PSI - Issue 13

Hichem Mazighi et al. / Procedia Structural Integrity 13 (2018) 1438–1441 H.MAZIGHI et al./ Structural Integrity Procedia 00 (2018) 000–000

1439

2

In this paper, a numerical model is implemented to calculate water pressure distribution in concrete dam, the approach is based on Drucker Prager model, consists in an isotropic elastic-plastic mechanics under hydrostatic pressure at upstream face of two geometries cases to study the influence of the slope to the global behavior of the dam.

Nomenclature α

internal cohesion angle. hardening of the material.

K



friction angle.

I 1 J 2

the first invariant of the stress tensor. (N/m 2 ) the second invariant of the deviatoric tensor (N/m 2 )

2. Material and methods 2.1. Drucker Prager model

For a geomaterial, it is not realistic to imagine a hydrostatic loading without the material being subjected to any transformation. For this purpose, the Von Mises criterion has been modified in order to introduce a sensitivity to hydrostatic pressure. The Drucker-Prager criterion is thus expressed as:

3 0 J I K     ,

(1)

2

1

where:

2sin 3 sin 2cos 3 sin



(2)





 



(3)

K



 

I

1 (4) If  =0, the criterion is reduced to that of Von Mises. The model is implemented in CAST3M with QUA8 (8-node quadratic) with three degrees of freedom in plane strain analysis. 2.2. Case study In the present study, two geometries sections of the Kinta roller compacted concrete dam are considered as case studies, the geometry of deepest section are shown in Fig. 1. The case one is characterized by upstream inclined (1/24) that leads us to have two components of the hydrostatic pressure (horizontal and vertical), contrary to the second case with a single component of the water pressure. The material properties can be seen in table 1. 1 2 3      

Table 1. Material properties.

Properties

Dam body

Young modulus (N/m 2 )

3.4e+10

Poisson’s ratio

0.2

Mass density (kg/m 3 )

2400

Biot's modulus

7500e+6 3.27e+6

Yield tensile strength (N/m 2 )

Permeabilty (m/s)

4e-10

The Fig.2 shows the horizontal displacement due to hydrostatic pressure at upstream face, the distribution is the same for both cases but we see in Fig.2(a) the horizontal displacement at the crest of the dam in case one is more important than in case two (Fig.2 (b)), due to additional vertical hydrostatic pressure caused by upstream slope, leads to supplementary force that affect proportionally the horizontal displacement.