In situ-based assessment of soil liquefaction potential–Case study of an earth dam in Tunisia

Abstract

The present paper examines the evaluation of liquefaction potential of an earth dam foundation in Tunisia. The assessment of soil liquefaction was made using deterministic and probabilistic simplified procedures developed from several case histories. The data collected from the field investigation performed before and after the vibrocompaction are analyzed and the results are reported. The obtained results show that after vibrocompaction, a significant improvement of the soil resistance reduces the liquefaction potential of the sandy foundation. Indeed, in the untreated layers, the factor of safety FS drops below 1 which means that the soil is susceptible for liquefaction. However, in the compacted horizons, the values of FS exceed the unit which justifies the absence of liquefaction hazard of the foundation.

Keywords

liquefaction / cone penetration test (CPT) / standard penetration test (SPT) / vibrcompaction / sand

Introduction

Liquefaction phenomenon is one of the critical problems in geotechnical engineering. It primarily occurs in saturated and cohesion-less soils located in seismically active regions. Thus, the prediction of liquefaction is an important interest design engineering practice. Two basic approaches are available to analyze liquefaction potential using cyclic laboratory test results and in situ-based simplified procedures.

In this regards, the Sidi El Barrak earth dam, a large hydraulic project, provides an interesting case for assessing the liquefaction susceptibility of soils and evaluating the foundation stability. Within the scope of this paper, liquefaction potential has been investigated by simplified approaches based on standard penetration test (SPT) and cone penetration test (CPT) results. The field investigation comprises collecting data before and after soil densification using the vibrocompaction technique. A focus is made on the most widely accepted methods used for evaluating soil liquefaction resistance. The state of the art of SPT is Idriss & Boulanger [ 1]. The state of the art of CPT is Robertson & Wride [ 2].

Site conditions

Sidi El Barrak earth dam is situated in the extreme North Western coast of Tunisia (Fig. 1). The site of dam is located at 6.5 km from the Mediterranean Sea, 15 km from the Nefza region and 20 km North East of Tabarka city [ 3]. Total area of the watershed is about 896 km² and the reservoir level is equivalent to 29 m height. The total capacity of the reservoir is about 275 Million cubic meters. The Sidi El Barrak dam provides irrigation water for fertile lands that extend over an area of 4000 ha. The heterogenous foundation of dam is predominantly composed by sandy formations. The latter of Quaternaries, Neogene’s and Paleogene age consist in alluvial sand and eolian dunes [ 4]. The rigid stratum level is composed by gneiss and marlstone which are apparent at the right side (Fig. 2).

According to the Tunisian Central Bureau, ground motions recorded in the western north of Tunisia are characterized by a maximum peak ground Acceleration equal to 0.15 g and variable intensities of VII to VIII.

In addition, two wells were executed respectively in the left side and in the bed river of Sidi El Barrak dam for samples laboratory testing. Figure 3 presents two typical grain size envelopes obtained from a granulometric analysis of depths where the two wells are performed. The results show the sands to be graded from coarse to medium to fine. The uniformity coefficient varies between 2.37 and 7.5 in the left bank and between 2 and 13.6 in the bed river. The median diameter (D₅₀) varies from 0.14 to 1.3 mm in the former zone while it varies from 0.13 to 1.4 mm in the latter zone.

The study area has been the subject of a soil densification using the vibrocompaction technique. The treatment of Sidi El Barrak foundation soil, at about 10 m depth, has been achieved in equilateral triangular zone of spacing 2.94 m. Figure 4 shows the location of zones where vibrocompaction took place.

A strict quality control program of the vibrocompaction pursued in the project has implemented the SPT tests in some locations in the foundation such as meshes C4 and D2 (Fig. 4). Additional CPTs were performed at meshes C4 and F4 in order to examine strength of soil after vibrocompaction.

SPT-based liquefaction analysis of the dam foundation

The SPT is a widely available sampling method that indicates a soil’s compactness. The SPT measures the number of blows (N) produced by a hammer falling freely that are required to drive a standard split-spoon sampling tube to a depth of 30cm. The SPT blow count or “N value” is low in loose soils and increases with increasing stiffness of the soil, and this value can thus be used as an index of the soil’s in situ strength.

Using the SPT results, the evaluation of the liquefaction potential of the dam foundation is made by determining the critical value of the standard penetration resistance, N_cri, separating liquefiable from nonliquefiable conditions [ 5]:

(1) {\mathrm{N}}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}={\mathrm{N}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\times (\mathrm{1}+\mathrm{0.125}\times (d_s-\mathrm{3})+\mathrm{0.05}\times (d_w-\mathrm{2})),

where d_s is the depth of the sandy layer (m); d_w is the depth below level of water table (m); N_ref is the number of cycles for penetration equals to 30 cm. It is equal to 6, 10 and 16 for earthquake intensities of VII, VIII and IX respectively.

Several factors affect the SPT results. One of the most important of these factors is the energy delivered to the SPT sampler. Indeed, the energy delivered by a particular SPT setup depends primarily on the type of hammer, the anvil in the drilling system and on the method of hammer release. An energy ratio, ER, of 60% has generally been accepted as the reference value. The value of (N₁)₆₀ is computed as:

(2) {(N_{\mathrm{1}})}_{\mathrm{60}}=N\times {\displaystyle \frac{ER}{\mathrm{60}}},

where N is the measured blow count, ER is the measured delivered energy ratio as a percentage and (N₁)₆₀ is the blow count for an energy ratio of 60%.

Additional correction factors are required for overburden pressure, rod lengths, borehole diameters and sampling method. The resulting relationship is given by:

(3) {(N_1)}_{60}=N\times C_N\times C_E\times C_B\times C_R\times C_S.

In which C_N is the overburden stress correction factor, C_E is the energy ratio correction factor, C_B is a correction factor for borehole diameter, C_R is a correction factor for rod length, and C_S is a correction factor for a sampler type.

Figures 5 and 6 illustrate the variation in depth of the corrected SPT blow count (N₁)₆₀ and the critical penetration resistance, N_crit, for different earthquake intensities in zones C4 before and after soil densification. From these figures, the results show increased (N₁)₆₀ values in looser soil layers when compared with results obtained in the corresponding material prior to vibrocompaction. In fact, the (N₁)₆₀ values increased from an average of 25 to 43 blows /0.3 m in the mesh C4. In addition, before vibrocompaction, the SPT borings data are plotted below the threshold curve and are so liquefiable (Fig. 5). After vibrocompaction, the SPT data has exceeded the threshold curve and are not expected to liquefy (Fig. 6).

Seed & Idriss [ 6] proposed a stress-based procedure to analyze liquefaction risk of soils. This approach requires an estimate of the liquefaction loading (expressed in term of cyclic stress ratio CSR) (Eq. (2)) and the liquefaction resistance (presented in term of cyclic resistance ratio CRR).

(4) CSR=\mathrm{0.65}\times {\displaystyle \frac{{\sigma }_{\mathrm{v}}}{{{\sigma }^{\prime }}_{\mathrm{v}}}}\times {\displaystyle \frac{{\alpha }_{\max }}{g}}\times r_{\mathrm{d}},

where, σ_v and {\sigma }_{\mathrm{v}}^{\prime } are total and effective vertical overburden stresses respectively, a_max is the peak horizontal acceleration, g is the acceleration of gravity and r_d is a stress reduction coefficient.

In the site of Sidi El Barrak dam, it is noted that the a_max is equal to 0.2 g.

Furthermore, Boulanger & Idriss [ 1] agreed that the soil characteristics, such as soil plasticity may affect liquefaction resistance. They found that for a given (N₁)₆₀, the soil resistance increases with increased of the fines content. Hence, the following equations are recommended for correcting standard penetration resistance to an equivalent clean sand penetration resistance (N₁)_60CS:

(5) {(N_{\mathrm{1}})}_{\mathrm{60}CS}={(N_{\mathrm{1}})}_{\mathrm{60}}+{(N_{\mathrm{1}})}_{\mathrm{60}},

(6) \mathrm{\Delta }{(N_{\mathrm{1}})}_{\mathrm{60}}=\exp \left(\mathrm{1.63}+{\displaystyle \frac{\mathrm{9.7}}{FC+\mathrm{0.01}}}-{\left({\displaystyle \frac{\mathrm{15.7}}{FC+\mathrm{0.01}}}\right)}^{\mathrm{2}}\right),

where FC is the fines content measured from laboratory tests on retrieved soil sample.

Boulanger & Idriss [ 1] suggested that the derived boundary lines or CRR can be calculated as a function of the fine content corrected penetration resistance (N₁)_60CS. The derived boundary lines or the cyclic resistance ratio CRR adjusted to M = 7.5 and {\sigma }_{\mathrm{v}}^{\prime } = 1 atm for cohesionless soils can be calculated on the basis of the (N₁)_{60 CS} values via the equation presented below:

(7) CRR=\exp \left({\displaystyle \frac{{(N_{\mathrm{1}})}_{\mathrm{60}\mathrm{C}\mathrm{S}}}{\mathrm{14.1}}}+{\left({\displaystyle \frac{{(N_{\mathrm{1}})}_{\mathrm{60}\mathrm{C}\mathrm{S}}}{\mathrm{126}}}\right)}^{\mathrm{2}}+{\left({\displaystyle \frac{{(N_{\mathrm{1}})}_{\mathrm{60}\mathrm{C}\mathrm{S}}}{\mathrm{23.4}}}\right)}^{\mathrm{3}}+{\left({\displaystyle \frac{{(N_{\mathrm{1}})}_{\mathrm{60}CS}}{\mathrm{25.4}}}\right)}^{\mathrm{4}}-\mathrm{2.8}\right).

Figures 7 and 8 show the resulting proposed deterministic relationship between CSR and (N₁)_60CS in C4 and D2.

The solid dots represent the pre-treatment point data for which liquefaction can be triggered. However, the post-treatment data represent non liquefaction cases.

The calculated CRR must be compared to CSR in order to determine the factor of safety (FS) as follows:

(8) FS={\displaystyle \frac{CRR}{CSR}}.

In theory, liquefaction is predicted to occur if F_S≤ 1, and no liquefaction is predicted if F_S > 1.

Figure 9 shows the FS profile calculated from the Boulanger & Idriss approach in zones C4 and D2 before and after soil improvement. The FS profile obtained from the pre-treatment data are less than the critical value (FS = 1). So, the dam foundation may be prone to liquefaction during the design earthquake event. Nevertheless, the gaps in the critical value data represent soil layers that are not susceptible to liquefaction due to their densification by vibrocompaction.

CPT-based liquefaction analysis of the dam foundation

The CPT has proved to be a valuable tool for characterizing subsurface conditions and assessing various soil properties, including estimating the potential for liquefaction.

A typical CPT involves pushing a 35.7-mm-diameter conical penetrometer into the ground at a standard rate of 2 cm/sec. while electronic transducers record the force on the conical tip and the drag force on a short sleeve section behind the tip.

The tip force is divided by the cross-sectional area of the penetrometer to determine the tip resistance, q_c, and the sleeve drag force is divided by the sleeve surface area to determine the sleeve friction, f_s.

Zhou [ 7] (in Seed et al. [ 8]) had considered the critical resistance q_crit under which liquefaction risk is potential. The CPT data collected before and after the soil improvement of the case study (in the mesh C4) and the threshold curves given by Zhou [ 7] for different earthquake intensities are illustrated in Figs. 10 and 11.

Before vibrocompaction, the measured values of the CPT tip cone resistance q_c are generally lower than the critical resistance values q_crit, showing vulnerability of the dam foundation to liquefaction. The q_c values in the compacted sand increase significantly due to the soil consolidation and rearrangement of particles after soil densification.

Robertson & Wride [ 2] suggested that the boundary curve or CRR can be estimated as a function of the equivalent clean sand normalized penetration resistance (q_c1N)_cs. Figs. 12 and 13 show calculated CSR plotted as a function of the corrected and normalized resistance q_c1N from Sidi El Barrak site (in meshes C4 and F4). The pre-treatment data points (solid circles) are plotted below the boundary curve which indicates that the soils in zone C2 and zone F4 are susceptible to the cyclic liquefaction. However, the post-treatment data (open circle) fall above the boundary curve, in the non- liquefaction zone.

Figure 14 presents the FS profile in mesh C4 a when the case of the dam foundation is analyzed using the Robertson & Wride [ 2] simplified procedure.

Before vibrocompaction, the soils appear liquefiable with factor of safety smaller than the unit. After vibrocompaction, the derived profile of FS shows that the majority of soil layers have a factor of safety greater than 1.

Actually, researchers suggested that the Robertson method must be calibrated so that the meaning of the calculated FS is understood in terms of likelihood or probability of liquefaction. CPT data at the mesh C4 are used as example to represent the profiles of the probability of liquefaction (PL) obtained from the Robertson method (Fig. 15). Before vibrocompaction, the profiles suggest that the calculated probabilities are high, ranging from 0.4 to 1. The average of probabilities of liquefaction values is about 68%. This value falls into the class of “very likely” in the Juang and Chen classification. After vibrocompaction, the average of the calculated probability of liquefaction drops below 35%, indicating a low likelihood of liquefaction of the dam foundation.

Conclusions

Based on the results of the presented case study, the SPT and CPT tests are shown to be an effective tool for characterizing the liquefaction potential of the dam site. The effectiveness of soil densification in reducing the liquefaction potential, as mentioned in literature, is confirmed in this case study. Indeed, the results show that the undensified alluvial sands of foundation were prone to liquefaction hazard (FS < 1). However, after vibrocompaction, the dam foundation was not susceptible to liquefaction (FS > 1). The liquefaction evaluation results based on the SPT data are similar to those based on the CPT data. A comparison shows general agreement between the deterministic and probabilistic correlations.

References

[1] Boulanger R W, Idriss I M. Soil liquefaction during earthquake. Engineering monograph-EERI, California, 2008, 266

[2] Robertson P K, Wride C. Evaluating cyclic liquefaction potential using the cone penetration test. Canadian Geotechnical Journal, 1998, 35(3): 442-459

[3] Technical document. Drainage and treatment of the foundation of Sidi El Barrak dam. Ministry of agriculture, Tunis, 1990, 63

[4] Blanchin M, Michalsky E R, Dequidt O, Giafferi J. La fondation du barrage de Sidi El Barrak. Journées Nationales de Géotechnique et de Géologie de l'ingénieur, 2002, 1-15

[5] Corté J P. Evaluation du risque de liquéfaction à partir des essais en place. Génie parasismique, Nantes, 1978, 12

[6] Seed B, Idriss I M. Simplified procedures for evaluating soil liquefaction potential. JSME, 1971, 97: 1249-1273

[7] Zhou S. Evaluation of the liquefaction of sand by static cone penetration test. In: Proceedings of the7th world conference on earthquake Engineering. Istanbul, Turkey, 1980, 3: 156-162

[8] Seed B, Idriss I M, Arango I. Evaluation of liquefaction potential using field performance data. Geotechnical Engineering, 1983, 109(3): 458-482

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