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Impact of wall movements on the location of passive Earth thrust

  • Meriem F. Bouali , Mahdi O. Karkush EMAIL logo and Mounir Bouassida
Published/Copyright: May 19, 2021
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Open Geosciences
From the journal Open Geosciences Volume 13 Issue 1

Abstract

The general assumption of linear variation of earth pressures with depth on retaining structures is still controversial; investigations are yet required to determine those distributions of the passive earth pressure (PEP) accurately and deduce the corresponding centroid location. In particular, for rigid retaining walls, the calculation of PEP is strongly dependent on the type of wall movement. This paper presents a numerical analysis for studying the influence of wall movement on the PEP distribution on a rigid retaining wall and the passive earth thrust location. The numerical predictions are remarkably similar to existing experimental works as recorded on scaled test models and full-scale retaining walls. It is observed that the PEP varies linearly with depth for the horizontal translation, but it is nonlinear when the movement is rotational about the top of the retaining wall. When rotation is around the top of the wall, the resultant of PEP is located at a depth that varies between 0.164 and 0.259H of the wall height measured from the base of the wall, which is lesser than 1/3 of the wall height. The passive earth thrust location is highly affected by the soil–wall friction angle, especially when the friction angle of the backfill material increases. Despite the herein presented results, further experiments are recommended to assess the corresponding numerical predictions.

Keywords: passive pressure; numerical analysis; rotation; translation movement; wall

1 Introduction

Earth pressure distribution is an important condition for the economical and secure design of retaining walls, sheet piles, and diaphragm walls. The soil pressures determined by the theory of Rankine [1] or Coulomb [2] assumed a linear surface of failure and the resultant of the passive earth pressure (PEP) is located at 1/3H measured from the wall base. The geotechnical engineers still follow these ideas in the analysis and design of retaining walls until now. Several experimental studies suggested that the movement of the wall greatly affects the distribution of PEP and its centroid [3,4,5,6,7,8,9]. Based on the existing contributions in this field, the coefficient of PEP (K p) and the normalized depth (h/H) where the resultant of PEP acts are considered the key parameters in estimating the distribution of PEP. Literature review showed that few investigations are available as related to PEP induced by retaining walls. Earlier, Fang et al. (1994) [4] studied different displacement modes and various densities of sand to analyze the distribution of PEP.

Later, Fang et al. (2002) [10] conducted series of experiments dealing with PEP distribution using loose cohesionless backfill material. Those authors concluded that the passive pressure distribution is linear and in good agreement with a classical solution.

Recently, Dou et al. [5] carried out experimental and analytical investigations for studying the distribution of the passive soil pressure exerted on a wall model subjected to rotation around its top. Those authors analyzed the effect of relative density of the backfill material on PEP distribution and the centroid of passive earth force.

Regarding analytical contributions, the solution provided by Kérisel and Absi [11] enables the effect of soil–wall frictional contact to derive the PEP.

Studying the effects of the types of movement on the distribution of PEP exerted on a retaining wall is very useful because of its substantial importance in the practice of design and analysis of retaining structures. As the first example, coal mining activities and ships operations during berthing represent some of the main applications of induced passive earth stress by quay wall. The second example corresponds to buildings comprising basement levels when subjected to the wind solicitation and also generates the passive earth state.

The numerical analysis applications have been extended to several problems; it has been concluded that such tools are suitable to analyze geotechnical problems [12,13,14,15,16]. However, the FEM requires calibration by selecting appropriate parameters or a soil constitutive model. Accordingly, this numerical investigation’s main objective is to investigate the distribution of PEP on a rigid retaining wall subjected to a horizontal translation movement and rotational movement around its top. Applicability of the translation and rotation movements is essentially viewed from the in situ observed failure modes. Meanwhile, one can adopt that translation movement applies for soil failure only produced over the retaining structure’s height. However, rotation failure mode essentially involves in a more significant volume of landslide surrounding the retaining structure. In this paper, a numerical analysis is performed to predict a purely frictional soil behavior subject to translation and rotation movements by a rigid wall. The computed passive earth force, for different values of the interface soil–wall resistance, is compared to existing analytical and experimental results. Two main parameters govern the passive earth force: its intensity and normalized location with respect to normalized location regarding the rigid wall height. Therefore, the present work focuses on the determination of PEP induced by two types of rigid wall movements, e.g., translation and rotation around the top, on which very few contributions exist. Indeed, the proposed results highlighted the significant influence of the type of wall movement on the distribution and the resultant of PEP for cohesionless backfill material.

2 Numerical analysis

A numerical model is adopted to predict the PEP distribution on a rigid wall undergoing two movement types. The first type of movement is a horizontal translation (T), where S represents the maximum uniform horizontal displacement as shown in Figure 1a. The second type of movement is a rotation around the top of the wall (RT) (Figure 1b), where θ indicates the rotation angle. In both cases, the PEP is mobilized along with a purely frictional contact between the soil and the wall.

Figure 1 Assumed wall movements. (a) Translation, (b) rotation about top.
Figure 1

Assumed wall movements. (a) Translation, (b) rotation about top.

A rigid retaining wall model is analyzed in plane strain condition using 2D finite-difference element code FLAC [17]. The cohesionless backfill material is assumed dry and homogenous. Preliminary numerical trials were implemented to select the suitable geometry of retaining wall, size of mesh, boundary conditions, and rate of displacements, (S in T movement) and (θ in RT movement), applied at the nodes over the wall height. Figure 2 shows the geometry of the wall model of 1 m height. Following the guidelines provided in FLAC [17], the dimensions of the soil model are chosen to be equal to 6 times the wall height in horizontal (x coordinate) and vertical (y coordinate) directions to mitigate the boundary effects. Boundary conditions are the following (Figure 2):

  • At x = 6H and 0 ≤ y ≤ 6H, only vertical displacement is permitted.

  • Two different boundary conditions are adopted at x = 0 and 0 ≤ y ≤ 6H:

    1. x = 0 and 5H ≤ y ≤ 6H, there are two cases: uniform horizontal displacement as shown in Figure 1a and rotational displacement as shown in Figure 1b.

    2. x = 0 and 0 ≤ y < 5H, the horizontal displacement is zero; the vertical displacement is allowed.

  • y = 0 and 0 ≤ x ≤ 6H, the horizontal and vertical displacements are not allowed (zero values).

Figure 2 The adopted mesh of the proposed numerical model.
Figure 2

The adopted mesh of the proposed numerical model.

Several numerical models were performed to choose the most appropriate one to ensure that the developed failure surface is entirely located in the backfill material, i.e., it does not intercept the vertical right-hand boundary. The mesh size is refined near the wall-soil interface, where the maximum deformations are distributed, as shown in Figure 2. The discretization of the experimental model requires introducing a suitable interface element to characterize the friction soil–wall contact. Hence, joints of zero thickness are used to simulate the interface element. The cohesionless interface is characterized by a normal stiffness K n = 103 MPa/m and a shear stiffness K s = 103 MPa/m; the frictional contact at the soil and wall interface takes the following normalized values: δ/φ = 0; 1/3; 1/2; 2/3; 1. The friction angle of the backfill material (φ) varies as 20, 25, 30, 35, and 40° (Fang et al. 1994) [4]. Following the recommendations given in the FLAC [17] users guide, the values of normal and tangent stiffnesses, K n and K s, of the soil–wall interface are assumed equal ten times the equivalent stiffness of the adjacent element. The stress–strain behavior of soil is supposed to be linear elastic-perfectly plastic and to obey Mohr–Coulomb failure criteria with related flow rule. The soil properties are: unit weight (γ) is 20 kN/m3, the Young modulus (E) is 27 MPa, Poisson’s ratio (ν) is 0.35, the shear modulus (G) is 10 MPa, and the bulk modulus (K) is 30 MPa [18]. It is noted that the magnitude of the PEP coefficient (K p) does not depend on the soil’s elastic properties [19].

The rigid retaining wall moves towards the backfill material to create the passive soil failure. In the case of the translation movement (T), a prolonged displacement rate of 10−6 m/step is applied to all wall elements (Figure 3a). For the rotational movement (RT), a rotation angle of magnitude 2.10−4 rad is applied around the wall’s top edge (Figure 3b). As the wall starts to move towards the soil, a steady plastic flow is induced in it, which is accompanied by gradual increase in the PEP. The corresponding PEP to the displacement causing the plastic condition describes the ultimate passive earth force as shown in Figure 4, where P p corresponds to the ultimate passive force’s recorded asymptotic value. Hence, the coefficient of PEP (K p) can be calculated using equation (1):

(1) K p = 2 P p / ( γ H 2 cos δ )

Figure 3 Predicted displacements field in the backfill material at the passive state. (a) Translation movement (T), (b) rotation around the top (RT).
Figure 3

Predicted displacements field in the backfill material at the passive state. (a) Translation movement (T), (b) rotation around the top (RT).

Figure 4 Variation of the passive earth force versus the number of iterations.
Figure 4

Variation of the passive earth force versus the number of iterations.

The centroid of the resultant of the PEP is normalized to the wall height (h/H); where h is the distance between the wall base and the location of the PEP resultant.

3 Results and discussion

3.1 Analysis of rigid wall under translation movement

Assessment of the numerical model’s predictions is carried out through comparison with available experimental results and theoretical solutions of the PEP coefficient (K p), the PEP distribution, and the centroid of the PEP force.

3.2 Predictions of the coefficient of PEP (K p)

First, K p’s numerical results are compared with the existing solutions offered in research [11,18,20]. Figures 5 and 6 show the variation of PEP coefficient (K p) obtained from those existing solutions versus the friction angle of backfill material (φ) and the angle of frictional contact between the soil and the wall (δ). Four prediction methods are considered, including the analytical methods suggested in ref. [11,20]. Numerical predictions correspond to the present analysis and the analysis by Benmeddour et al. [18]. Note that Benmeddour et al. [18] did not calculate the K p value for δ = φ. Figure 6 shows the comparison corresponding to this case only considered with ref. [11,20].

Figure 5 Analytical and numerical K p values versus friction angle of backfill material for different interface friction angles (δ/φ = 0, 1/3, 1/2, 2/3).
Figure 5

Analytical and numerical K p values versus friction angle of backfill material for different interface friction angles (δ/φ = 0, 1/3, 1/2, 2/3).

Figure 6 Variation of K p with the friction angle (φ) of backfill material for δ = φ.
Figure 6

Variation of K p with the friction angle (φ) of backfill material for δ = φ.

From Figure 5, it is clear that in the range 0 ≤ δ/φ ≤ 1/3, the proposed numerical and analytical methods lead to the same value of the PEP coefficient K p. A little difference between K p values is noted when the backfill material’s friction angle exceeds 35°. The conservative prediction is that obtained by the present analysis; the maximum prediction of K p corresponds to the research proposed by ref. [20]. In turn, from δ/φ = 2/3 to 1, Figure 6 shows significant differences between the values of K p obtained by the present analysis and the existing numerical and analytical methods. For the most considered assumption, i.e., δ/φ = 2/3, the maximum difference is marked between K p values 6 and 7 for φ = 35°, then between 10.8 and 12.5 for φ = 40°. This difference becomes more remarkable when assuming a total adhesion between the soil and wall interface: δ = φ. Regardless the relative differences between the results herein presented and those proposed by Kérisel and Absi [11] and Soubra and Macuh [20], one notes that the kinematic approach of limit analysis often provides an upper bound solution that is visible from Figure 6. Absi and Kérisel’s analytical solution is found between the upper bound solution and the proposed numérical results deduced from FLAC 2D code. The latter, as perceived as an approximation of an exact solution, may lead to underestimated predictions.

3.3 PEP distribution

Figure 7 shows the normalized distribution of PEP on a rigid vertical wall, where the earth pressure is divided by the overburden pressure (γH), and the depth (z) is divided by the wall height (H). Linear variation of the PEP is almost predicted over 90% of the rigid wall height; meanwhile, close to the wall base, a nonlinear variation of the PEP is obtained, particularly in case of a perfectly rough wall (δ = φ). First, the results shown in Figure 7 indicate that the present numerical investigation’s predictions are confirmed by the analytical solution proposed by the Rankine’s theory up to a depth that equals 0.93H. The nonlinearity observed at the wall base is attributed to the boundary conditions applied to the node in discretizing the wall by the finite-difference method. One notes that the increase in the angle of friction of the soil–wall contact causes the PEP growth with an exception made to the case δ = φ.

Figure 7 Normalized earth pressure versus normalized depth for rigid wall subjected to translation movement (φ = 30°).
Figure 7

Normalized earth pressure versus normalized depth for rigid wall subjected to translation movement (φ = 30°).

Figure 8 shows the variation of maximum shear strains behind the rigid wall undergoing a translation movement in cases of the smooth soil–wall interface (δ = 0) and rough soil–wall interface (δ = φ) for φ = 30°. When a smooth soil–wall interface is considered, the shear failure surface is linear and oriented from the wall base to the ground surface and the failure angle (θ) is about 29.214° (Figure 8a). The angle of the failure plane, concerning horizontal direction, is approximately equal to the theoretical value by Rankine theory, i.e., θ = tan−1(45 − φ/2) = 29.985° [1]. In contrast, Figure 8b shows that the shear failure surface is somewhat curved log-spiral one for a rough soil–wall contact. The corresponding predicted failure mechanism is quite similar to that of the limit equilibrium Prandlt’s solution.

Figure 8 Distribution of shear strains behind a rigid wall subjected to the horizontal movement for smooth and rough contacts with the backfill material (φ = 30°). (a) Smooth soil–wall interface (δ = 0), (b) rough soil–wall interface (δ = φ).
Figure 8

Distribution of shear strains behind a rigid wall subjected to the horizontal movement for smooth and rough contacts with the backfill material (φ = 30°). (a) Smooth soil–wall interface (δ = 0), (b) rough soil–wall interface (δ = φ).

Using the critical state concept, Fang et al. [10] analyzed the effect of the relative density (D r) of backfill material on the PEP. The experiments were performed for horizontal cohesionless backfill material retained by a vertical rigid wall undergoing horizontal translation movement. Fang et al. [10] concluded, for a loose backfill material (D r = 38%), that the passive condition occurred when the normalized wall displacement is about S max/H = 0.17. In the case of medium dense (D r = 63%) and very dense (D r = 80%) backfill material, the peak of PEPs were recorded for normalized horizontal displacements of S max/H = 0.03 and S max/H = 0.01, respectively. After that, adopting the residual shear strength of backfill material, the predicted PEP is reduced; the ultimate passive force was recorded at normalized horizontal displacement S max/H = 0.10 for medium dense backfill material and S max/H = 0.20 for dense backfill material. Table 1 compares PEP’s predicted coefficient (K p) by FLAC code with those suggested by Fang et al. [10].

Table 1

Comparison of predicted K p and S max values with recorded data by Fang et al. [10]

Shear strength Backfill density D r (%) δ (°) φ p (°) Fang et al. [6] Present analysis
K p S max/H K p S max/H
Peak shear strength Loose 38 9.8 33.0 5.0 0.17 5.366 0.17
Medium 63 12.6 38.3 6.5 0.03 6.500 0.03
Dense 80 14.0 42.1 8.2 0.01 6.786 0.02
Residual shear strength Loose 38 9.8 31.5 5.0 0.17 5.008 0.17
Medium 63 12.6 31.5 4.8 0.10 5.306 0.11
Dense 80 14.0 31.5 4.8 0.20 5.453 0.20

The present analysis results provide an acceptable estimation of the PEP coefficient (K p) with a maximum relative difference of −20.84, 9.54, and 6.82% for the dense, medium dense, and loose backfill materials, respectively. When adopting the peak shear strength for the dense backfill material, the maximum difference in the normalized horizontal displacement is equal to 50%. Indeed, in the case of dense sand, from Table 1, the normalized horizontal displacement is between 0.01 and 0.2. Based on the maximum relative differences of K p values, one notes that friction angles adopted by Fang et al. of 42.1°, 38.30°, and 33° for dense, medium, dense, and loose sands, respectively, are overestimated. More likely, Fang et al. [10] adopted those failure values in a range exceeding the small strain one, i.e., greater than 5%.

Indeed, for sands, current friction angle values of those three density states are rather equal to 28–29°, 30–31°, and 38–39°, respectively Kérisel and Absi [11]. As such, the high relative difference for the dense sand can be argued.

4 Analysis of rigid wall under rotational movement

Early experimental work presented by Fang et al. [4] showed a nonlinear distribution for the PEP on the rigid wall, which depends on the wall movement’s type before reaching the failure phase. Experimental results of those authors are used to assess the predictions by the present numerical analysis. The main parameters used in the study are the backfill material’s friction angle φ = 30.9° and the friction angle of soil–wall is δ = 19.2°. When a rigid wall undergoes a translation movement, Figure 9 indicates that the variation of experimental normalized PEP with depth well agrees with the predicted one up to a normalized depth equal to 0.8. Precisely, from the ground surface to a depth equaling to 0.38H, numerical predictions are underestimated compared to the experimental results; the maximum relative difference equals 24%. Meanwhile, for depth between 0.38 and 0.8H, the numerical predictions overestimate the experimental results obtained by Fang et al. [4] with a maximum relative difference of 23%.

Figure 9 Distribution of PEP with experimental results by Fang et al. [4] (φ = 30.9° and δ = 19.2°).
Figure 9

Distribution of PEP with experimental results by Fang et al. [4] (φ = 30.9° and δ = 19.2°).

From Figure 9, when a rigid wall undergoes a rotation around the top RT, between depths 0.37 and 0.95H, the predicted PEP significantly overestimates the recorded values [4]. The experimental centroid is located at a depth equal to 0.18H above the rigid wall base (Table 2). However, the predicted numerical centroid equals 0.26H above the rigid wall base. The relative difference between the two results is not negligible, i.e., 30.77%. Although the experimental and numerical normalized horizontal displacement of the rigid wall is in good agreement, the discrepancy in terms of recorded and predicted passive stresses can be attributed to the adopted value of soil–wall contact’s friction angle.

Table 2

Predicted maximum horizontal displacement, S max, and the centroid of PEP force compared with results of Fang et al. [4]

Wall movement φ (°) δ (°) Fang et al. [4] Present analysis
S max/H Centroid S max/H Centroid
Translation (T) 30.9 19.2 0.18 0.36 0.18 0.334
Rotation around the top (RT) 0.20 0.18 0.20 0.260

From the results suggested by Fang et al. [4], one concludes that the magnitude of the passive force and its location significantly depend on the type of wall movement (Figure 9).

Further, the assessment of numerical predictions using Dou et al.’s [5] experimental data leads to a good agreement between the values of the centroid of passive force predicted by FLAC 2D code which clearly appears in Table 3. For the loose and the medium dense backfill, the maximum relative difference is 0.57 and 0.09%, respectively. However, for the dense sand case, the passive force’s centroid is applied at depth of 0.8032H, which is slightly different from the experimental result, i.e., 0.735H. Scatter is about 8.18% for recorded data and 7.28% for analytical results. Also, at depths less than 0.3H, there is no effect of the relative density of the backfill material on PEP’s value; the numerical results agree well with those recorded from the experiments.

Table 3

Comparison of the calculated centroid of PEP with results of Dou et al. [5]

Backfill density φ (°) δ (°) The centroid of earth pressure from the soil surface
Dou et al. [5] Present analysis
Experimental Theoretical
Loose sand 32.60 10.87 0.7547 0.7796 0.7590
Medium sand 34.00 11.33 0.7786 0.7827 0.7793
Dense sand 42.99 14.33 0.7375 0.7448 0.8032

Figure 10 shows that the predicted PEP in loose sand is not confirmed by Dou et al. [5] results, significantly beyond a normalized depth equal to 0.5. In turn, for medium and dense sands, FLAC predictions are in good agreement with recorded data. Figure 10 shows the validation of FLAC 2D code predictions by the experimental results up to a depth equals the half of the wall height for medium sand retained by a rigid wall rotating around its top.

Figure 10 Variation of the PEP with depth from experimental results [5] and predictions by the numerical analysis.
Figure 10

Variation of the PEP with depth from experimental results [5] and predictions by the numerical analysis.

Beyond this depth, the results obtained by FLAC 2D code overestimate the experimental results by 33%. The results shown in Figure 10 show that the predicted PEP by the FLAC 2D code for loose, medium, and dense backfill materials underestimates the experimental results up to a depth equal to 0.63H. Beyond this depth, this trend is reversed.

5 Recommended design parameters

The proposed numerical model was used to investigate the effects of the friction angle (φ) of backfill material and the contact friction angle (δ) between the soil and rigid wall on the PEP coefficient and the centroid of resultant of passive pressure. Table 4 summarizes the calculated PEP coefficient and centroid for five values of the friction angle of backfill material (φ = 20°, 25°, 30°, 35°, and 40°) and five values of contact friction angle (δ = 0, 0.333φ, 0.5φ, 0.667φ, and φ). Overall, the predicted PEP coefficient and centroid in the present work, for both T and RT movements, are in good agreement with earlier solution suggested by Kérisel and Absi [11]. Moreover, the predicted PEP coefficient for translation movement (T) is higher than that of rotational movement (RT).

Table 4

Comparison of K p and the centroid of the resultant of PEP as obtained from the present analysis with Kérisel and Absi [11] solution

φ (°) φ/δ Kérisel and Absi [11] Present analysis
K p Centroid T-mode RT-mode
K p Centroid K p Centroid
20 0 2.05 0.333 2.076 0.322 2.052 0.235
1/3 2.40 2.403 0.327 2.311 0.240
1/2 2.55 2.564 0.328 2.438 0.246
2/3 2.75 2.720 0.329 2.549 0.249
1 3.10 2.956 0.336 2.717 0.259
25 0 2.45 0.333 2.515 0.320 2.45 0.214
1/3 3.10 3.079 0.326 2.893 0.223
1/2 3.40 3.376 0.327 3.110 0.232
2/3 3.70 3.676 0.329 3.283 0.239
1 4.40 4.205 0.336 3.658 0.241
30 0 3.00 0.333 3.070 0.316 2.970 0.196
1/3 4.00 4.024 0.325 3.685 0.210
1/2 4.60 4.571 0.326 4.040 0.220
2/3 5.30 5.163 0.330 4.313 0.234
1 6.50 6.291 0.340 5.070 0.236
35 0 3.70 0.333 3.786 0.311 3.651 0.183
1/3 5.40 5.418 0.325 4.828 0.203
1/2 6.50 6.480 0.326 5.479 0.213
2/3 8.00 7.669 0.327 6.170 0.217
1 10.50 10.180 0.332 7.703 0.218
40 0 4.50 0.333 4.729 0.309 4.381 0.164
1/3 7.60 7.605 0.323 6.397 0.183
1/2 9.60 9.676 0.323 7.817 0.192
2/3 12.00 11.970 0.328 9.511 0.202
1 18.00 18.710 0.351 13.560 0.225

Figure 11 shows, in normalized scale, in case of RT movement, the variation of the PEP with depth for different values of the contact friction angle (δ) between the soil and wall and the friction angle of backfill material is (φ = 30°). It is evident from the results shown in Figure 11 that the normalized PEP is marginal and not influenced by the contact friction angle (δ) from the top of the wall to a depth equal to 0.4H. Then, from depth equaling to 0.4H to a depth equaling to 0.83H, the normalized pressure increases linearly with a noticeable effect on the contact angle (δ). In this range of depth, when the value of δ increases, the PEP also increases. There is an arbitrary distribution at depth greater than 0.94H for the normalized PEP, which can be related to the boundary conditions at the base of the rigid wall both for the T and RT movements.

Figure 11 The effect of contact angle (δ) on the variation of the normalized PEP (φ = 30° and RT-movement).
Figure 11

The effect of contact angle (δ) on the variation of the normalized PEP (φ = 30° and RT-movement).

Based on the results shown in Figure 12, it is clear at depth equaling to 0.32H from the wall base in the case of translation movement, the centroid of PEP is almost constant. Therefore, the soil–wall friction angle (δ) and the friction angle of backfill material (φ) have negligible effects on the variation of PEP with depth. The centroid of passive earth distribution decreases significantly in the range from 0.259 to 0.164H measured from the rigid wall base in the case of rotational movement (RT). In this case, one concludes the noticeable effects both of angles (δ) and (φ) on the predictions

Figure 12 Location of the resultant of PEP for various friction angles of the backfill material considering translation and rotation around the wall movements.
Figure 12

Location of the resultant of PEP for various friction angles of the backfill material considering translation and rotation around the wall movements.

A slight change was noticed in PEP’s magnitude when the contact friction angle (δ) increases from zero to φ. The centroid of PEP moves towards the wall base due to the increase in the soil density and its friction angle. Therefore, the horizontal displacement of the wall can be neglected. The present analysis’s numerical predictions indicate that PEP’s centroid can be taken to H/3 from the wall base for a horizontal translation movement (T). However, the centroid of PEP for rotation about the top of the wall (RT) is lesser than H/3 from the wall base. Values given in Table 5 are recommended for estimating the centroid of PEP on a rigid wall undergoing a rotational movement about its top.

Table 5

The recommended centroid of PEP for several backfill materials

Angle of friction of backfill material φ (°) 20 25 30 35 40
Distance from the base of wall to the resultant of PEP 0.235–0.259H 0.214–0.241H 0.196–0.236H 0.183–0.218H 0.164–0.225H

6 Conclusion

This paper aims at the numerical determination of the passive earth force generated by a rigid wall movement, either in translation or in rotation around the top, against a purely frictional soil. Implemented parametric study considered the influence of the friction angle, e.g., density, of the cohesionless soil and the soil–wall friction angle on the PEP.

The main findings from the numerical analysis conducted by the 2D FLAC code are the following:

  • The type of wall movement highly influenced the resultant of the PEP and its location. Good agreements are observed between the obtained numerical predictions, analytical results by Kérisel and Absi (1990), and experimental data proposed by Fang et al. (1994, 2002) and Dou et al. (2017).

  • The variation of the PEP force predicted by the proposed numerical wall model for translation and rotation around the top movements (T and RT) is in good accordance with those obtained from previous studies.

  • For a horizontal movement of a rigid wall (of height H) and various friction angles of backfill material, the numerical predictions showed a linear variation of the earth pressure with depth. Besides, passive pressure is located between 0.309 and 0.354H from the wall base. However, a nonlinear variation of the PEP was predicted in the case of rotational movement (RT), and the resultant of passive pressure is located at 0.4H from the wall base.

  • The distance between the resultant of PEP and the wall base decreases as the backfill material density increases.

  • The centroid of PEP is somewhat different from the classical solutions’ values when the rigid wall experienced rotational movement around its top. The centroid is approximately under 1/3H estimated from the wall base. Therefore, consideration of the suggested values (given in Table 5) is more useful for the analysis of rigid retaining walls subjected to rotational movement around the top.

  • The proposed results require further developments by investigating other types of walls and related movements by using other numerical codes. In such a way, much better update of recommendations for the design of retaining walls can be confirmed.

Acknowledgments

The authors thank the staff of the University of Mohamed Chérif Messaadia, Souk Ahras/Algeria, Staff of Civil Engineering at University of Baghdad/Iraq, and Staff of University of El Manar, Tunis, Tunisia for their help. Also, thanks extended to the General Directorate of Scientific Research and Technological Development (DGRSDT); Ministry of Higher Education and Scientific Research/Algeria for support publishing this work.

  1. Author contributions: Conceptualization: M. F. B., M. O. K., and M. B.; methodology: M. F. B. and M. O. K.; software: M. F. B.; validation: M. F. B.; formal analysis: M. F. B. and M. B.; investigation: M. F. B.; resources: M. F. B.; writing original draft preparation: M. F. B.; writing – review and editing: M. F. B., M. O. K., and M. B.; visualization: M. O. K. and M. B.; supervision: M. B.; project administration: M. O. K.; funding acquisition: M. F. B. All authors have read and agreed to the published version of the manuscript.

  2. Conflict of interest: The authors declared no conflict of interest.

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Received: 2020-12-14
Revised: 2021-03-17
Accepted: 2021-04-08
Published Online: 2021-05-19

© 2021 Meriem F. Bouali et al., published by De Gruyter

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

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https://doi.org/10.1515/geo-2020-0248
Keywords for this article
passive pressure; numerical analysis; rotation; translation movement; wall
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Lithopetrographic and geochemical features of the Saalian tills in the Szczerców outcrop (Poland) in various deformation settings
  3. Spatiotemporal change of land use for deceased in Beijing since the mid-twentieth century
  4. Geomorphological immaturity as a factor conditioning the dynamics of channel processes in Rządza River
  5. Modeling of dense well block point bar architecture based on geological vector information: A case study of the third member of Quantou Formation in Songliao Basin
  6. Predicting the gas resource potential in reservoir C-sand interval of Lower Goru Formation, Middle Indus Basin, Pakistan
  7. Study on the viscoelastic–viscoplastic model of layered siltstone using creep test and RBF neural network
  8. Assessment of Chlorophyll-a concentration from Sentinel-3 satellite images at the Mediterranean Sea using CMEMS open source in situ data
  9. Spatiotemporal evolution of single sandbodies controlled by allocyclicity and autocyclicity in the shallow-water braided river delta front of an open lacustrine basin
  10. Research and application of seismic porosity inversion method for carbonate reservoir based on Gassmann’s equation
  11. Impulse noise treatment in magnetotelluric inversion
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  13. Comparative application of photogrammetry, handmapping and android smartphone for geotechnical mapping and slope stability analysis
  14. Geochemistry of the black rock series of lower Cambrian Qiongzhusi Formation, SW Yangtze Block, China: Reconstruction of sedimentary and tectonic environments
  15. The timing of Barleik Formation and its implication for the Devonian tectonic evolution of Western Junggar, NW China
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  17. Effect of microbial combination with organic fertilizer on Elymus dahuricus
  18. An OGC web service geospatial data semantic similarity model for improving geospatial service discovery
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  23. Geospatial assessment of wetland soils for rice production in Ajibode using geospatial techniques
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  37. East Asian monsoon during the past 10,000 years recorded by grain size of Yangtze River delta
  38. Influence of diagenetic features on petrophysical properties of fine-grained rocks of Oligocene strata in the Lower Indus Basin, Pakistan
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  40. Ecological risk assessment of toxic metal pollution in the industrial zone on the northern slope of the East Tianshan Mountains in Xinjiang, NW China
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  46. Structural deformation characteristics of the Lower Yangtze area in South China and its structural physical simulation experiments
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  49. Research on the improvement of single tree segmentation algorithm based on airborne LiDAR point cloud
  50. Research on the conservation and sustainable development strategies of modern historical heritage in the Dabie Mountains based on GIS
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  53. Water deep mapping from HJ-1B satellite data by a deep network model in the sea area of Pearl River Estuary, China
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  65. Toward rainfall prediction by machine learning in Perfume River Basin, Thua Thien Hue Province, Vietnam
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  67. Compressive strength and thermal properties of sand–bentonite mixture
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  76. Spatial modeling of ground subsidence susceptibility along Al-Shamal train pathway in Saudi Arabia
  77. Pore throat characteristics of tight reservoirs by a combined mercury method: A case study of the member 2 of Xujiahe Formation in Yingshan gasfield, North Sichuan Basin
  78. Geochemistry of the mudrocks and sandstones from the Bredasdorp Basin, offshore South Africa: Implications for tectonic provenance and paleoweathering
  79. Apriori association rule and K-means clustering algorithms for interpretation of pre-event landslide areas and landslide inventory mapping
  80. Lithology classification of volcanic rocks based on conventional logging data of machine learning: A case study of the eastern depression of Liaohe oil field
  81. Sequence stratigraphy and coal accumulation model of the Taiyuan Formation in the Tashan Mine, Datong Basin, China
  82. Influence of thick soft superficial layers of seabed on ground motion and its treatment suggestions for site response analysis
  83. Monitoring the spatiotemporal dynamics of surface water body of the Xiaolangdi Reservoir using Landsat-5/7/8 imagery and Google Earth Engine
  84. Research on the traditional zoning, evolution, and integrated conservation of village cultural landscapes based on “production-living-ecology spaces” – A case study of villages in Meicheng, Guangdong, China
  85. A prediction method for water enrichment in aquifer based on GIS and coupled AHP–entropy model
  86. Earthflow reactivation assessment by multichannel analysis of surface waves and electrical resistivity tomography: A case study
  87. Geologic structures associated with gold mineralization in the Kirk Range area in Southern Malawi
  88. Research on the impact of expressway on its peripheral land use in Hunan Province, China
  89. Concentrations of heavy metals in PM2.5 and health risk assessment around Chinese New Year in Dalian, China
  90. Origin of carbonate cements in deep sandstone reservoirs and its significance for hydrocarbon indication: A case of Shahejie Formation in Dongying Sag
  91. Coupling the K-nearest neighbors and locally weighted linear regression with ensemble Kalman filter for data-driven data assimilation
  92. Multihazard susceptibility assessment: A case study – Municipality of Štrpce (Southern Serbia)
  93. A full-view scenario model for urban waterlogging response in a big data environment
  94. Elemental geochemistry of the Middle Jurassic shales in the northern Qaidam Basin, northwestern China: Constraints for tectonics and paleoclimate
  95. Geometric similarity of the twin collapsed glaciers in the west Tibet
  96. Improved gas sand facies classification and enhanced reservoir description based on calibrated rock physics modelling: A case study
  97. Utilization of dolerite waste powder for improving geotechnical parameters of compacted clay soil
  98. Geochemical characterization of the source rock intervals, Beni-Suef Basin, West Nile Valley, Egypt
  99. Satellite-based evaluation of temporal change in cultivated land in Southern Punjab (Multan region) through dynamics of vegetation and land surface temperature
  100. Ground motion of the Ms7.0 Jiuzhaigou earthquake
  101. Shale types and sedimentary environments of the Upper Ordovician Wufeng Formation-Member 1 of the Lower Silurian Longmaxi Formation in western Hubei Province, China
  102. An era of Sentinels in flood management: Potential of Sentinel-1, -2, and -3 satellites for effective flood management
  103. Water quality assessment and spatial–temporal variation analysis in Erhai lake, southwest China
  104. Dynamic analysis of particulate pollution in haze in Harbin city, Northeast China
  105. Comparison of statistical and analytical hierarchy process methods on flood susceptibility mapping: In a case study of the Lake Tana sub-basin in northwestern Ethiopia
  106. Performance comparison of the wavenumber and spatial domain techniques for mapping basement reliefs from gravity data
  107. Spatiotemporal evolution of ecological environment quality in arid areas based on the remote sensing ecological distance index: A case study of Yuyang district in Yulin city, China
  108. Petrogenesis and tectonic significance of the Mengjiaping beschtauite in the southern Taihang mountains
  109. Review Articles
  110. The significance of scanning electron microscopy (SEM) analysis on the microstructure of improved clay: An overview
  111. A review of some nonexplosive alternative methods to conventional rock blasting
  112. Retrieval of digital elevation models from Sentinel-1 radar data – open applications, techniques, and limitations
  113. A review of genetic classification and characteristics of soil cracks
  114. Potential CO2 forcing and Asian summer monsoon precipitation trends during the last 2,000 years
  115. Erratum
  116. Erratum to “Calibration of the depth invariant algorithm to monitor the tidal action of Rabigh City at the Red Sea Coast, Saudi Arabia”
  117. Rapid Communication
  118. Individual tree detection using UAV-lidar and UAV-SfM data: A tutorial for beginners
  119. Technical Note
  120. Construction and application of the 3D geo-hazard monitoring and early warning platform
  121. Enhancing the success of new dams implantation under semi-arid climate, based on a multicriteria analysis approach: Case of Marrakech region (Central Morocco)
  122. TRANSFORMATION OF TRADITIONAL CULTURAL LANDSCAPES - Koper 2019
  123. The “changing actor” and the transformation of landscapes
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