Startseite Comparison of several seismic active earth pressure calculation methods for retaining structures
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Comparison of several seismic active earth pressure calculation methods for retaining structures

  • Xin Huang , Yanyang Qiao , Xiaoguang Cai EMAIL logo , Jingshan Bo , Sihan Li und Yueqiang Li
Veröffentlicht/Copyright: 15. Oktober 2025
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Abstract

Earthquake earth pressure is one of the key parameters for the seismic design of retaining structures. In this work, the seismic earth pressure calculation methods used in the design specifications of retaining walls, bridge abutments, and other retaining structures in various countries are summarized. Moreover, different calculation methods and examples are analysed and compared. A comparison shows that most of the specifications used or modified the M-O method for calculating seismic active earth pressure, and the calculation approach is basically consistent. The difference in the seismic active earth pressure at the bottom of the retaining walls calculated with various specifications gradually increases with increasing seismic peak acceleration. The coefficient of seismic active earth pressure and the resultant force of seismic active earth pressure both increase with increasing seismic peak acceleration. The calculation method, which considers the additional load at the top, results in a seismic earth pressure resultant force point at a height of above 1/3H. When calculating the seismic active earth pressure of reinforced soil structures under various specifications, the effect of reinforcement materials on the reduction in wall back earth pressure is not considered, and the calculation results are relatively conservative. The comparison results can provide a reference for the optimization and improvement of the seismic design of retaining structures, such as reinforced earth retaining walls.

Keywords: retaining structure; seismic active earth pressure; seismic design specifications; comparison of calculation methods

1 Introduction

In the design of seismic stability in internal and external retaining structures, the calculation of the seismic active earth pressure on the wall back is considered a core component of structural strength verification. Scholars from various countries have conducted extensive research on the seismic earth pressure of retaining structures, employing five primary methods: limit equilibrium analysis, limit displacement theory, pseudodynamic research, finite element analysis, and experimental research. The limit equilibrium method is a quasistatic calculation method. Owing to its simplicity, clear physical significance, and small computational workload, this method is widely used in practice.

On the basis of the Coulomb earth pressure theory, Japanese scholars Mononobe and Matsuo [1] and Okabe [2] proposed the Mononobe–Okabe (M-O) method for calculating the active earth pressure on the back of retaining structure walls. In essence, this method is a quasistatic method that considers the horizontal and vertical seismic acceleration. This method has the following shortcomings according to Wu [3]: (1) the horizontal magnification factor of the retaining walls along the height direction is not considered; (2) the influence of the horizontal seismic inertia of the retaining wall is ignored; (3) the method is only applicable to cohesionless soil as the filler behind the wall without considering the cohesion of the filler; and (4) the acting point of the seismic earth pressure resultant force is considered to be located at 1/3 the height of the retaining wall. Seed and Whitman [4] modified the M-O method to obtain the seismic earth pressure through the peak acceleration of ground motion and the internal friction angle of fill. Sherif and Fang [5] considered the influence of wall rotation on earth pressure of retaining walls and demonstrated the accuracy of the – M-O method. In the study of highway abutment by Li [6], a formula for calculating seismic earth pressure by the horizontal seismic coefficient was derived to eliminate the seismic angle. Liang [7] overcame the drawbacks of the M-O method (requiring the seismic angle to be less than the friction angle) by studying the characteristics of the earth pressure error and railway load when the wall back inclination is large, and the scholars derived a new formula. Zhao [8] reported the corresponding calculation formula of earth pressure for cohesionless soil and cohesive soil. Chen et al. [9] derived the generalized physical part of the M-O calculation formula and applied it to the cohesive soil retaining walls through the re-exploration and research of the generalized Coulomb theory. Wang et al. [10] proposed the calculation model for the seismic active earth pressure that considers time and phase changes for cohesive soil and cohesionless soil, respectively, on the basis of the pseudodynamic method. Zhang and Song [11] investigated the earth pressure coefficient with the strain increment ratio on the basis of the law of change. They proposed a practical calculation method in which the seismic earth pressure can be considered the lateral deformation of fill. The reasonableness of the method was verified through the earth pressure model test results. Yang et al. [12] deduced the seismic earth pressure calculation formula for reinforced gravity retaining walls according to the force polygon method. Zhou et al. [13] considered the effects of the rotation of the principal stresses, time effects, and wall–back inclination, and derived a new solution for the seismic active failure angle by the pseudodynamic method, according to the total force equilibrium of the sliding soil mass. Through a horizontal differential layer method, new differential equations of the normal seismic active earth pressure and the coefficient for an inclined rigid retaining wall were obtained while considering translation. Yu [14], on the basis of the upper bound method of plastic limit analysis and the quasistatic method, adopted a logarithmic spiral surface as the slip surface, and established a calculation method for the seismic earth pressure of the reinforced gravity wall. Wang et al. [15] established a calculation method for the active earth pressure of unsaturated fill under earthquake action for gravity retaining walls on the basis of the upper bound principle of limit analysis. Du et al. [16] proposed two calculation methods for the earth pressure of gravity reinforced earth retaining walls under different reinforcement strength and pressure conditions on the basis of the quasicohesion method and working stress principle of reinforced earth. Li et al. [17,18] deduced a calculation method for the seismic active earth pressure considering the displacement modes of reinforced earth retaining walls on the basis of the force polygon method and Winkler foundation beam model, and analysed the influences of different panel forms on the seismic earth pressure distributions of reinforced earth retaining walls.

Owing to different project types and industries, the calculation methods of seismic earth pressure vary in the seismic design specifications for various retaining structures in different countries. In this work, the calculation methods of seismic earth pressure in seismic design specifications of several common types of retaining structures are discussed, and the calculation results of the seismic earth pressure of retaining walls under different seismic loads in retaining wall structures with overlying loads are compared and analysed.

2 Calculation method of seismic earth pressure

2.1 M-O method

The M-O method was proposed by Japanese scholars Mononobe and Okabe in 1924 to calculate the active earth pressure at the back of the retaining structure wall on the basis of the Coulomb earth pressure theory. In essence, this method is a quasistatic method considering the horizontal and vertical seismic acceleration. This method has four basic assumptions: (1) The fill behind the wall is homogeneous and cohesionless and composed of unsaturated soil, and the internal friction angle of the fill is a fixed value. (2) The retaining wall can produce enough lateral displacement to yield the filling at the back of the wall with a shear sliding fracture surface. (3) At this time, the earth pressure acting on the back of the wall is the minimum. (4) The fracture surface is the plane passing through the heel of the wall. The retaining wall is in plane plane-strain state.

The calculation formulas of seismic active earth pressure E ea and active earth pressure coefficient K ea obtained from limit equilibrium conditions and Coulomb earth pressure theory are as follows.

(1) E e a = 1 2 γ H 2 K e a ( 1 − K v ) ,

(2) K e a = cos 2 ( φ − α − θ ) cos θ cos 2 α cos ( α + θ + δ ) 1 + sin ( φ + δ ) sin ( φ − β − θ ) cos ( α − β ) cos ( α + θ + δ ) 2 ,

(3) tan θ = K h 1 − K v ,

where γ is the gravity of soil mass, H is the height of the retaining wall, K h is the horizontal acceleration coefficient, K v is the vertical acceleration coefficient, θ is the seismic angle, φ is the internal friction angle of the soil, δ is the friction angle between the wall and soil, α is the angle between the retaining wall and the vertical direction, and β is the angle between the fill and horizontal direction. The stress of the sliding soil wedge behind the wall is shown in Figure 1.

Figure 1 Schematic diagram of the force on the sliding soil wedge behind the wall.
Figure 1

Schematic diagram of the force on the sliding soil wedge behind the wall.

2.2 Guidelines for seismic design of highway bridges (JTG/T B02-01-2008) [19]

This code is a standard for the highway engineering industry. The calculation of the seismic dynamic earth pressure at the back of the abutment wall in this code considers the cohesion of the fill, the adhesion on the contact surface between the abutment and soil at the back of the wall, and the uniformly distributed load on the sliding soil wedge. The calculation formula is derived on the basis of the M-O formula. The specific formulas of the seismic active earth pressure E ea and active earth pressure coefficient K a are as follows:

(4) E e a = 1 2 γ H 2 + q H cos α cos ( α - β ) K a − 2 c H K c a ,

(5) K a = cos 2 ( φ − α − θ ) cos θ cos 2 α cos ( α + θ + δ ) 1 + sin ( φ + δ ) sin ( φ − β − θ ) cos ( α − β ) cos ( α + θ + δ ) 2 ,

(6) K c a = 1 − sin φ cos φ ,

where γ is the filling weight, H is the height of the abutment retaining wall, q is the uniformly distributed load on the sliding soil wedge, α is the angle between the retaining wall and the vertical direction, β is the angle between the filling surface and the horizontal plane, c is the cohesion of the cohesive fill, δ is the friction angle between the wall and soil, θ is the seismic angle, φ is the internal friction angle of the soil, and K ca is the cohesive earth pressure coefficient of the fill. When the overlying load is q = 0, the location of the action point of seismic earth pressure can be taken as H/3 from the bottom of the abutment. When q ≠ 0, the position of the seismic earth pressure action point is H/3 plus the fill height converted by q. The calculation diagram is shown in Figure 2.

Figure 2 Schematic diagram of the seismic active earth pressure calculation (JTG/T B02-01-2008) [19].
Figure 2

Schematic diagram of the seismic active earth pressure calculation (JTG/T B02-01-2008) [19].

When the filling behind the abutment is cohesionless soil, the following simplified formula can be used to calculate the seismic active earth pressure E ea and the active earth pressure coefficient K a :

(7) E e a = 1 2 γ H 2 K A 1 + 3 C i A g tan φ ,

(8) K A = cos 2 φ ( 1 + sin φ ) 2 ,

where C i is the seismic importance coefficient, A is the peak horizontal seismic acceleration design, and g is the acceleration due to gravity. The action point of the seismic active earth pressure is 0.4H away from the abutment bottom.

2.3 Code for seismic design of railway engineering (2009) (GB 50111-2006) [20]

This code is a railway engineering industry standard, which stipulates that in the seismic design of bridge abutments, the seismic action of bridge abutments shall be calculated using the static method according to the design earthquake, and the seismic active earth pressure acting on the back of the abutment is calculated according to Coulomb’s theory. However, the gravity γ of the fill, the internal friction angle φ of the fill, and the friction angle δ between the wall soil and the back of the wall should be corrected by the seismic angle θ in the Coulomb formula before calculation, according to the influence of the seismic action. The seismic active earth pressure E ea , active earth pressure coefficient K a , and parameter correction formula of the abutment are as follows:

(9) E e a = 1 2 γ E H 2 K a ,

(10) K a = cos 2 ( φ E − α ) cos 2 α cos ( α + δ E ) 1 + sin ( φ E + δ E ) sin ( φ E − β ) cos ( α + δ E ) cos ( α − β ) 2 ,

(11) γ E = γ cos θ ,

(12) φ E = φ − θ ,

(13) δ E = δ + θ ,

where γ E is the corrected filling weight, H is the height of the abutment retaining wall, α is the angle between the retaining wall and the vertical direction, β is the angle between the surface of the filled soil and the horizontal plane, φ E is the corrected internal friction angle of the filled soil, δ E is the corrected friction angle between the wall and the soil behind the wall, and θ is the seismic angle. The action point of the seismic active earth pressure is H/3 away from the abutment bottom.

2.4 Code for seismic design of urban bridges (CJJ166-2011) [21]

This code is a standard for the urban construction industry. The code considers that, in general, only horizontal seismic actions can be considered for urban bridge structures, and seismic actions along and across the bridge can be considered for straight-line bridges. The formulas for calculating the active earth pressure E ea and the active earth pressure coefficient K a of the abutment back under earthquake loading are as follows:

(14) E e a = 1 2 γ H 2 K A 1 + 3 A g tan φ ,

(15) K A = cos 2 φ ( 1 + sin φ ) 2 ,

where γ is the filling weight, H is the height of the abutment retaining wall, A is the peak value of the horizontal design ground motion acceleration, φ is the internal friction angle of the soil, and g is the acceleration due to gravity. The action point of the seismic active earth pressure is 0.4H away from the bottom of the abutment.

Compared with the calculation method of the guidelines for seismic design of highway bridges (JTG/T B02-01-2008), the calculation method of seismic active earth pressure in this code ignores the seismic importance coefficient of the abutment, and does not consider the nature of the fill, the fill and wall back angle, the top load, etc. It belongs to a simplified calculation method.

2.5 Code for design of highway reinforced earth engineering (JTJ 015-91) [22]

This code is specifically applicable to highway reinforced soil slopes, reinforced soil embankments, etc. When calculating the seismic active earth pressure in the code, the structural importance of different highway grades, reinforced soil structure types, and horizontal seismic coefficients under different intensities is considered. The specific formulas of the seismic active earth pressure E ea and active earth pressure coefficient K a are as follows:

(16) E e a = 1 2 γ H 2 K a ( 1 + 3 C i C z K h tan φ ) ,

(17) K a = tan 2 45 ° − φ 2 ,

where γ is the filling weight, H is the height of the abutment retaining wall, C i is the structural importance correction coefficient of the highway grade, C Z is the comprehensive influence coefficient of the structure type, K h is the horizontal seismic coefficient, and φ is the internal friction angle of the soil. The action point of the seismic active earth pressure is 0.4H away from the bottom of the abutment.

In addition, when the filling surface at the back of the wall is an embankment slope, the unit weight γ, the internal friction angle φ, and the friction angle δ of the filling in (16) and (17) should be corrected according to the seismic angle. The specific correction formulas are as follows.

(18) γ E = γ cos θ ,

(19) φ E = φ − θ ,

where γ E is the corrected filling weight, φ E is the corrected internal friction angle of the fill, δ E is the friction angle between the wall and the soil at the back of the wall after correction, and θ is the seismic angle.

2.6 U.S. NCMA code (National Concrete Masonry Association, 2012) [23]

The code provides an analysis and design method for ensuring the stability of segmental retaining walls (SRW) under seismic loads. The M-O method is used to calculate the seismic dynamic earth pressure in the seismic design. The horizontal and vertical accelerations are assumed to be constant in the face slab, reinforced area, and backfill area. The calculation formulas for the seismic active earth pressure E ea and active earth pressure coefficient K ea are as follows:

(20) E e a = 1 2 γ H 2 K e a ( 1 ± K v ) ,

(21) K e a = cos 2 ( φ + ω − θ ) cos θ cos 2 ω cos ( δ − ω + θ ) 1 + sin ( φ + δ ) sin ( φ − β − θ ) cos ( ω + β ) cos ( δ − ω + θ ) 2 ,

(22) tan θ = K h 1 ± K v ,

(23) δ = 2 φ 3 ,

where γ is the filling weight, H is the height of the retaining wall, K h is the horizontal acceleration coefficient, K v is the vertical seismic acceleration coefficient, “+” corresponds to the downward seismic inertia force, “−” corresponds to the upward seismic inertia force, θ is the seismic angle, φ is the internal friction angle of the soil, ω is the angle between the retaining wall and the vertical direction, and is considered a positive value when the retaining wall is inclined in the filling direction at the back of the wall, δ is the friction angle between the wall and the soil, and β is the angle between the fill and the horizontal direction.

2.7 Design standards for railway structures are explained in the same way as those for retaining structures (2012) [24]

This code is a Japanese railway structure design standard applicable to retaining structures. The code provides a more comprehensive design method for reinforced earth retaining walls and reinforced earth abutments. In the code, the ground motion levels are divided into L1 and L2. L1 is the conventional earthquake that will inevitably occur within the design life of the structure, and L2 is the ground motion with a very low probability of occurrence but very high intensity within the design life of the structure. Compared with the Chinese seismic design specifications, L1 and L2 correspond to the design earthquake and rare earthquake in China, respectively [25].

The seismic active earth pressure (p AE) and active earth pressure coefficient (K AE ) of the reinforced earth abutment under the L1 ground motion level are calculated by the M-O method, and the calculation formulas are as follows.

(24) p AE = γ h K AE + q cos α cos ( α − β ) K AE ,

(25) K AE = cos 2 ( φ − α − θ ) cos θ cos 2 α cos ( α + θ + δ ) 1 + sin ( φ + δ ) sin ( φ − β − θ ) cos ( α − β ) cos ( α + θ + δ ) 2 ,

(26) tan θ = a max g ,

(27) δ = φ 2 ,

where γ is the filling weight, H is the height of the retaining wall, q is the uniformly distributed load on the sliding soil wedge, α is the angle between the retaining wall and the vertical direction, β is the angle between the filling and the horizontal direction, φ is the internal friction angle of the soil, θ is the inclination angle between the resultant force and the vertical direction, δ is the friction angle between the wall and the soil, a max is the design ground motion peak acceleration, and g is the acceleration due to gravity. The action point of seismic active earth pressure is located at a height of H/3 from the bottom of the abutment.

During L2 ground motion, the dynamic characteristics (i.e. peak strength and residual strength) of the fill behind the wall after a strong earthquake are considered; thus, the M-O method is modified. The calculation formulas of the modified seismic active earth pressure coefficient K AE are as follows:

(28) K AE = cos ( ψ − φ ) ( 1 + tan 2 α ) ( 1 + tan α tan β ) [ tan ( ψ − φ ) + tan θ ] cos ( ψ − φ − α − δ ) ( tan ψ − tan β ) ,

(29) cot ( ψ − β ) = − tan ( φ + δ + α − β ) + sec ( φ + δ + α − β ) cos ( α + δ + θ ) sin ( φ + δ ) cos ( α − β ) sin ( φ − β − θ ) ,

where ψ is the angle between the sliding surface and the horizontal plane. The meanings of other symbols are the same as above. Compared with the previous M-O method, the change in the earth pressure with increasing ground motion is more in line with field monitoring practices, and the active earth pressure during an earthquake can be reasonably calculated even for a large earthquake inertia force.

2.8 French code for design of reinforced soil (NF P 94-270, 2020) [26]

The calculation method of the seismic earth pressure of reinforced earth structure under seismic action in this code is also based on the M-O method, which is similar to the calculation method in the National Concrete Masonry Association code (NCMA, 2012). However, this code considers the influences of the top filling plane angle and horizontal displacement of the panel. The seismic active earth pressure E d and the active earth pressure coefficient K of the homogeneous soil layer can be calculated by the M-O method:

(30) E d = 1 2 γ H 2 K ( 1 ± k v ) .

When β ≤ φ d ′ − θ ,

(31) K = sin 2 ( ψ + φ d ′ − θ ) cos θ sin 2 ψ sin ( ψ − θ − δ d ) 1 + sin ( φ d ′ + δ d ) sin ( φ d ′ − β − θ ) sin ( ψ + β ) sin ( ψ − θ − δ d ) 2 .

When β > φ d ′ − θ ,

(32) K = sin 2 ( ψ + φ d ′ − θ ) cos θ sin 2 ψ sin ( ψ − θ − δ d ) ,

(33) tan θ = k h 1 ± k v ,

(34) ψ = π 2 + η 2 ,

(35) k h = S r ⋅ a g g ,

where γ is the filling weight, H is the height of the retaining wall, K h is the horizontal acceleration coefficient, K v is the vertical seismic acceleration coefficient, “+” corresponds to the downward seismic inertia force, “−” corresponds to the upward seismic inertia force, β is the angle between the filling and the horizontal direction, φ d ′ is the internal friction angle of fill, θ is the seismic angle, η 2 is the angle between the retaining wall and the vertical direction, ψ is the angle between the potential fracture surface passing through the wall heel and the horizontal direction, δ d is the friction angle between the wall and soil, S is the geotechnical coefficient under different site types, r is the horizontal seismic coefficient correction value, a g is the design ground motion peak acceleration, and g is the acceleration due to gravity.

2.9 Other specifications

In addition, the calculation methods for seismic dynamic earth pressure given in the specification of seismic design for highway engineering (JTG B02-2013) [27] and specifications for design of highway subgrades (JTG D30-2015) [28] are the same as those in the guidelines for seismic design of highway bridges (JTG/T B02-01-2008). In the local standard technical code for technical specifications for design and construction of flexible ecological reinforced earth retaining wall (DB33/T 988-2022) [29], the limit state design method is used to obtain the calculation method of active earth pressure to evaluate the external stability of reinforced retaining walls. However, the relevant provisions in the specification of seismic design for highway engineering (JTG B02-2013) are still used in the seismic design calculation, and the calculation method is the same as that in the guidelines for seismic design of highway bridges (JTG/T B02-01-2008).

3 Comparison of various calculation methods

The M-O method is generally used in the calculation of seismic earth pressure in various codes. However, some methods involve modifying the M-O formula according to the assumption considered, while keeping the calculation idea and process of seismic earth pressure basically the same. The objectives of these methods are as follows: (1) determine the importance coefficient of the project or structure; (2) determine the horizontal seismic influence coefficient and calculate the seismic angle; (3) determine the parameters in other earth pressure coefficients according to the design drawing of the retaining structure; (4) calculate the seismic earth pressure coefficient; and (5) calculate the value of the seismic dynamic earth pressure and determine the position of the resultant force action point. The differences between the calculation methods for seismic active earth pressure in the above specifications are shown in Table 1.

Table 1

Comparison list of seismic active earth pressure calculation methods in various specifications

Specification name Considerations or assumptions
Code for highway engineering in China (JTG/T B02-01-2008, JTG B02-2013, JTG D30-2015, DB33T 988-2022) The cohesion of the fill and the uniformly distributed load on the top of the fill are considered, but the horizontal seismic coefficient is not considered
Code for seismic design of railway engineering (2009) (GB 50111-2006) The influence of earthquake action on the weight of the fill, the internal friction angle of the fill, and the friction angle between the wall and soil behind the wall is considered
Code for seismic design of urban bridges (CJJ166-2011) The seismic importance coefficient of the abutment is ignored, and the nature of the fill and the horizontal seismic coefficient are not considered
Code for design of highway reinforced earth engineering (JTJ 015-91) The structural importance of different highway grades, the type of reinforced earth structure, and whether the filling surface is an embankment slope are considered
Design manual for SRW (National Concrete Masonry Association, 2012) It is assumed that the horizontal and vertical accelerations are constant in the face slab, reinforced area, and backfill area. That is, the acceleration amplification effect of the structure is ignored
Japanese railway standards, 2012 The changes in the ground motion level and dynamic characteristics (peak strength and residual strength) of the fill are considered
French reinforced earth code (NF P 94-270, 2020) The influences of the top filling plane angle and the horizontal displacement of the panel are considered

To compare the practical application differences in seismic earth pressure calculation methods in the above specifications, a reinforced earth retaining wall structure with an overlying load is selected, and the calculation results of the seismic active earth pressure of the reinforced earth retaining wall under 0.1, 0.2, and 0.4g seismic peak accelerations are compared and analysed. The following conditions are assumed: (1) the back of the structural wall is vertical and smooth; (2) filling level is at the top of the reinforced earth retaining wall; (3) the project site is classified as class II site in Chinese specifications and class B site in European and American specifications; and (4) only horizontal seismic action is considered. The calculation diagram of the retaining wall is shown in Figure 3, and the structural design parameters are presented in Table 2.

Figure 3 Calculation schematic diagram of the reinforced soil retaining wall calculation example.
Figure 3

Calculation schematic diagram of the reinforced soil retaining wall calculation example.

Table 2

Structural design parameters for the reinforced soil retaining wall calculation example

Index Parameter value
Type of fill behind the wall Fine-gravel sand
Volume weight of the fill behind the wall γ (kN/m3) 16.9
Cohesion of fill behind the wall c (kPa) 0
Internal friction angle of the wall backfill φ (°) 42
Height of the wall H (m) 4
Overlying uniform load q (kPa) 20
Structural importance correction coefficient C i of highway grade 0.8
Comprehensive influence coefficient C Z of the structure type 0.35

According to the seismic earth pressure calculation methods in the above specifications, the distribution curves of the seismic active earth pressure along the wall height of the reinforced earth retaining wall shown in this case can be obtained under the peak ground acceleration of 0.1, 0.2, and 0.4g under various calculation methods (Figure 4). The figures show that the seismic active earth pressure of each specification is linearly distributed along the wall height. The seismic active earth pressure value at the top of the wall in the Chinese highway bridge standard (JTG/T B02-01-2008) and Japanese railway standard (2012) is not zero. The greater the peak ground acceleration, the greater the difference. The seismic active earth pressure value at the top of the wall is zero according to the United States NCMA code (2012), the code for seismic design of railway engineering (2009) (GB 50111-2006), the code for design of highway reinforced earth engineering (JTJ 015-91), the code for seismic design of urban bridges (CJJ166-2011), and the French reinforced earth code (NF p94-270,2020). Under a seismic peak acceleration of 0.1g, the calculation results of the seismic active earth pressure of each method from small to large are the United States NCMA code (2012), the code for seismic design of railway engineering (2009) (GB 50111-2006), the code for design of highway reinforced earth engineering (JTJ 015-91), the code for seismic design of urban bridges (CJJ166-2011), the French reinforced earth code (NF p94-270,2020), the Japanese railway standards (2012), and the guidelines for seismic design of highway bridges (JTG/T B02-01-2008). At seismic peak accelerations of 0.2 and 0.4g, the calculation result of the seismic active earth pressure of the United States NCMA specification (2012) is greater than that of the code for seismic design of railway engineering (2009) (GB 50111-2006), and the calculation result of Japanese railway standards (2012) is greater than that of the guidelines for seismic design of highway bridges (JTG/T B02-01-2008). With increasing seismic peak acceleration, the difference in the seismic active earth pressure at the bottom of the wall calculated by various codes increases.

Figure 4 Seismic active earth pressure distribution curve along the wall height. (a) Seismic peak acceleration 0.1g. (b) Seismic peak acceleration 0.2g. (c) Seismic peak acceleration 0.4g.
Figure 4

Seismic active earth pressure distribution curve along the wall height. (a) Seismic peak acceleration 0.1g. (b) Seismic peak acceleration 0.2g. (c) Seismic peak acceleration 0.4g.

According to the seismic active earth pressure calculation methods specified in the above codes, the seismic active earth pressure coefficient of the reinforced earth retaining wall shown in this case can be obtained under different peak ground accelerations. Then, based on the distribution curve of seismic active soil pressure along the wall height obtained from Figure 4, the magnitude and location of the resultant force of seismic active soil pressure under different peak accelerations can be plotted, as shown in Figure 5. The figures show that the seismic active earth pressure coefficients in the code for seismic design of urban bridges (CJJ166-2011) are the same under different seismic peak accelerations because the seismic active earth pressure coefficient calculation method in the code is related only to the internal friction angle of the fill, and the seismic active earth pressure coefficients obtained in other specifications increase with increasing ground motion acceleration. The seismic active earth pressure resultant force obtained in each code increases with increasing ground motion acceleration, and the calculation value in the guidelines for seismic design of highway bridges (JTG/T B02-01-2008) increases the fastest. The guidelines for seismic design of highway bridges (JTG/T B02-01-2008) and the Japanese railway standards (2012) both consider the additional load on the top when calculating the seismic earth pressure. Thus, the acting point of the seismic earth pressure resultant force is 0.37 of the wall height, which is higher than 1/3 of the wall height. The acting point of the seismic earth pressure resultant force calculated by other specifications is 1/3 of the wall height.

Figure 5 Relationship curve between the seismic active earth pressure resultant force and seismic motion during earthquakes. (a) Coefficient of seismic active earth pressure. (b) Resultant force of seismic active earth pressure. (c) Height of the resultant force action point.
Figure 5

Relationship curve between the seismic active earth pressure resultant force and seismic motion during earthquakes. (a) Coefficient of seismic active earth pressure. (b) Resultant force of seismic active earth pressure. (c) Height of the resultant force action point.

4 Discussion

For reinforced earth retaining walls, the reduction effect of reinforcement on the seismic active earth pressure at the back of the wall is not considered in all specifications. However, many studies on the earth pressure of reinforced retaining walls [12,30,31,32] have shown that friction reinforcement is a main factor that reduces the earth pressure at the back of the retaining wall. Therefore, in theory, the calculation method of the seismic active earth pressure in this work can be considered conservative when applied to reinforced earth retaining walls.

5 Conclusions

  1. The M-O method is essentially used in the calculation of seismic earth pressure in various codes. Conversely, the M-O formula is modified according to the assumption considered. However, the calculation idea and process of seismic earth pressure are basically the same.

  2. In the comparison of calculation examples of retaining wall structures, the difference in the seismic active earth pressure at the bottom of the wall, according to calculations by various codes, gradually increases with increasing seismic peak acceleration. The coefficient of seismic active earth pressure and the resultant force of seismic active earth pressure obtained from each code increase with increasing ground motion acceleration. The guidelines for seismic design of highway bridges (JTG/T B02-01-2008) and the Japanese railway standards (2012) consider the additional load on the top. Therefore, the acting point of seismic earth pressure resultant force is at 0.37H, which is higher than 1/3H, while those of the other codes are at 1/3H.

  3. In this work, only the theoretical calculations of various specifications are compared, but these results need to be further compared with large-scale model tests and specific seismic damage monitoring data from engineering projects. These comparisons will allow for the analysis of the applicability of the calculation methods of various specifications in specific engineering applications.

  1. Funding information: This research was funded by the Fundamental Research Funds for the Central Universities, grant number ZY20215120, and the Earthquake Technology Spark Program of China, grant number XH23067YA.

  2. Author contributions: Conceptualization, X.H. and X.C.; writing paper, Y.Q.; supervision, J.B.; resources, S.L. and Y.L. All authors have read and agreed to the published version of the manuscript.

  3. Conflict of interest: The authors declare no conflict of interest.

  4. Informed consent statement: All study participants provided informed consent.

  5. Data availability statement: Data openly available in a public repository.

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Received: 2025-03-18
Revised: 2025-06-03
Accepted: 2025-06-12
Published Online: 2025-10-15

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

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https://doi.org/10.1515/geo-2025-0829
Schlagwörter für diesen Artikel
retaining structure; seismic active earth pressure; seismic design specifications; comparison of calculation methods
Creative Commons
BY 4.0

Artikel in diesem Heft

  1. Research Articles
  2. Seismic response and damage model analysis of rocky slopes with weak interlayers
  3. Multi-scenario simulation and eco-environmental effect analysis of “Production–Living–Ecological space” based on PLUS model: A case study of Anyang City
  4. Remote sensing estimation of chlorophyll content in rape leaves in Weibei dryland region of China
  5. GIS-based frequency ratio and Shannon entropy modeling for landslide susceptibility mapping: A case study in Kundah Taluk, Nilgiris District, India
  6. Natural gas origin and accumulation of the Changxing–Feixianguan Formation in the Puguang area, China
  7. Spatial variations of shear-wave velocity anomaly derived from Love wave ambient noise seismic tomography along Lembang Fault (West Java, Indonesia)
  8. Evaluation of cumulative rainfall and rainfall event–duration threshold based on triggering and non-triggering rainfalls: Northern Thailand case
  9. Pixel and region-oriented classification of Sentinel-2 imagery to assess LULC dynamics and their climate impact in Nowshera, Pakistan
  10. The use of radar-optical remote sensing data and geographic information system–analytical hierarchy process–multicriteria decision analysis techniques for revealing groundwater recharge prospective zones in arid-semi arid lands
  11. Effect of pore throats on the reservoir quality of tight sandstone: A case study of the Yanchang Formation in the Zhidan area, Ordos Basin
  12. Hydroelectric simulation of the phreatic water response of mining cracked soil based on microbial solidification
  13. Spatial-temporal evolution of habitat quality in tropical monsoon climate region based on “pattern–process–quality” – a case study of Cambodia
  14. Early Permian to Middle Triassic Formation petroleum potentials of Sydney Basin, Australia: A geochemical analysis
  15. Micro-mechanism analysis of Zhongchuan loess liquefaction disaster induced by Jishishan M6.2 earthquake in 2023
  16. Prediction method of S-wave velocities in tight sandstone reservoirs – a case study of CO2 geological storage area in Ordos Basin
  17. Ecological restoration in valley area of semiarid region damaged by shallow buried coal seam mining
  18. Hydrocarbon-generating characteristics of Xujiahe coal-bearing source rocks in the continuous sedimentary environment of the Southwest Sichuan
  19. Hazard analysis of future surface displacements on active faults based on the recurrence interval of strong earthquakes
  20. Structural characterization of the Zalm district, West Saudi Arabia, using aeromagnetic data: An approach for gold mineral exploration
  21. Research on the variation in the Shields curve of silt initiation
  22. Reuse of agricultural drainage water and wastewater for crop irrigation in southeastern Algeria
  23. Assessing the effectiveness of utilizing low-cost inertial measurement unit sensors for producing as-built plans
  24. Analysis of the formation process of a natural fertilizer in the loess area
  25. Machine learning methods for landslide mapping studies: A comparative study of SVM and RF algorithms in the Oued Aoulai watershed (Morocco)
  26. Chemical dissolution and the source of salt efflorescence in weathering of sandstone cultural relics
  27. Molecular simulation of methane adsorption capacity in transitional shale – a case study of Longtan Formation shale in Southern Sichuan Basin, SW China
  28. Evolution characteristics of extreme maximum temperature events in Central China and adaptation strategies under different future warming scenarios
  29. Estimating Bowen ratio in local environment based on satellite imagery
  30. 3D fusion modeling of multi-scale geological structures based on subdivision-NURBS surfaces and stratigraphic sequence formalization
  31. Comparative analysis of machine learning algorithms in Google Earth Engine for urban land use dynamics in rapidly urbanizing South Asian cities
  32. Study on the mechanism of plant root influence on soil properties in expansive soil areas
  33. Simulation of seismic hazard parameters and earthquakes source mechanisms along the Red Sea rift, western Saudi Arabia
  34. Tectonics vs sedimentation in foredeep basins: A tale from the Oligo-Miocene Monte Falterona Formation (Northern Apennines, Italy)
  35. Investigation of landslide areas in Tokat-Almus road between Bakımlı-Almus by the PS-InSAR method (Türkiye)
  36. Predicting coastal variations in non-storm conditions with machine learning
  37. Cross-dimensional adaptivity research on a 3D earth observation data cube model
  38. Geochronology and geochemistry of late Paleozoic volcanic rocks in eastern Inner Mongolia and their geological significance
  39. Spatial and temporal evolution of land use and habitat quality in arid regions – a case of Northwest China
  40. Ground-penetrating radar imaging of subsurface karst features controlling water leakage across Wadi Namar dam, south Riyadh, Saudi Arabia
  41. Rayleigh wave dispersion inversion via modified sine cosine algorithm: Application to Hangzhou, China passive surface wave data
  42. Fractal insights into permeability control by pore structure in tight sandstone reservoirs, Heshui area, Ordos Basin
  43. Debris flow hazard characteristic and mitigation in Yusitong Gully, Hengduan Mountainous Region
  44. Research on community characteristics of vegetation restoration in hilly power engineering based on multi temporal remote sensing technology
  45. Identification of radial drainage networks based on topographic and geometric features
  46. Trace elements and melt inclusion in zircon within the Qunji porphyry Cu deposit: Application to the metallogenic potential of the reduced magma-hydrothermal system
  47. Pore, fracture characteristics and diagenetic evolution of medium-maturity marine shales from the Silurian Longmaxi Formation, NE Sichuan Basin, China
  48. Study of the earthquakes source parameters, site response, and path attenuation using P and S-waves spectral inversion, Aswan region, south Egypt
  49. Source of contamination and assessment of potential health risks of potentially toxic metal(loid)s in agricultural soil from Al Lith, Saudi Arabia
  50. Regional spatiotemporal evolution and influencing factors of rural construction areas in the Nanxi River Basin via GIS
  51. An efficient network for object detection in scale-imbalanced remote sensing images
  52. Effect of microscopic pore–throat structure heterogeneity on waterflooding seepage characteristics of tight sandstone reservoirs
  53. Environmental health risk assessment of Zn, Cd, Pb, Fe, and Co in coastal sediments of the southeastern Gulf of Aqaba
  54. A modified Hoek–Brown model considering softening effects and its applications
  55. Evaluation of engineering properties of soil for sustainable urban development
  56. The spatio-temporal characteristics and influencing factors of sustainable development in China’s provincial areas
  57. Application of a mixed additive and multiplicative random error model to generate DTM products from LiDAR data
  58. Gold vein mineralogy and oxygen isotopes of Wadi Abu Khusheiba, Jordan
  59. Prediction of surface deformation time series in closed mines based on LSTM and optimization algorithms
  60. 2D–3D Geological features collaborative identification of surrounding rock structural planes in hydraulic adit based on OC-AINet
  61. Spatiotemporal patterns and drivers of Chl-a in Chinese lakes between 1986 and 2023
  62. Land use classification through fusion of remote sensing images and multi-source data
  63. Nexus between renewable energy, technological innovation, and carbon dioxide emissions in Saudi Arabia
  64. Analysis of the spillover effects of green organic transformation on sustainable development in ethnic regions’ agriculture and animal husbandry
  65. Factors impacting spatial distribution of black and odorous water bodies in Hebei
  66. Large-scale shaking table tests on the liquefaction and deformation responses of an ultra-deep overburden
  67. Impacts of climate change and sea-level rise on the coastal geological environment of Quang Nam province, Vietnam
  68. Reservoir characterization and exploration potential of shale reservoir near denudation area: A case study of Ordovician–Silurian marine shale, China
  69. Seismic prediction of Permian volcanic rock reservoirs in Southwest Sichuan Basin
  70. Application of CBERS-04 IRS data to land surface temperature inversion: A case study based on Minqin arid area
  71. Geological characteristics and prospecting direction of Sanjiaoding gold mine in Saishiteng area
  72. Research on the deformation prediction model of surrounding rock based on SSA-VMD-GRU
  73. Geochronology, geochemical characteristics, and tectonic significance of the granites, Menghewula, Southern Great Xing’an range
  74. Hazard classification of active faults in Yunnan base on probabilistic seismic hazard assessment
  75. Characteristics analysis of hydrate reservoirs with different geological structures developed by vertical well depressurization
  76. Estimating the travel distance of channelized rock avalanches using genetic programming method
  77. Landscape preferences of hikers in Three Parallel Rivers Region and its adjacent regions by content analysis of user-generated photography
  78. New age constraints of the LGM onset in the Bohemian Forest – Central Europe
  79. Characteristics of geological evolution based on the multifractal singularity theory: A case study of Heyu granite and Mesozoic tectonics
  80. Soil water content and longitudinal microbiota distribution in disturbed areas of tower foundations of power transmission and transformation projects
  81. Oil accumulation process of the Kongdian reservoir in the deep subsag zone of the Cangdong Sag, Bohai Bay Basin, China
  82. Investigation of velocity profile in rock–ice avalanche by particle image velocimetry measurement
  83. Optimizing 3D seismic survey geometries using ray tracing and illumination modeling: A case study from Penobscot field
  84. Sedimentology of the Phra That and Pha Daeng Formations: A preliminary evaluation of geological CO2 storage potential in the Lampang Basin, Thailand
  85. Improved classification algorithm for hyperspectral remote sensing images based on the hybrid spectral network model
  86. Map analysis of soil erodibility rates and gully erosion sites in Anambra State, South Eastern Nigeria
  87. Identification and driving mechanism of land use conflict in China’s South-North transition zone: A case study of Huaihe River Basin
  88. Evaluation of the impact of land-use change on earthquake risk distribution in different periods: An empirical analysis from Sichuan Province
  89. A test site case study on the long-term behavior of geotextile tubes
  90. An experimental investigation into carbon dioxide flooding and rock dissolution in low-permeability reservoirs of the South China Sea
  91. Detection and semi-quantitative analysis of naphthenic acids in coal and gangue from mining areas in China
  92. Comparative effects of olivine and sand on KOH-treated clayey soil
  93. YOLO-MC: An algorithm for early forest fire recognition based on drone image
  94. Earthquake building damage classification based on full suite of Sentinel-1 features
  95. Potential landslide detection and influencing factors analysis in the upper Yellow River based on SBAS-InSAR technology
  96. Assessing green area changes in Najran City, Saudi Arabia (2013–2022) using hybrid deep learning techniques
  97. An advanced approach integrating methods to estimate hydraulic conductivity of different soil types supported by a machine learning model
  98. Hybrid methods for land use and land cover classification using remote sensing and combined spectral feature extraction: A case study of Najran City, KSA
  99. Streamlining digital elevation model construction from historical aerial photographs: The impact of reference elevation data on spatial accuracy
  100. Analysis of urban expansion patterns in the Yangtze River Delta based on the fusion impervious surfaces dataset
  101. A metaverse-based visual analysis approach for 3D reservoir models
  102. Late Quaternary record of 100 ka depositional cycles on the Larache shelf (NW Morocco)
  103. Integrated well-seismic analysis of sedimentary facies distribution: A case study from the Mesoproterozoic, Ordos Basin, China
  104. Study on the spatial equilibrium of cultural and tourism resources in Macao, China
  105. Urban road surface condition detecting and integrating based on the mobile sensing framework with multi-modal sensors
  106. Application of improved sine cosine algorithm with chaotic mapping and novel updating methods for joint inversion of resistivity and surface wave data
  107. The synergistic use of AHP and GIS to assess factors driving forest fire potential in a peat swamp forest in Thailand
  108. Dynamic response analysis and comprehensive evaluation of cement-improved aeolian sand roadbed
  109. Rock control on evolution of Khorat Cuesta, Khorat UNESCO Geopark, Northeastern Thailand
  110. Gradient response mechanism of carbon storage: Spatiotemporal analysis of economic-ecological dimensions based on hybrid machine learning
  111. Comparison of several seismic active earth pressure calculation methods for retaining structures
  112. Review Articles
  113. Humic substances influence on the distribution of dissolved iron in seawater: A review of electrochemical methods and other techniques
  114. Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies
  115. Ore-controlling structures of granite-related uranium deposits in South China: A review
  116. Shallow geological structure features in Balikpapan Bay East Kalimantan Province – Indonesia
  117. A review on the tectonic affinity of microcontinents and evolution of the Proto-Tethys Ocean in Northeastern Tibet
  118. Special Issue: Natural Resources and Environmental Risks: Towards a Sustainable Future - Part II
  119. Depopulation in the Visok micro-region: Toward demographic and economic revitalization
  120. Special Issue: Geospatial and Environmental Dynamics - Part II
  121. Advancing urban sustainability: Applying GIS technologies to assess SDG indicators – a case study of Podgorica (Montenegro)
  122. Spatiotemporal and trend analysis of common cancers in men in Central Serbia (1999–2021)
  123. Minerals for the green agenda, implications, stalemates, and alternatives
  124. Spatiotemporal water quality analysis of Vrana Lake, Croatia
  125. Functional transformation of settlements in coal exploitation zones: A case study of the municipality of Stanari in Republic of Srpska (Bosnia and Herzegovina)
  126. Hypertension in AP Vojvodina (Northern Serbia): A spatio-temporal analysis of patients at the Institute for Cardiovascular Diseases of Vojvodina
  127. Regional patterns in cause-specific mortality in Montenegro, 1991–2019
  128. Spatio-temporal analysis of flood events using GIS and remote sensing-based approach in the Ukrina River Basin, Bosnia and Herzegovina
  129. Flash flood susceptibility mapping using LiDAR-Derived DEM and machine learning algorithms: Ljuboviđa case study, Serbia
  130. Geocultural heritage as a basis for geotourism development: Banjska Monastery, Zvečan (Serbia)
  131. Assessment of groundwater potential zones using GIS and AHP techniques – A case study of the zone of influence of Kolubara Mining Basin
  132. Impact of the agri-geographical transformation of rural settlements on the geospatial dynamics of soil erosion intensity in municipalities of Central Serbia
  133. Where faith meets geomorphology: The cultural and religious significance of geodiversity explored through geospatial technologies
  134. Applications of local climate zone classification in European cities: A review of in situ and mobile monitoring methods in urban climate studies
  135. Complex multivariate water quality impact assessment on Krivaja River
  136. Ionization hotspots near waterfalls in Eastern Serbia’s Stara Planina Mountain
  137. Shift in landscape use strategies during the transition from the Bronze age to Iron age in Northwest Serbia
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Heruntergeladen am 16.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/geo-2025-0829/html
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