Seismic Conditions Required to Cause Structural Failures in Tectonic Earthquakes

Abstract

It is found that the failure of the structure conforming to the current seismic design code can only occur in the shear band of the tectonic earthquake, and with the increase in the amount of shear banding, the boundary conditions of the structure gradually deviate from the original design ones; therefore, the seismic insufficiency of structures therefore continues to increase. With the increase of the seismic insufficiency of the structure, the structure will appear more and more serious damage such as cracking, tilting and subsidence, and collapse. Based on the findings of this study, the author suggests that the main task of the seismic design of structures is to prevent the shear banding of tectonic earthquakes from extending to each element of the structure, rather than continuously increasing the level of vibration fortification of each structural element. Only in this way can it be ensured that the structures complying with the seismic design specifications will not be damaged such as cracks, tilting and subsidence, and collapse due to the deviation of the boundary conditions from the original design ones in shear banding.

1. Introduction

Although Zhang Heng invented the first ground vibration measuring instrument as early as 132 AD, and subsequent to that the seismic design codes of countries located within earthquake zones have specified increasingly strict vibration fortification standards for structures, it can be seen from Table 1 that the death toll of tectonic earthquakes remains high.

No.	Year	Country	Death
1	1556	China	830,000
2	1976	China	655,000
3	2010	Haiti	316,000
4	2004	Indonesia	280,000
5	2010	Haiti	316,000
6	526	Turkey	300,000
7	1920	China	273,400
8	1923	Japan	142,800
9	1948	Russia	110,000
10	1922	Philippines	100,000

Table 1.

The 10 major earthquakes that have caused the highest number of deaths around the world [1].

It has been established that traditional earthquake disaster mitigation scholars, in the absence of a clear definition of the seismic conditions that result in structural failure during tectonic earthquakes, have attributed such failures (illustrated in Figures 1–4) to insufficient protection against ground vibration resistance, and thus the vibration fortification specifications for structures have continued to be increased after tectonic earthquakes that have had a large impact. The main effect of a tectonic earthquake however results from shear banding, which accounts for more than 90% of the total energy dissipated by a seismic event; the secondary effect is ground vibration, whose energy accounts for less than 10% of the total seismic energy dissipation [6]. In fact, the earthquake disaster prevention methods proposed, based on this flawed understanding, including vibration isolation and vibration reduction, actually only increase the vibration resistance of structures under earthquake conditions that would not result in failure in any case. Since the seismic design specifications do not properly reflect the seismic conditions that result in structural failure during tectonic earthquakes, it is not possible to ensure that structures that fully comply with the seismic design specifications will not fail during earthquakes. In view of this, this chapter will first define the seismic conditions that do result in structural failure during tectonic earthquakes and then analyze the reasons why the traditional methods of earthquake disaster prevention cannot perform their desired functions.

Figure 1.

Damage sustained by the Zhenong Building in Taipei during the 418 Hualien earthquake of 2019 [2]: (a) building appearance; (b) cracks in the floor slab.

Figure 2.

Damage sustained by the Yutai Building in Taipei during the 418 Hualien earthquake of 2019 [3]: (a) failure of tilting and subsidence; (b) close-up of damage caused by tilting and subsidence.

Figure 3.

The Dongshing Building in Taipei collapsed during the 921 Jiji earthquake of 1999 [4].

Figure 4.

During the 921 Jiji earthquake of 1999: (a) Sanmin Junior High School in Hualien, Taiwan remained stable [5]; (b) Guangfu Junior High School in Taichung, Taiwan suffered severe damage. Note: The red line in (b) indicates the position of the first floor.

2. Seismic conditions that result in structural failure

Building seismic design codes are formulated and revised by experts in structural dynamics and soil dynamics and thus only pertain to ground vibration fortification. Hsu et al. [2] showed (using Figures 1–3) that the increase in the amount of shear banding during tectonic earthquakes in Taipei caused problems such as the cracking of the floor slab of the Zhenong Building, tilting and subsidence of the Yutai Building and collapse of the Dongshing Building.

As illustrated in Figures 1–3, it was determined that the seismic conditions that resulted in structural failure during tectonic earthquakes were the boundary conditions at the bottom ends of a part or all of the columns of a building gradually deviating from being a fixed end as specified in the original design, due to an increase in the accumulated amount of shear banding. The degree of damage sustained by the building increases with an increase in the extent of this deviation, i.e., it increases with an increase in the cumulative amount of shear banding.

Secondly, by comparing Figures 4a and b we see that during the 921 Jiji earthquake the school building located in a non-shear banding area (Figure 4a) remained stable and sustained no damage; however, the school building located in a shear banding area (Figure 4b) could not maintain stability and suffered serious failure.

As illustrated in Figures 1–4, it has thus been determined that (1) the seismic conditions that result in structural failure during earthquakes are the boundary conditions at the bottom ends of a part of the columns or all the columns of a building being unable to maintain the fixed end conditions of the original design; (2) the seismic conditions that do not result in structural failure during earthquakes are the boundary conditions at the bottom ends of all columns of the building maintaining the fixed end conditions of the original design.

2.1 Traditional pushover analysis and test results

Figure 5 shows the hyperbolic deformation mechanism after the bottom end of a column was set as the fixed end in a traditional pushover analysis and test, and Figure 6 shows the deformed mesh of a school building model obtained using traditional pushover analysis.

Figure 5.

The deformation mechanism generated after the bottom end of a column was set as the fixed end in a traditional pushover analysis and test [7].

Figure 6.

The deformed mesh for the model of Kouhu Elementary School building, Yunlin, Taiwan, for a traditional pushover analysis [8].

Figure 7a shows that before the traditional pushover test was conducted, the boundary conditions at the bottom end of each column of the selected physical school building had the fixed end conditions of the original design after the 921 Jiji earthquake; in other words, the school building had the required seismic conditions that would not result in structural failure during a tectonic earthquake. Figure 7b also shows that after the traditional pushover test of the physical school building was conducted, the boundary conditions at the bottom ends of all columns maintained the fixed end conditions of the original design.

Figure 7.

The traditional pushover test for the physical Kouhu Elementary School building, Yunlin, Taiwan [9]: (a) before test; (b) after test.

From Figure 4b, it can be seen that after the 921 Jiji earthquake, the boundary conditions of each column base of the physical school building of Guangfu Junior High School had deviated from the fixed end conditions of the original design, which is the seismic condition that results in structural failure during tectonic earthquakes, thus suffering serious damage. From Figures 6 and 7b, it can be deduced that whether traditional pushover analysis or traditional pushover testing is conduced, the boundary conditions of each column bottom in the structural analysis model maintained the fixed end conditions of the original design. Therefore, it is clear that the results obtained using these methods are not valid.

2.2 Shaking table test results

A shaking table is a rigid thick plate capable of vibrating according to an input ground vibration acceleration history. Before a shaking table test is conducted, the bottom ends of all the columns of the building model are fixed to the shaking table; in other words, the building model is set up prior to testing under the seismic conditions in which structural failure does not actually occur. Secondly, during the shaking table test, the model is pushed down under these same seismic conditions. Therefore, the failure pattern of the building model after the shaking table test has the same flaws as the pushover analysis result shown in Figure 6 and the pushover test result shown in Figure 7b, and therefore the results of the shaking table test are not valid.

It can be seen from Figures 6 and 7b that the failure mode of the building model during a shaking table test is that of collapse due to lateral forces under the condition of weak columns and strong beams. Since buildings designed by structural engineers must meet the requirements of the building seismic design code, this problem of weak columns and strong beams does not occur in practice; however, because the results of the shaking table test directly show that when the model fails, the bottom ends of its columns still maintain their fixed end boundary condition and fail in the weak column and strong beam mode; thus, the validity of the shaking table test results is further undermined.

2.3 Shear banding table test results

Figure 8 shows a building model placed on a shear banding table. When the left side of the shear banding table was lifted up obliquely relative to the right, the failure pattern of the building model was similar to that of the Guangfu Junior High School building in Taichung, Taiwan during the 921 Jiji earthquake (Figure 4b). Therefore, it is known that in the failure process of the building model during the earthquake, the building model first changed to have the seismic conditions that resulted in structure failure caused by shear banding. With the increase in the amount of shear banding, the degree of inability of the building model increases, and finally fails.

Figure 8.

The shear banding table test results of a building model [10].

Figure 9a shows a bridge model placed on a shear banding table. When the left side of the shear banding table was tilted and uplifted relative to the right side, the bridge model also underwent tilting and uplift. The failure pattern was similar to that of the Wuxi Bridge in Taichung, Taiwan due to the 921 Jiji earthquake as shown in Figure 9b. Therefore, it is known that during tectonic earthquakes, when a bridge is deformed by tilting and uplift, the seismic conditions shift from those that do not result in failure to those that do result in failure due to shear banding.

Figure 9.

Comparison of the tilting uplift failure of a model bridge and a real bridge [10]: (a) model bridge after the shear banding table test; (b) Wuxi Bridge in Taichung, Taiwan after the 921 Jiji earthquake.

Figure 10 shows another example of bridge failure by further uplift and tilting due to shear banding. Figure 10a shows a bridge model placed on the shear banding table. When the right side of the shear banding table was further tilted and uplifted relative to the left side, the failure pattern of the falling bridge model was similar to that of the Shiwei Bridge in Taichung, Taiwan during the 921 Jiji earthquake as shown in Figure 10b. Therefore, before the bridge fell during the tectonic earthquake, the initial seismic conditions that would not have resulted in failure are changed to those that would result in failure due to shear banding. Ultimately, the bridge collapsed after the amount of shear banding had increased significantly.

Figure 10.

Comparison of falling bridge phenomena [10]: (a) model bridge after a shear banding test; (b) the Shiwei Bridge in Taichung, Taiwan after the 921 Jiji earthquake.

Figure 11a shows a model of a weir placed on a shear banding table. When the right side of the shear banding table was tilted and uplifted relative to the left side, the failure pattern of the weir model was similar to that of the Shigang weir in Taichung, Taiwan during the 921 Jiji earthquake shown in Figure 11b. Therefore, before the weir failed during the tectonic earthquake, the initial seismic conditions that would not have resulted in weir failure were changed to those that would result in failure because of shear banding. Ultimately, the weir failed as the amount of shear banding was greatly increased.

Figure 11.

Comparison of the collapse of a model weir and a real weir [10]: (a) the model weir after the shear banding table test; (b) the weir in Shigang, Taichung, Taiwan after the 921 Jiji earthquake.

3. Seismic failure of a caisson pier

Since the traditional soil liquefaction safety factor, FS_L, is defined such that the ratio of the cyclic stress ratio of liquefaction resistance (CSRRL) to the period stress ratio of an earthquake (CSRE) be less than 1.0 [11], from the point of view of plastic mechanics this actually indicates soil yield, and it is thus quite easy to misjudge the cause of soil yield as soil liquefaction. Taking the 921 Jiji earthquake as an example, the rear line region of the caisson pier in Taichung Port, Taiwan (Figure 12) showed three different types of failure: subsidence, a pothole, and the spouting of silt, sand, and gravel.

Figure 12.

Different types of seismic failures at the rear line region of the caisson pier of Taichung port [12].

After the 921 Jiji earthquake, most traditional scholars believed that all three types of failure were caused by soil liquefaction. The reason they provided was that under the ground vibration of a tectonic earthquake and the densification process of the saturated loose sand below the groundwater table, the effective stress would have been reduced to zero or less than zero with the increase in the excess pore water pressure; therefore, soil liquefaction, by definition, would have occurred. Thus, it is believed by traditional scholars that the significant subsidence, the large pothole, and the ejection of silt, sand, and gravel shown in Figure 12 were all caused by soil liquefaction.

Only after identifying the major causes of the three different types of failures that occurred at Taichung Port during the 921 Jiji earthquake can we develop effective suppression methods to prevent such failures from taking place in the rear line region of other caisson piers.

In 2017, Hsu et al. [13] presented evidence that soil liquefaction occurs only in shear banding or shear texturing zones induced by the plastic strain softening of dense soil, but not in the yield failure of loose soil. In addition, the compacted soil of the rear line region of the caisson pier had already passed the field density quality test. According to the contract of the entrusted project, the degree of compaction was greater than 90%, and the corresponding relative density was greater than 70%. Therefore, the compacted soil was dense; however, the compacted soil of the rear line region of the caisson pier was misjudged as loose by conventional scholars in Taiwan.

Figure 13 shows a schematic profile of a caisson pier. It can be seen that the caisson pier is placed directly on the cobble base of the seabed. At low tide and in the absence of embedded depth, D_f when depth h₂ from the seawater table to the seabed is less than depth h₁ from the groundwater table of the rear line region to the seabed and the hydraulic gradient i of the water exit point E (shown in Figure 13) is greater than the critical hydraulic gradient i_c, then some sandy gravel backfill in the rear line region of the caisson pier flows out to the seabed below the seawater table due to piping failure (as shown schematically in Figure 14), and then large piping holes appear such as those shown in Figures 12 and 14, respectively.

Figure 13.

Schematic diagram of the caisson pier profile [14].

Figure 14.

Schematic diagram of the propagation of the arching effect and the appearance of a piping hole in the rear line region of a caisson pier (reproduced from [12]).

Furthermore, Figure 15a shows the test model of the caisson pier with very dense backfill in its rear line region. Figure 15b shows that when the caisson pier is turned seawards, its rear line region appears to have shear textures with different strikes, resulting in substantial subsidence. The shear textures shown in Figure 15c include the principal shear D, thrust shear P, and Riedel shear R. During tectonic earthquakes, when shear textures of different strikes are dislocated, high excess pore water pressure will locally appear in the shear textures, and so the groundwater in the shear textures will entrain the brittle fractured silt, sand, and gravel and eject upward (see Figure 12) along the outlet tunnel formed by the pore space of the shear texture.

Figure 15.

Test results of shear textures and subsidence induced by the inclined caisson pier [12]: (a) before test; (b) after test; (c) the induced shear textures and uneven subsidence.

The test results in Figure 15 show that the subsidence shown in Figure 12 was caused by the caisson pier turning seawards, rather than by soil liquefaction as claimed in the past.

Hsu et al. [13] proposed the three constituent elements that must exist in order to induce soil liquefaction based on real-world data: (1) local shear banding or shear texturing during tectonic earthquakes; (2) high excess pore water pressure localized in the shear band or in the shear texture; (3) groundwater entrained silt, sand, and/or gravel ejection upward along the outlet tunnel formed by the pore space of the brittle fractured shear band or shear texture. For the ejected silt, sand, and gravel shown in Figure 12, the cause was soil liquefaction since the three elements required for soil liquefaction clearly existed.

4. Methods of earthquake-resistance and building reinforcement

Traditional building earthquake-resistance and reinforcement methods include the installation of vibration isolation pads, the installation of dampers, and increasing the stiffness of superstructural elements such as columns, beams, panels, and walls, thereby inducing vibration isolation, vibration reduction, and vibration resistance. Therefore, traditional earthquake-resistance and reinforcement methods only improve the vibration fortification level of a building under the seismic conditions required to prevent structural failure, but do not have an impact on the conditions in which structural failure does in fact occur due to shear banding during tectonic earthquakes. Therefore, buildings will still fail under the shear banding effect in future tectonic earthquakes.

The school building earthquake-resistance and reinforcement methods provided by the National Center for Research on Earthquake Engineering of Taiwan after the 921 Jiji earthquake included the reinforced concrete (RC) jacketing retrofit method, the RC wing wall retrofit method, the shear wall retrofit method, and the composite column retrofit method. It turns out that these methods can only improve the fortification level of a building against seismic vibration conditions required to prevent structural failure, but do not protect the building from failing under the shear banding effect of future tectonic earthquakes.

Since the failure of buildings during tectonic earthquakes is mainly caused by the shear band or shear texture extending into the area surrounding the shear failure plane induced in the foundation soil under the ultimate load, when the safety factor of the earthquake bearing capacity of a foundation is less than 1.0, earthquake subsidence will be induced; after the foundation loses its stability, an asymmetrical general shear failure plane will be generated, which will lead to the failure of the foundation and building [15]. Therefore, in order to effectively prevent the collapse of buildings during tectonic earthquakes, earthquake-resistance and reinforcement methods need to restrain the shear band or the shear texture that is induced by the ultimate load of a tectonic earthquake from extending into the area surrounding the shear failure plane in the foundation soil (see Figure 16). Only in this way can it be ensured that buildings complying with the seismic design specifications for ground vibration fortification will not be affected by shear banding or shear texturing, thereby ensuring the stability and safety of buildings during tectonic earthquakes.

Figure 16.

Schematic diagram of effective structural earthquake-resistance and reinforcement methods for restraining the propagation of shear banding or shear texturing [16].

5. Conclusions

It has been 1890 years since the invention of the first ground vibration measuring instrument. During the whole of recorded history, the vibration fortification level specified by earthquake-resistant design codes has continued to increase, but the associated death toll due to earthquakes is still high. In view of this, the author has outlined the seismic conditions in which structural failure does in fact occur during tectonic earthquakes so as to explore the causes of failure of different structures and thereby reached the following six conclusions:

1. During a tectonic earthquake, the failure of the structure is caused by the shear banding or shear texturing induced by the tectonic earthquake, resulting in the seismic conditions changing to those that do cause structural failure.

2. In the pushover test and shaking table test, the failure of the building model occurs under the seismic conditions that do not, in reality, result in structural failures. Therefore, the failure modes of the building models are completely different to the failure modes of the physical buildings in actuality; the results of the pushover tests and the shaking table tests are therefore unrealistic.

3. In the shear banding table test, the failure of the building model occurs when the shear banding of the tectonic earthquake induces the seismic conditions to change from those that do not result in structural failure to those that do, and the failure of the physical buildings also follow such a pattern. In other words, the failure mode obtained from these tests are similar to those of actual buildings under the shear banding effect of tectonic earthquakes. Therefore, the results of the shear banding test are realistic.

4. Traditional scholars define the yield failure of saturated loose sand as soil liquefaction, without including the three constituent elements required for soil liquefaction of dense sand produced in the process of strain softening caused by the shear banding or shear texturing of tectonic earthquakes.

5. Seismic failure of the rear line region of a particular caisson pier included great subsidence, a large pothole, and the spouting of silt, sand, and gravel. The great subsidence was caused by the rotation or movement of the pier towards the sea; the cause of the large pothole was a piping failure, and the cause of the ejection of silt, sand, and gravel was soil liquefaction induced by shear texturing. These causes are different from the conclusions drawn by traditional scholars.

6. After the 921 Jiji earthquake, Taiwan completed the earthquake-resistance and reinforcement of school buildings at a total cost of more than NT$40 billion. The methods provided by the National Centre for Research on Earthquake Engineering only increased the fortification level of the columns, beams, and slabs under seismic vibration conditions to prevent structural failure, and so the school building will still collapse from the shear banding effect of future tectonic earthquakes.

Acknowledgments

The previous work of this research is a part of the preliminary studies on the stability of existing earth structures as part of the Repair, Evaluation, Maintenance, and Rehabilitation Research Program (REMR). Financial support provided by the office of Chief of Engineers, U. S. Army is acknowledged with thanks. Close consultation with Dr. S. K. Saxena and Dr. J. F. Peters was of great benefit in determining the results of the computer analyses. The chance to use the computer facilities in the U. S. Army Engineer, Waterways Experiment Station to finish most of the computer work in this research is highly appreciated.