dynamic lateral earth pressures on …€¦ · pressures, and also the rankine active earth...

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International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 10, October 2017, pp. 1050–1063, Article ID: IJCIET_08_10_109

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

DYNAMIC LATERAL EARTH PRESSURES ON

BASEMENT WALLS INDUCED BY HARMONIC

GROUND MOTIONS

Widjojo A. Prakoso

Civil Engineering Department

Universitas Indonesia, Depok, Indonesia

Rustama Berangket



Feny Yuzanda



ABSTRACT

In recent years, a number of publications on dynamic lateral earth pressures

acting on basement walls induced by seismic ground motions has appeared due to

good performance of basement walls during relatively large earthquakes. The main

concern is whether the current methods would provide excessively conservative lateral

earth pressures. In this paper, the 2-D plane strain dynamic finite element models

were used to examine the lateral earth pressures acting on 2-story concrete basement

walls. The seismic ground motions were constant-peak, harmonic ground motions;

three different peak acceleration values were considered. The Mohr-Coulomb

constitutive soil model was used in the analyses to represent a sands deposit. The

observed parameters were the horizontal wall acceleration, the lateral earth pressures

and their changes, and the lateral total thrusts (PAE). The overall results showed the

complex nature of the dynamic soil-structure interaction of basement structures. Some

of the findings include the effect of limiting soil tensile strength on the envelope of

change in lateral earth pressures (∆pAE), the non-linear increase in and complex

distribution of ∆pAE with an increase in the peak input acceleration, highly non-linear

relationship between PAE and wall acceleration, a discussion on phase difference, and

the effect of the embedment wall depths.

Keywords: Basement, Horizontal Acceleration, Lateral Earth Pressure, Dynamic Finite

Element.

Dynamic Lateral Earth Pressures on Basement Walls Induced by Harmonic Ground Motions


Cite this Article: Widjojo A. Prakoso, Rustama Berangket and Feny Yuzanda,

Dynamic Lateral Earth Pressures on Basement Walls Induced by Harmonic Ground

Motions, International Journal of Civil Engineering and Technology, 8(10), 2017,

pp. 1050–1063

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=10

1. INTRODUCTION

The Indonesia seismic building code [1] requires that basement walls be designed against the

increased lateral earth pressures associated with seismic ground motions. However, the code

does not specify any methods to estimate the increased pressures. In recent years at the

international level, this topic has attracted discussions due to good performance of basement

walls during relatively large earthquakes (e.g., [2, 3, 4, 5]). Many different design estimation

methods have been proposed in the literature (e.g., [4]). One of the concerns is whether the

typical estimation methods would yield in overly conservative the increased pressures.

These studies examined different factors affecting the increased dynamic lateral earth

pressures. As an example, Winner and Prakoso [5] examined the effects of seismic ground

motion parameters and soil constitutive models on the dynamic lateral earth pressures behind

basement wall and the wall bending moments; the basement structures considered had no

embedded walls. They found that the pressures and bending moments are dependent on the

peak value and frequency of the input acceleration. The pressures are also dependent on the

limiting soil tensile strength provided by the soil cohesion, but the bending moments are

relatively independent of the soil tensile strength.

The objective of this study is to identify the dynamic lateral earth pressures acting on

basement walls for different peak input acceleration and for different wall embedment depths.

For this paper, the seismic ground motions considered are synthetic, harmonic ground

motions with constant peak acceleration values. The basements considered is a 2-level, 8 m

deep basements typically constructed in Jakarta area; no pile foundations are considered in the

basement model. This paper describes the finite element model used and cases evaluated, as

well as the numerical results, particularly in terms of the lateral earth pressures and wall

acceleration

2. RESEARCH METHOD

The research method was to employ two-dimensional, finite element models to examine the

increased lateral earth pressures. The assumed geotechnical conditions were a 25 m thick

sands deposit overlying an engineering bedrock. The depth and width of the concrete

basement considered are 8 m and 18 m, respectively. The thickness of the basement concrete

wall is 0.6 m, while the embedment depths was varied from 4 m to 10 m (total wall length 12

m to 18 m).

The typical 2-D plane strain finite element model is shown in Figure 1. Fifteen-node

triangular finite elements were used to model the soils, and concrete walls; the number of

elements was 1,018 elements. Much finer elements were used for the basement walls and the

soil directly behind the walls in order capture the increased pressures and bending moments

(See Figure 1.). Beam elements were used to model the basement structural elements (e.g.,

columns and beams).

The constitutive soil model used for all the soil elements was the Mohr-Coulomb

constitutive soil model. The soil was assumed to be medium sands, and the properties were

adapted from [6] for convenient model verification purposes. The soil properties are given in

Table 1. The constitutive model used for the basement wall elements was the elastic model;

the properties are given in Table 2. The structural elements were assumed to remain elastic

Widjojo A. Prakoso, Rustama Berangket and Feny Yuzanda


throughout the analyses; the properties of these elements are given in Table 3. Interface

elements were used between the soil elements and the wall elements. Absorbent boundaries

were specified for the sides to avoid spurious reflection during dynamic analyses. The

damping used was the Rayleigh damping model with factors of α = 0 and β = 0.0022,

representing a damping ratio of about 5% [7]. The geotechnical finite element software used

was Plaxis 2-D version 8 [8].

The input seismic motion reported in this paper was a constant frequency, constant

amplitude harmonic acceleration. The harmonic acceleration was 3 Hz and 4 second long (12

cycles). The range of the peak ground acceleration was varied from 0.2 g, 0.5 g, and 0.7 g.

The typical harmonic acceleration time history is shown in Figure 2. The acceleration was

applied using the prescribed displacement option at the base of the mesh. The dynamic

calculations were performed in 1,000 dynamic calculation steps (∆t = 0.004 s). The observed

outputs include the wall acceleration and bending moments, as well as the lateral earth

pressure behind wall. The dynamic calculation was performed after the static construction

stage (basement excavation, wall and structure installation).

Figure 1 Finite element mesh (top), wall and soil nodes (bottom-left), wall and soil stress points

(bottom-right)

Table 1 Soil properties

Soil Property Symbol Value Unit

Unit weight γ 17 kN/m3

Modulus E 40 MN/m2

Friction angle φ 35 degree

Cohesion C 0.2 kN/m2

Poisson’s ratio υ 0.33 -

Rinterface R 0.7 -

Table 2 Wall properties



Modulus E 20 GN/m2

Thickness T 600 mm



Table 3 Structural element properties



Modulus E 20 GN/m2

Beam

dimensions

Bf 3500 mm

Bw 300 mm

H 600 mm

Spacing 6 m

Column

dimensions

B 400 mm

H 400 mm

Spacing 6 m

Figure 2 Typical input acceleration (3 Hz, 4 second long)

3. RESULTS

3.1. Model Verification

The model verification was conducted by checking the resulting static lateral earth pressures

(pA) and the resulting dynamic wall acceleration. The static pressures examined were the

pressures along the basement at the end of construction stage. Figure 3 shows the resulting

pressures, and also the Rankine active earth pressure line and the at-rest lateral earth pressure

line. These lines were determined based on the soil friction angle of 35°. It can be seen that

the resulting pressures at the upper wall part were about the same as the Rankine active line to

depth of about 4 m. The pressures then increased to about the same as the at-rest line at depth

of 4 m. Subsequently, the resulting pressures decreased to the Rankine active line at the wall

tip level.

The resulting dynamic wall acceleration is compared directly with the peak input

acceleration in Figure 4. For lower acceleration values, the wall acceleration was higher than

the input acceleration, indicating amplification of the ground motions. However for higher

values, the former became lower than the latter, indicating de-amplification of the ground

motions. The general trend shown is similar to that published in [6]. In addition, a dynamic

model verification for a soil retaining system has been given in [9].

-6

-4

-2

0

2

4

6

0 1 2 3 4

Inp

ut

Acc

ele

rati

on

(m

/s2)

Time (s)



3.2. Basement Wall Acceleration

The time history of the horizontal basement wall acceleration for input acceleration = 0.2 g is

shown in Figure 5 (top), while that for input acceleration = 0.7 g is shown in Figure 5

(bottom). Three monitoring locations are considered: 0.67 m (about top floor slab level), 4.0

m (middle floor slab level), and 8.0 m (bottom floor slab level). In general, the absolute

values of maximum and minimum wall acceleration are relatively the same, following the

pattern of the input harmonic acceleration. The peak wall acceleration values were greater

than the peak input acceleration. The amplification factors could then be calculated as the

ratio of peak wall acceleration to peak input acceleration. Table 4 summarizes the

amplification factors at top and bottom floor slab levels. As expected, the amplification

factors at top floor slab level were greater than those at bottom floor slab level, and the factors

for input acceleration = 0.2 g were greater than those input acceleration = 0.7 g.

Figure 3 Static model verifications

Figure 4 Dynamic model verification

0

2

4

6

8

10

12

14

16

18

0 20 40 60 80 100 120

De

pth

(m

)

pA (kPa)

Basement Level

Emb. Depth = 4 m

Emb. Depth = 6 m

Emb. Depth = 8 m

Emb. Depth = 10 m

Active (Rankine)

At-Rest

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8

Wa

ll A

cce

lera

tio

n (

g)

Input Acceleration (g)

Emb. Depth = 4 m

Emb. Depth = 6 m

Emb. Depth = 8 m

Emb. Depth = 10 m



Table 4 Amplification factors

Depth (m) Input acc. = 0.2 g Input acc. = 0.2 g

0.67 2.845 1.697

8.00 1.934 1.445

The wall acceleration maximum value at depth of 8 m for input acceleration = 0.2 g was

about 3.5 m/s2, while that for input acceleration = 0.7 g was about 10 m/s

2. The increase in

wall acceleration appears not to be linearly proportional to the increase in the peak input

acceleration.

It is clear that there was a phase difference between the peaks of horizontal wall

acceleration; for example, the peak at depth of 8.0 m occurred first, followed subsequently by

that at depth of 4.0 m and 0.67 m. This suggests that, although it was of high stiffness (t = 0.6

m, supported by 3 levels of floor slabs), the basement did not act as a completely rigid body.

The time history of the horizontal wall acceleration (at bottom floor slab level, input

acceleration = 0.5 g) for basements with different wall lengths beneath the excavation level or

wall embedment depths (4 m, 6 m, 8 m, and 10 m) is shown in Figure 6. It can be seen that

the acceleration of walls with different embedment depths was relative similar to each other.

Therefore, it can be concluded that the embedment depths had a minor effect on the wall

acceleration.

Figure 5 Horizontal wall acceleration at different depths: Input acceleration 0.2g (top) and 0.7g

(bottom)

-15

-10

-5

0

5

10

15

0 1 2 3 4

Wal

l Acc

eler

atio

n (m

/s2 )

Time (s)

z=0.67m z=4.00m z=8.00m

-15

-10

-5

0

5

10

15

0 1 2 3 4

Wal

l Acc

eler

atio

n (m

/s2 )

Time (s)

z=0.67m z=4.00m z=8.00m



Figure 6 Horizontal wall acceleration: Effect of wall embedment depths

3.3. Lateral Earth Pressures

The time history of the total dynamic lateral earth pressures (pAE) acting on the basement wall

for input acceleration = 0.2 g is shown in Figure 7 (top), while the corresponding time history

of change in lateral earth pressures (= total dynamic lateral earth pressure – static lateral earth

pressure, ∆pAE) is shown in Figure 7 (bottom). It is noted that a positive pressure is a

compressive pressure. Five monitoring locations are considered: 0.85 m (about ground surface

level), 1.8 m (about midway between top and middle floor slabs), 4.0 m (middle slab level),

6.2 m (about midway between middle and bottom floor slabs), and 7.9 (slightly above bottom

floor slab). In general, pAE and ∆pAE followed harmonic nature of the input acceleration time

history. In all observation points, pAE remained in compression. The envelope of ∆pAE was

relatively symmetrical (absolute values of maximum and minimum change in pressures

relatively the same).

The time history of pAE for input acceleration = 0.7 g is shown in Figure 8 (top), while

∆pAE is shown in Figure 8 (bottom). The minimum values of pAE were about zero due to

limited soil tensile strength, and the resulting ∆pAE was not symmetrical. This condition was

observed for relatively shallow stress points (0.85 m and 1.8 m). The difference in results for

input acceleration = 0.2 g and 0.7 g suggested that the general trend of ∆pAE would be

affected by the soil tensile strength.

-15

-10

-5

0

5

10

15

0 1 2 3 4

Wal

l Acc

eler

atio

n (m

/s2)

Time (s)

ED = 4 m ED = 6 m

ED = 8 m ED = 10 m

0

100

200

300

0 1 2 3 4

pA

E(k

N/m

2)

z=0.85m z=1.82m z=4m

z=6.18m z=7.92m



Figure 7 Lateral earth pressure acting on basement wall (0.2g): Total pressure (top) and change in

pressure (bottom)

The maximum value of ∆pAE for input acceleration = 0.2 g was in the order of 45 kPa,

while that for input acceleration = 0.7 g was in the order of 135 kPa. The increase in ∆pAE

appears not to be linearly proportional to the increase in the peak input acceleration.

It is clear that there was a phase difference between the peaks of ∆pAE. For input

acceleration = 0.2 g, the first local peaks of ∆pAE for depths = 0.8 m and 1.8 m occurred at

slightly different times, but ∆pAE for depths = 4.0 m, 6.2 m, and 7.9 m decreased and reached

the local minimum values at slightly different times. A moment latter, the first local peaks of

∆pAE for depths = 4.0 m, 6.2 m, and 7.9 m occurred at slightly different times, but ∆pAE for

depths = 0.8 m and 1.8 m decreased and reached the local minimum values at slightly

different times. Nevertheless, the harmonic nature of pAE could clearly be seen. For input

acceleration = 0.7 g, a similar trend could be observed. However, the harmonic nature of pAE

and ∆pAE became less clearer.

The time history of ∆pAE (at middle floor slab level, input acceleration = 0.5 g) for

basements with different wall embedment depths is shown in Figure 9. It can be seen that

∆pAE of walls with different embedment depths was relative similar to each other, or in other

words, the embedment depths had a minor effect on ∆pAE.

-100

0

100

200

0 1 2 3 4

Δp

AE

(kN

/m2)

Time (s)

z=0.85m z=1.82m

z=4m z=6.18m

z=7.92m

0

100

200

300

pA

E(k

N/m

2)

z=0.85m z=1.82m

z=4m z=6.18m

z=7.92m



Figure 8 Lateral earth pressure acting on basement wall (0.7g): Total pressure (top) and change in

pressure (bottom)

Figure 9 Change in lateral earth pressure: Effect of wall embedment depths

The distribution of ∆pAE with depth for five (5) conditions is shown as Figure 10 (top) for

input acceleration = 0.2 g. In the first and second conditions in which ∆pAE at depth = 0.8 m

and 1.8 m was maximum respectively, ∆pAE decreased with depth, and ∆pAE even became

negative. In the third through fifth conditions in which ∆pAE at depth = 4.0 m, 6.2 m, and 7.9

m was maximum respectively, ∆pAE was relatively uniform to depth of about 6 m, and it

increased with depth. The maximum ∆pAE values for all conditions were relatively the same.

The distribution of ∆pAE with depth for five (5) conditions is shown as Figure 10 (bottom)

for input acceleration = 0.7 g. In the first and second conditions, ∆pAE remained relatively

uniform to depth of about 2 m, then decreased with depth to depth of about 4 m, then

remained relatively uniform to depth of about 7 m, and finally increased. In the third through

fifth conditions, ∆pAE was relatively uniform to depth of about 3 m, and it increased with

depth. The maximum ∆pAE values for all conditions increased gradually from the first to the

fifth conditions. In addition, the use of ∆pAE envelope for both input acceleration values

would lead to a very conservative design.

-100

0

100

200

0 1 2 3 4

Δp

AE

(kN

/m2)

Time (s)

z=0.85m z=1.82m z=4m

z=6.18m z=7.92m

-100

0

100

200

0 1 2 3 4

∆∆ ∆∆p A

E(k

N/m

2 )

Time (s)

ED = 4 m ED = 6 m

ED = 8 m ED = 10 m



For a given condition in Figure 10, the distribution with depth and maximum value of

∆pAE for input acceleration = 0.2 g were not linearly proportional to those for input

acceleration = 0.7 g. For the first condition, the distribution of ∆pAE could be negative in the

lower wall part for 0.2 g case, but that for 0.7 g case was all positive. For the third condition,

the distribution of ∆pAE decreased in the upper wall part, but increased in the lower wall part,

with an increase in peak input acceleration. For the fifth condition, the distribution of ∆pAE up

to depth of 3 m was relatively similar for both cases, but that below that depth was

significantly different.

3.4. Lateral Total Thrusts

The change in lateral earth pressures (∆pAE) can be subsequently integrated to obtain the

lateral total thrusts (PAE). The time history of PAE can also be obtained. Figure 11 (top) shows

the time history of PAE for input acceleration = 0.2 g, while Figure 11 (bottom) shows that for

input acceleration = 0.7 g. The harmonic nature of PAE could clearly be seen. For the

considered cases, the dynamic thrust appears to be stable after time about 2 seconds. For input

acceleration = 0.2 g, the maximum and minimum PAE values in the stable time period were

about 200 to 250 kN/m and 50 to 100 kN/m, respectively. For input acceleration = 0.7 g, the

maximum and minimum PAE values in the stable time period were about 500 to 550 kN/m and

200 to 250 kN/m, respectively. The increase in maximum and minimum PAE values, as well in

the increase in difference between the maximum and minimum PAE values, appear not to be

linearly proportional to the increase in the peak input acceleration.

0

1

2

3

4

5

6

7

8

-40 0 40 80 120 160

De

pth

(m

)

∆∆∆∆pAE (kN/m2)

z = 0.85 m (t = 1.016 s)

z = 1.82 m (t = 3.691 s)

z = 4.00 m (t = 1.880 s)

z = 6.18 m (t = 2.562 s)

z = 7.92 m (t = 1.900 s)



Figure 10 Distribution of lateral earth pressure with depth for five conditions: Input acceleration 0.2g

(top) and 0.7g (bottom)

Figure 11 Lateral total thrusts: Input acceleration 0.2g (top) and 0.7g (bottom)

0

1

2

3

4

5

6

7

8

-40 0 40 80 120 160

De

pth

(m

)

∆∆∆∆pAE (kN/m2)

z = 0.85 m

(t = 0.976 s)

z = 1.82 m

(t = 1.952 s)

z = 4.00 m

(t = 3.498 s)

z = 6.18 m

(t = 3.855 s)

z = 7.92 m

(t = 3.867 s)

-200

0

200

400

600

0 1 2 3 4

PA

E(k

N/m

)

-200

0

200

400

600

0 1 2 3 4

PA

E(k

N/m

)

Time (s)



4. DISCUSSIONS

The absolute values of maximum and minimum wall acceleration were relatively the same in

each case of input acceleration = 0.2 g and 0.7 g, following the pattern of the input harmonic

acceleration. The peak wall acceleration values were greater than the peak input acceleration.

The amplification factors (= peak wall acceleration / peak input acceleration) at top floor slab

level were greater than those at bottom floor slab level. The factors for input acceleration =

0.2 g were greater than those input acceleration = 0.7 g, consistent with outputs from other

soil retaining system studies [e.g., 6].

The time histories of change in lateral earth pressures (∆pAE) for both input acceleration =

0.2 g and 0.7 g had different characteristics. The envelope of ∆pAE for the former was

relatively symmetrical, while that for the latter was not symmetrical due to the minimum

values of pAE about zero due to the limiting soil tensile strength. This behavior is consistent

with the behavior observed in [5].

The distribution with depth and maximum value of ∆pAE were also examined. for input

acceleration = 0.2 g were not linearly proportional to those for input acceleration = 0.7 g. Not

only the values, the shape of the distribution with depth of ∆pAE varied considerably,

indicating a complex nature of the soil-structure interaction of basement structures.

Nevertheless, the use of ∆pAE envelope for both input acceleration values would lead to a very

conservative design.

Figure 12 Relationship between total thrust and wall horizontal acceleration: Input acceleration 0.2g

(top) and 0.7g (bottom)

-100

0

100

200

300

400

500

600

-8 -6 -4 -2 0 2 4 6 8

Tota

l Th

rust

(kN

/m)

Wall Acceleration @ 4 m (m/s2)

-100

0

100

200

300

400

500

600

-8 -6 -4 -2 0 2 4 6 8

Tota

l Th

rust

(k

N/m

)

Wall Acceleration @ 4 m (m/s2)



The lateral total thrusts (PAE) could be examined against the horizontal wall acceleration.

Figure 12 shows PAE taken from Figure 11 and wall acceleration taken from Figure 5. For the

stable time period after 2 seconds, the relationship between PAE and wall acceleration is

highly non-linear for both input acceleration = 0.2 g and 0.7 g, although the latter appears to

be at a higher complexity level. A negative wall acceleration (to left of the model) caused the

maximum PAE, while the positive acceleration caused the minimum PAE in the stable time

period. This behavior emphasizes the complex nature of the soil-structure interaction of

basement structures.

It was observed that there was a phase difference between the peaks of horizontal wall

acceleration at different depths. Furthermore, it was also observed that there was a phase

difference between the peaks of ∆pAE. At certain depths, the difference could be significant,

an increase in ∆pAE at a certain depth accompanied with a decrease in ∆pAE at a different

depth and vice versa. This phase difference was clear, although the wall had a relatively high

stiffness (t = 0.6 m, supported by 3 levels of floor slabs). The harmonic time history pattern of

∆pAE became less apparent for a higher peak input acceleration, possibly due to the soil linear

behavior. This phase difference was also observed in centrifuge test results [10] and other

numerical simulations [6]. Nevertheless, the relationship between PAE and wall acceleration

suggests that the phase difference might not be of great importance in the overall behavior.

The time history of the horizontal wall acceleration and that of ∆pAE for basements with

different wall lengths beneath the excavation level or wall embedment depths (4 m, 6 m, 8 m,

and 10 m) were shown in Figures 4 and 9. In both figures, the acceleration and ∆pAE of walls

with different embedment depths were relative similar to each other. Therefore, it can be

concluded that the embedment depths had a minor effect on the wall acceleration and ∆pAE.

5. CONCLUSIONS

The absolute values of maximum and minimum wall acceleration were relatively the same in

each case of input acceleration = 0.2 g and 0.7 g, following the pattern of the input harmonic

acceleration. The peak wall acceleration values were greater than the peak input acceleration.

The amplification factors (= peak wall acceleration / peak input acceleration) at top floor slab

level were greater than those at bottom floor slab level. The factors for input acceleration =

0.2 g were greater than those input acceleration = 0.7 g, consistent with outputs from other

soil retaining system studies [e.g., 6 The 2-D plane strain dynamic finite element models were

used to examine the lateral earth pressures on 2-story basement walls induced by constant

peak value, harmonic ground motions. The soil constitutive model used was the Mohr-

Coulomb model with very limited tensile strength to represent a sands deposit. Four different

embedment wall depths were also considered. The overall results showed the complex nature

of the dynamic soil-structure interaction of basement structures. Some highlighted qualitative

points are as follows:

• The envelope of ∆pAE was dependent on the peak input acceleration due to the

limiting soil tensile strength.

• The increase in horizontal wall acceleration, ∆pAE, and PAE appeared not to be

linearly proportional to the increase in the peak input acceleration.

• The relationship between PAE and wall acceleration was highly non-linear, and the

complexity appears to increase with a higher input acceleration.

• A phase difference was observed in horizontal wall acceleration and ∆pAE.

• The embedment wall depths had a minor effect on the wall acceleration and ∆pAE.



ACKNOWLEDGEMENTS

The authors gratefully acknowledge the partial support from the 2017 PITTA research grant

provided by Universitas Indonesia.

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dynamic lateral earth pressures on …€¦ · pressures, and also the rankine active earth...

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