.975 | 64.70 |
5 | Electronic | 35.6 | 41.8 | 1.003 | 77.52 | 0.269 | 62.26 |
6 | Electronic | 22.9 | 31.1 | 1.307 | 141.60 | 0.858 | 62.86 |
7 | Electronic | 18.6 | 30.5 | 1.376 | 137.94 | 0.676 | 87.89 |
8 | Electronic | 17.9 | 29.2 | 1.023 | 78.74 | 0.622 | 62.87 |
9 | Electronic | 16.9 | 28.0 | 0.902 | 76.90 | 0.590 | 22.50 |
Layout of blast holes and initiation time (unit: ms). (a) Using nonelectric detonator. (b) Using digital electronic detonator.
Time history of velocity and Fourier amplitude of
As seen in Table
A complete investigation of damage types and locations of masonry buildings due to tunnel blasting vibration is performed by on-site survey. The damage caused by intensive blasting vibration is classified into four types according to the damage location.
The stress concentration points are the parts of a structure that are most likely to crack under tunnel blasting vibration. Common stress concentration points include door corners, window corners, and wall corners (Figure
Cracks of the stress concentrated area.
The higher strength and elastic modulus of concrete relative to brick lead to great change in stiffness and uneven force. The stress along the contact between a brick wall and concrete floor is greater than other contacts. Cracking of the floor and wall contact is shown in Figure
Cracks of floor and wall contact area.
Precast floors have a significantly different structure from other common floors. Because of use of concrete to grout seal between prefabricated floors without steel connection, it leads to a weak connection between each precast floor section. Because of this weak connection and stiffness mutation, joints between prefabricated floors are prone to cracking under tunnel blasting vibration. Joints may further lead to numerous other negative effects. Rainfall could erode the floor and walls and other appurtenances, as shown in Figure
Cracks of precast floor slab joint.
Because of their lower strength and elastic modulus, infilled walls or non-load-bearing walls are prone to cracking under high transient tensile and shear stress induced by tunnel blasting. Cracking of infilled walls or non-load-bearing walls is shown in Figure
Cracking of infilled walls.
Above all, damage in the masonry structure commonly occurred in local members. The reasons are explored by analyzing the simulation results using the modal analysis method. Before that, the finite element model, which represents the actual dynamic characteristics of the masonry structure, is established and updated based on the results of the OMA test.
The selected masonry building is a two-storey brick concrete building constructed in the early 1980s with a floor area of approximately 200 m2 (Figure
Photographs showing the two-storey masonry building.
The analytical model for the masonry building is constituted using the ANSYS finite element program. Modal analysis of the building is carried out to calculate natural frequencies and mode shapes. The analytical model is created after an in situ investigation of the building’s structure. In the analytical model, columns, walls, beams, and other members are modeled using solid elements with six degrees of freedom in each node (translation in
Analytical model of the masonry building. (a) Masonry building. (b) Section of the first floor. (c) Section of the second floor.
The mechanical properties of the building materials are given in Table
Mechanical properties of building materials.
Material | Density (kg/m3) | Modulus of elasticity (GPa) | Modulus of shear (GPa) | Poisson ratio |
---|---|---|---|---|
Masonry | 1800 | 2.70 | 1.08 | 0.15 |
Concrete | 2300 | 23.75 | 9.50 | 0.20 |
It is assumed that all degrees of freedom of the base points are fixed, and the first four natural frequencies and corresponding mode shapes are calculated. The first four natural frequencies range between 9 and 23 Hz. The first mode of the building is a first-order longitudinal buckling. The second mode is a first-order transverse buckling. The third mode is torsion, and the fourth mode is a second-order longitudinal buckling.
There are two different test methods available to experimentally identify dynamic system parameters of a structure, experimental modal analysis (EMA) and OMA [
Schematic diagram showing the layout of the measurement points (unit: cm). (a) First floor. (b) Second floor.
Photographs showing measurement equipment.
An 8-channel data logger (INV3060S) is used for acquiring the signals from the speedometers. Signals are transferred into a DASP program in the laptop via cross cable. Signals are transferred from the DASP program to obtain modal parameters. Tests are approximately 5 minutes long. Therefore, measurement begins at least 2 minutes before blasting and continued after blasting. A typical signal recorded in test is given in Figure
A typical recorded test signal (no. 1).
Autospectra of a recorded signal (no. 1).
The frequency response function obtained from the EFDD technique.
Modal parameters of masonry building under tunnel blasting vibration.
Mode number | Frequency (Hz) | Damping ratio (%) |
---|---|---|
1 | 9.224 | 3.11 |
2 | 11.596 | 3.52 |
3 | 15.640 | 5.79 |
4 | 25.351 | 4.23 |
The purpose of the OMA test is to identify the natural frequencies and mode shapes, which can be used to update the initial analytical model. Due to the limited number of measurement points, it is difficult to obtain the higher local modes for large buildings. The first through fourth global modes are acquired easily, and the initial analytical model is updated based on these modes.
Analytical dynamic characteristics do not coincide with experimental characteristics. These discrepancies mainly originate from the uncertainties in the materials and inaccurate boundary conditions. The main purpose of the model updating procedure is to minimize differences between analytical and experimental dynamic characteristics by varying uncertainty parameters such as material properties and boundary conditions [
Because the number of updating material parameters is larger than the four known modal parameters, a proper objective function is minimized to acquire the optimal material parameters using the manual tuning procedure. Therefore, the model updating objective function is
In equation (
The model updating of the masonry structure has been achieved by Guan [
Natural frequencies of the masonry building for initial and updated models.
Mode number | Natural frequencies (Hz) | ||
---|---|---|---|
Initial analytical model | Updated analytical model | Experimental | |
1 | 9.026 | 8.804 | 9.185 |
2 | 13.060 | 12.457 | 11.708 |
3 | 16.143 | 15.989 | 15.655 |
4 | 23.698 | 23.123 | 25.118 |
After changing the material parameters, the updated model is taken as the model that best represents the actual building. The local modes, dynamic response, and damage analysis are based on this updated model.
The building modes can be separated into global modes and local modes. Global modes are characterized by uniform deformation in the main structure. Local modes are characterized by relatively little deformation in the main structure and greater deformation in the local floor and shell. Local deformation is much larger than global deformation in local modes. Local modes are easily obtained by comparing the finite element modal analysis with the experimental method. Global modes and local modes of the masonry building are obtained by using ANSYS to carry out finite element modal analysis.
The first 20 natural frequencies of the structure range from 8.80–36.34 Hz. The dynamic characteristics of lower order global modes and higher order local modes of the masonry building are as follows: The first through fifth natural frequencies of the structure range from 8.80–24.99 Hz (Table
Natural frequencies of the masonry building for initial and updated models.
Modal no. | Frequency (Hz) | Modal shape |
---|---|---|
1 | 8.80 | First-order buckling longitudinal global deformation |
2 | 12.46 | First-order transverse buckling global deformation |
3 | 15.99 | Torsion global deformation |
4 | 23.12 | Second-order longitudinal buckling global deformation |
5 | 24.99 | Second-order transverse buckling global deformation |
6 | 26.10 | Left side wall of second floor and front parapet wall local deformation |
7 | 26.55 | Right side wall of second floor local deformation |
8 | 28.71 | Right side wall of second floor local deformation |
9 | 29.91 | Longitudinal partition wall of first floor and front parapet wall local deformation |
10 | 30.09 | Longitudinal partition wall of first floor local deformation |
11 | 30.16 | Longitudinal partition wall of first floor local deformation |
12 | 30.38 | Transverse partition wall of second floor and front parapet wall local deformation |
13 | 31.30 | Right side wall and transverse partition wall of second floor local deformation |
14 | 31.54 | Front parapet wall, right side wall, and transverse partition wall of second floor local deformation |
15 | 32.55 | Front parapet wall, right side wall, and transverse partition wall of second floor local deformation |
16 | 32.97 | Front parapet wall, transverse wall of first floor, and transverse partition wall of second floor local deformation |
17 | 33.60 | Partition wall of second floor, balcony, and front parapet wall local deformation |
18 | 33.98 | Balcony and front parapet wall local deformation |
19 | 35.47 | Balcony, transverse partition wall of second floor, and right window side wall local deformation |
20 | 36.34 | Balcony, transverse partition wall of second floor, and right window side wall local deformation |
The sixth through 20th natural frequencies of the structure range from 26.10–36.34 Hz (Table
Local modal shapes of the masonry building [
Mode 6 (
In local modes of the building, local deformation in the side wall, partition wall, and parapet wall (structure’s prominent part) is much greater than the main structure. In this study, by establishing two numerical models, the natural frequencies of the above local members are calculated. In order to simplify the analysis, masonry is assumed to be isotropic. The density of masonry is 1800 kg/m3, elastic modulus is 2.5E9Pa, and Poisson’s ratio is 0.15. With regard to the side wall or partition wall, it is assumed that
First through 10th natural frequencies of the building’s side wall and parapet wall.
Local member | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Side wall (Hz) | 21.94 | 37.57 | 68.70 | 88.92 | 93.27 | 93.57 | 98.38 | 136.84 | 146.16 | 157.55 |
Parapet wall (Hz) | 5.09 | 17.44 | 31.05 | 33.56 | 56.81 | 75.94 | 84.15 | 98.38 | 110.20 | 112.59 |
The first through 10th natural frequencies of the side wall and parapet wall range from 21.94–157.55 Hz and 5.09–112.59 Hz, respectively. The modal shapes of side wall and parapet wall are given in Figures
Modal shapes of side wall of the building. (a) Mode 1 (
Modal shapes of parapet wall of the building. (a) Mode 1 (
Different members, such as load-bearing walls, cantilever beams, floor, partition walls, side walls, parapet walls, and balconies, compose the masonry building. Global or local vibration modes depend on the dominant frequencies of external ground motion. The interaction between external ground motion and structure modes is given in Figure
The interaction between external ground motion and structure modes.
From Figure If the dominant external ground motion frequencies are close to global mode natural frequencies, the members will vibrate in those global modals and appear to have uniform and global deformation. Consider the earthquake as an example: since the frequency of the earthquake is 0–10 Hz, it will lead to the global deformation and global collapse. If the dominant external ground motion frequencies are close to local mode natural frequencies, members will vibrate in those local modals and appear to have different deformation. Under high-frequency ground motion, local members, such as the front parapet wall, longitudinal partition wall, side wall, partition wall, and balcony, appear to record greater deformation than the global structure. Seismic waves induced by shallow tunnel blasts are commonly high frequency. As given in Table
For any modal component
The total displacement vector
It should be noted that for most types of lower frequency loading, displacement is generally greatest for lower modes and tends to decrease for higher modes. Therefore, it is usually not necessary to include higher vibration modes in the superposition calculation. However, for high-frequency loading, higher vibration modes should be taken into superposition calculation.
The stresses or forces developed in various structural components can be evaluated directly from the displacements. The elastic forces
Because each modal contribution is multiplied by the square of the modal frequency in equation (
In order to investigate the change in stress of the masonry structure, high and low principal frequency seismic waves are applied only in one direction or two directions at the base of the building. Stresses on local members and main structural components are obtained by using LS-DYNA to perform a dynamic analysis. Regardless of floor live loads, dead loads, and blast vibration loads, the final calculated stress response is induced by gravity and blasting loads.
The masonry failure can be divided into three different modes (Figure
Graph showing the strength envelope in the
The masonry structure is mainly under pressure subjected to the blasting seismic waves. Firstly, the PCS of the masonry structure caused by blasting seismic waves in
PCS contour of the structure (
PCS contour of first floor section the structure (
PCS and PCS ratio of local members under different peak particle velocities.
Type | Different members | Typical elements | Maximum PCS (MPa) | PCS ratio | Maximum PCS (MPa) | PCS ratio | Maximum PCS (MPa) | PCS ratio |
---|---|---|---|---|---|---|---|---|
1.0 (cm/s) | 3.0 (cm/s) | 6.0 (cm/s) | ||||||
Main structure | Longitudinal wall | H116939 | 0.17 | 1.00 | 0.18 | 1.00 | 0.25 | 1.00 |
Local members | Partition wall | H99361 | 0.53 | 3.12 | 0.57 | 3.17 | 0.69 | 2.76 |
Front parapet wall | H41244 | 0.40 | 2.35 | 0.49 | 2.72 | 0.68 | 2.72 | |
Stress concentration | Window corners | H30050 | 0.61 | 3.59 | 0.67 | 3.72 | 0.84 | 3.36 |
Door corners | H117493 | 0.76 | 4.47 | 0.88 | 4.89 | 1.12 | 4.48 | |
Floor and wall contact area | First floor and wall contact area | H52535 | 0.98 | 5.76 | 1.07 | 5.94 | 1.40 | 5.60 |
The PCS curve of local members under different peak particle velocities.
From Table Due to the sudden change of stiffness, the stress concentration of floor and wall contact area is caused. As a result, the stress level of the brick wall at the interface is the highest, and the PCS of floor and wall contact area is about 6 times larger than that of the longitudinal wall stress, which is prone to damage. Secondly, due to the obvious stress concentration in the corner, the PCS of the door corner and window corner is about 3 to 5 times larger than that of the longitudinal wall. Next, the PCS of local members of high-order local modes is about 2 to 3 times larger than that of the longitudinal wall because of intensive vibration. The PCS of the longitudinal wall is lowest. With the vibration velocity increasing, the PCS of members gradually increases. It indicates that the increase of velocity of blasting seismic wave will increase the corresponding dynamic response of the structure, and the peak value of the structural stress will also gradually increase, which will lead to increase the possibility of structural damage or aggravate structural damage.
The damage of masonry structure is controlled by the maximum principal tensile stress subjected to the blasting seismic waves. Firstly, the PTS of the masonry structure caused by blasting seismic waves in
PTS contour of the structure (
PTS contour on the first floor cross section (
PTS and PTS ratio of local members under different peak particle velocities.
Type | Different members | Typical elements | Maximum PTS (MPa) | PTS ratio | Maximum PTS (MPa) | PTS ratio | Maximum PTS (MPa) | PTS ratio |
---|---|---|---|---|---|---|---|---|
1.0 (cm/s) | 3.0 (cm/s) | 6.0 (cm/s) | ||||||
Main structure | Longitudinal wall | H116939 | 0.034 | 1.00 | 0.058 | 1.00 | 0.098 | 1.00 |
Local members | Balcony | H65943 | 0.24 | 7.06 | 0.16 | 2.76 | 0.22 | 2.24 |
Partition wall | H99337 | 0.27 | 7.94 | 0.37 | 6.38 | 0.49 | 5.00 | |
Front parapet wall | H90876 | 0.51 | 15.00 | 0.60 | 10.34 | 0.70 | 7.14 | |
Stress concentration | Window corners | H117694 | 0.34 | 10.00 | 0.28 | 4.83 | 0.38 | 3.88 |
Door corners | H86620 | 0.70 | 20.59 | 0.71 | 12.24 | 0.99 | 10.10 | |
Window corners of side wall | H101479 | 0.55 | 16.18 | 0.65 | 11.21 | 0.80 | 8.16 | |
Floor and wall contact area | First floor and wall contact area | H137665 | 0.35 | 10.29 | 0.36 | 6.21 | 0.40 | 4.08 |
The PTS curve of local members under different peak particle velocities.
The PTS ratio curve of local members under different peak particle velocities.
From Table The PTS of different local members of the masonry structure appears to vary widely. The PTS of the longitudinal wall is minimized. Due to the stress concentration in local members, such as window corners and door corners, their PTS is maximized. Besides this, the PTS of corners is about 3 to 21 times higher than that of the longitudinal wall. Next, the PTS of local members in local modes with intensive vibration, such as the balcony, partition wall, and front parapet wall, is approximately 2 to 15 times larger than the longitudinal wall. Finally, the PTS of floor and wall contact area is approximately 4 to 10 times larger than the longitudinal wall. With the vibration velocity increasing, the PTS of members gradually increases. It shows that the increase of velocity of blasting seismic wave will remarkably enlarge the dynamic response of the structure, which will lead to increase the possibility of structural damage or aggravate structural damage. The PTS ratio of local members decreases with the increase of peak particle velocities. The PTS of the longitudinal wall becomes larger significantly with the increase of peak particle velocities so that the PTS ratio becomes smaller.
The stress response is more significant than the displacement response for a structure under high-frequency ground motion induced by tunnel blasting. The damage is governed by the stress because of the short duration of the blasting vibration. Based on the modal analysis, the frequencies of blasting seismic waves in the near-zone are commonly close to local mode frequencies, which result in intensive vibration in the local members. On the other hand, by analyzing the dynamic responses of the masonry structure under tunnel blasting vibration, the tensile stress of local members is approximately several times larger than the main body structure. When the tensile stress of a local member exceeds the tensile strength of the material, the local member will be damaged and will crack. With regard to the masonry building, masonry is more vulnerable compared to concrete. Since the compressive strength of a brick wall is much larger than the tensile strength, compression failure of the brick walls does not occur while tensile failure of the brick wall is likely to occur. The stress concentration points, such as door corners and window corners, may crack at a relatively low peak velocity. With increasing peak particle velocity, the stress on local members with larger deformation and concrete and brick contact area, such as the parapet, mid-board, and balcony, floor-wall contact area, may exceed the mechanical strength of the material and crack. The main structure of the masonry building is unlikely to record damage due to the relatively low stresses. Damaged locations in the masonry structure found at the site are in accordance with the dynamic response result. The sequence diagram of structural damage is shown in Figure
The sequence diagram of structural damage.
Damage assessment and dynamic response of aging masonry structures for blast-induced ground motion are performed by using the modal analysis method. Based on the on-site survey and numerical results, the following conclusions can be drawn: (1) in the near shallow tunnel blasting, the blasting seismic waves always have a high frequency, large peak velocity, and short duration time. The damage is common in local members of the structure, consisting of stress concentration points, precast floor joints, and the contact between concrete floors and masonry walls. (2) The first five natural frequencies ranged from 8.80 to 24.99 Hz. The sixth through twentieth natural frequencies ranged from 26.10 to 36.34 Hz, and the deformation of sixth through twentieth was greater than the global deformation. Because the principal frequencies of tunnel blast vibration were closer to the natural frequencies of local members, local members experience more intense vibrations. (3) The principal compressive stress (PCS) and principal tensile stress (PTS) of local members were several times greater than those of the main body structure. Therefore, local members of the masonry building suffered most from the tunnel blasting vibration. With the vibration velocity increasing, the PCS and PTS of local members gradually increase. But, the PTS ratio of local members decreases with the increase of peak particle velocities. The dynamic response analysis result and the damage locations using high-order local modal analysis method are in accordance with the damage found at the site.
The data used to support the findings of this study are included within the article. All authors confirm that there are no restrictions on sharing of data and/or materials.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (project no. 51708317), first-class discipline project funded by the Education Department of Shandong Province, and China Postdoctoral Science Foundation (2017M612226).