Displacement and effective stresses changes underneath strip footing on stiff ground with single and double voids Reem Sabouni Department of Civil Engineering ALHOSN University, Abu Dhabi, Abu Dhabi, United Arab Emirates ABSTRACT Settlement of structures due to soil cavities is one of the common geotechnical problems in several areas of the world. In most cases the settlement usually happens due to the fact that the cavity develops after the construction and utilization of the structure, and it is not accounted for in the foundation design stage. In this research the effect of single and double voids on the settlement and effective stresses underneath a strip footing (carrying it allowable load) is numerically investigated by two dimensional plane strain finite element analysis. To fully understand the parameters that are of influence on strip footings on single and multiple voids, a parametric study is carried out in this research to examine the effect of void depth, void distance from footing center, and void size on the settlement and effective stresses underneath these strip footings. This paper describes the models used in the course of this research along with the results of various parts of the study. From the results of this study it can be concluded that the presence of voids will affect the displacements and stresses underneath a strip footing if they have widths larger than half the footing width (B), are located at depths less than 2.5B, and are at horizontal distances away from the center of the footing of less than 3B. RÉSUMÉ Le Règlement des structures due aux cavités du sol est l'un des problèmes géotechniques fréquents dans plusieurs régions du monde. Dans la plupart des cas, le règlement existe en raison du fait que la cavité se développe après la construction et l'utilisation de la structure, et il n'est pas pris en compte dans l étape de la conception des fondations. Dans cette recherche, l'effet du simple et de double vides sur le règlement et sur les contraintes effectives sous une bande de pied (transportant la charge de travail) est analysé numériquement par deux dimensions plates des éléments finis. Afin de bien comprendre les paramètres qui ont une influence sur le pied dans un ou plusieurs vides, une étude paramétrique a été effectuée au cours de cette recherche pour étudier l'effet de profondeur du vide, la distance entre le vide et le centre du pied et la taille du vide sur le règlement et les contraintes sous les bandes. Ce document décrit les modèles utilisés au cours de cette recherche ainsi que les résultats des diverses parties de l'étude. D'après les résultats de cette étude, on peut conclure que la présence de vides affectera les déplacements et souligne sous une bande de pied si leurs largeurs est supérieure que la moitié de la largeur du pied (B), si ils sont situés à des profondeurs moins de 2.5B, et sont à distances horizontales éloignés du centre du pied de moins de 3B. 1 INTRODUCTION The presence of single or multiple voids under a foundation can cause serious engineering problems in the foundation itself and the superstructure supported by it. The effect of these voids will become more sever if they are at shallow depth below the foundation. Several experimental and numerical studies have been conducted to examine the effect of the voids on the foundation bearing capacity, yielding strength and collapse load (Baus and Wang, 1983, Kiyosumi et al. 2007, Kiyosumi, et al., 2011, Sireesh et al., 2009 and Wang and Hsieh, 1987) Baus and Wang (1983) have carried out 47 plain strain small scale model tests of shallow foundations on compacted silty clay with a continuous rectangular void centered with the foundation. In the same study they also carried out two dimensional finite element analyses with elastic perfectly plastic material. Kiyosumi et al. (2007) has studied the effect of multiple voids on the yielding pressure of a strip footing by a two dimensional plain strain finite element model analysis. Kiyosumi, et al (2011) has conducted a series of loading tests on stiff ground with continuous square voids under the plain strain conditions. These tests simulated the condition of a shallow foundation on calcareous sediment rocks with voids due to their solubility to water dissolution. Through a series of laboratory scale model tests the potential benefits of providing geocell reinforced sand mattress over subgrade with voids have been studied by Sireesh, et al. (2009). Wang and Hsieh (1987) have studied the collapse load of a strip footing centered above a continuous circular void. In this study they used the upper bound theorem of limit analysis to develop the collapse footing pressure for the strip footing. In the course of this research a parametric study was carried out to study the effect of the size and location of small single and double voids on the response of a strip footing (carrying the allowable load). The voids that were considered in this investigation were square voids with widths equal to or smaller than the strip footing width (B).
To model the effect of the presence of a cavity under the strip footing a plain stain finite element analysis model was developed in Plaxis 2D finite element analysis program (Brinkgreve, 2002). 2 INVESTIGATION METHODOLOGY AND STAGES (PARAMETRIC STUDY) Settlement of structures due to soil cavities is one of the common geotechnical problems in several areas of the world. In most cases the settlement usually happens due to the fact that the cavity develops after the construction and utilization of the structure, so it was not accounted for in the foundation design stage. To simulate this situation and evaluate its effect on the settlement and stresses of a strip footing, a 2D plain strain finite element analysis model of a strip footing - carrying the allowable load with a factor of safety of 2- was developed in Plaxis 2D. In order to investigate the effect of void s size and location on the response of a strip footing under its allowable load a parametric study was conducted in two stages. The voids under consideration were square voids with width equal to or smaller than the footing s width (B) of 2 m. Figure 1 is a schematic diagram describing the parameters varied in this study. In the first stage the effect of the presences of a single void on the displacement and the effective stresses beneath the center of the footing was studied, and in the second stage that of double voids was investigated. At the beginning, the effect of the void depth on the strip footing response was studied. The void depth was varied from 1.5B to 10.5B in intervals of B (2 m). Next, the effect of void size (w) was investigated. The void sizes studied were 0.25B, 0.5B, 0.75B and 1.0B with void center at 1.5B for all cases. After that, the effect of the horizontal distance between the center of the footing and the center of the void (h) on the footing response was studied. The distance (h) was changed from 1.0B to 11B in B (2m) intervals. In the second stage, the effect of the presence of double voids was investigated. The results from the first stage were used as a guide in selecting the effective voids sizes and locations. The two voids were selected to be square and equal in size with a width (w) of B (2m). At first, the effect of two symmetrically spaced voids with a distance h varying between 1.0B to 5B was studied (Figure 1b). Then, the effect of the presence of two consequent voids - with center to center spacing of 2B on the response of the strip footing was studied. The depth of the two voids changed from d (from the center of the top void) of 1.5B to 8.5B with increments of B (Figure 1c). The finite element analysis models used in both stages of this research are described in the next section followed by the discussion and analysis of the results of this investigation. 2 m and was modeled using an elastic plate element with a large stiffness to represent a case of rigid spread footing. To minimize the possible boundary effects the model was assigned a width of 26 B and a depth of 12.5 B. The standard boundary fixities were assigned to the model (See Figure 2). The horizontal and vertical displacements were fixed at the bottom of the model and the horizontal displacements were fixed at sides of the model. The soil was modeled using the 15-noded triangular element that incorporates 12 Gauss points. The Very fine mesh size was chosen from the program in order to get a good accuracy of the results even with changing the void location in different modelling cases in the study. A typical mesh used is shown in Figure 2. The analysis time was still found to be reasonable in all modeled cases. The soil was assumed to be an elastic perfectly plastic material, obeying the Mohr Coulomb failure criterion. The geotechnical property values used in the model are shown in Table 1. a) b) d =1.5m h B =2m h B =2m B h w d w d =1.5m d 2B =4m 3 NUMERICAL MODEL c) To model the strip footing resting on a soil with voids, a plain strain finite element model was developed in Plaxis 2D finite element program. The footing had a width (B) of Figure 1. Schematic view of the strip footing with: a) A single void, b) Two symmetric horizontal voids, and c) Two consequent vertical voids
The numerical procedure was initiated by performing an initial stress analysis. Then, the soil clusters that represent the voids were deactivated to model the case of a foundation on voids. After that the footing distributed load (q) was applied and the analysis was performed. The value of the load was chosen to match the footings allowable bearing capacity in the case of no void and with a factor of safety of 2 which was equal to 480 kn/m 2. To evaluate this uniformly distributed strip load, load increments were applied on the footing, in an initial model with no void, until the ground reached the failure state. The load increments are automatically chosen by the Plaxis 2D program and the calculations were also automatically terminated when soil failure is reached. A model similar to the above described model but with no voids present was also developed to be used as a reference model. Figure 2 shows a typical Plaxis 2D model. % Max. vertical displacement increase = Max [1] vertical disp. withvoid Maxvertical disp. novoid 100 Maxvertical novoid In the first stage the effect of changing the location and size of a single void was investigated. Figure 3 shows that the displacements and stresses underneath a strip footing will be affected by the presence of a single void (with w=b) at a depth (d) equal to or less than 2.5B. After this depth the void will cause a marginal change in the displacement and effective stresses. When the void was located at a depth of 1.5B the vertical displacement at the center of the footing increased by about 270%, whereas the effective stresses slightly decreased. This decrease maybe attributed to the fact that the void - which is located in a relatively strong soil- caused the stresses to be transferred away from the center of the footing due to the soil arching effect. Table 1. Material properties used in the model Physical properties Soil Saturated unit weight γ unsat 19 Saturated unit weight γ sat 21 Poisson s ratio v 0.3 Young s modulus E [MN/m 2 ] 100 Cohesion c [80 kn/m 2 ] 80 Internal friction angle [deg] 35 Uniformly distributed strip load Potential void locations 12.5B (25 m) Standard boundary fixities 26B (52 m) Figure 2. Typical finite element model and mesh 4 ANALYSIS AND DISCUSSION OF RESULTS The analysis and discussion of the results from both stages of the investigation are carried out in the following paragraphs. The scope mainly concentrated on the change in the vertical displacement and the effective stresses underneath the strip footing. The vertical stress increase was calculated based on the formula below Figure 3. Effect of void depth on: a) Footing displacement and b) Effective stresses underneath footing center The effect of the void width on the footing center displacement and the effective stresses is presented in Figure 4. This figure shows that if the void width is less than 0.5B it has a marginal effect on both parameters.
When the void width reaches 0.75B it causes a 50% increase in the vertical displacement and a slight increase in the effective stresses. At a void width of 1.0B the results match those from the first point in Figure 3, where, the footing s vertical displacement exhibits large increase, and the effective stresses exhibits small decrease. Figure 5. Effect of void horizontal distance (h) on: a) Footing displacement and b) Effective stresses underneath footing center Figure 4. Effect of void width on: a) Footing displacement and b) Effective stresses underneath footing center Figure 5 shows the effect of the voids horizontal distance (h) from the center of the footing on the displacement and effective stresses underneath the strip footing. The depth (d) and width (w) of the void in this part of the study was chosen to be -the critical values found from the previous two discussions- 1.5B and 1.0B, respectively. The results show that when the center of the void is located at a distance larger than 3B away from the center of the strip footing it will have a marginal effect on the displacement and effective stresses underneath the footing. If the void is at a distance of 1.0B to 3B the displacement increases by 25% to 5% and effective stresses increases by less than 5%. In the second stage of this study the effect of the presence of two voids was investigated. First, Figure 6 shows the effect of two symmetric horizontal voids. The location of the two voids is displayed in the schematic diagram in Figure 1b. The results show that the effect of the two symmetric voids on the displacement and effective stresses underneath the footing is marginal after 3B which matches the results of a single void. The percentage vertical displacement increase for the two symmetric voids at a distance less than 3B is about twice as that for a single void. Whereas for the two voids the effective stresses are slightly effected even with a void distance less than 3B.
Figure 6. Effect of two symmetric horizontal voids on: a) Footing displacement and b) Effective stresses underneath footing center Figure 7. Effect of two consequent vertical voids on: a) Footing displacement and b) Effective stresses underneath footing center Second, Figure 7 shows the effect of two consequent voids on the displacement and effective stresses underneath the footing. The location of the two voids is displayed in the schematic diagram in Figure 1c. The results show that the presence of the second void do not cause any change to the displacement and effective stresses above that for the single void. This may be attributed to the fact that the second void is located at a distance 2.5B or larger. 5 CONCLUSIONS In the course of this research, a parametric study was carried out to investigate the effect of the presence of small single and double voids on the displacement and effective stresses underneath a strip footing. The footing was loaded with the allowable load to study the case of the formation of voids in the soil below the foundation level during the usage stage of a structure. Square voids were considered in this study and their locations and sizes were varied. To model the strip footing on soil with voids a plain strain finite element analysis model was developed in Plaxis 2D. The results of the parametric study showed that the presence of a single void will affect the displacements and stresses underneath a strip footing if it has a width larger than half the footing width (B). The void has to be at depths less than or equal to 2.5B and at a horizontal distance distances away from the center of the footing of less than 3B. For double voids the same conclusions for the single void apply. It was found that for two symmetrical horizontal voids the percentage vertical displacement increase was almost twice as that for the comparable single void case. On the other hand the effective stresses were almost equal for both single and symmetrical horizontal double voids. For the two consequent voids the presence of the second void did not affect the displacement or effective stresses underneath the foundation due to the fact that it was at a depth more than 2.5B.
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