of New Hampshire, USA

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1 Centrifuge Test to Evaluate Internal Strut Loads in Shallow Underground Retaining Structures Adrienne HILL a, Jill GETCHELL a and Majid GHAYOOMI b,1 a Research Assistant, Department of Civil and Environmental Engineering, University of New Hampshire, USA b Assistant Professor, Department of Civil and Environmental Engineering, University of New Hampshire, USA Abstract. Underground structures are important civil infrastructure in modern urban areas. They are used in a wide range of engineering applications including building foundations, underground transportation systems, and underground storage facilities. The stability of the excavated ground is a major challenge in the design and construction processes. Bracing approaches have been implemented in the current state-of-practice to ensure the safety of the excavation. One common braced excavation system involves vertical retaining walls on both sides of the excavated ground held in place using horizontal internal struts. These struts are designed using empirical lateral pressure distribution envelopes. A set of scaled physical models were designed and tested to evaluate these internal strut loads and compare them with empirically predicted values. The empirical equations predicted lower strut loads than what were measured experimentally. Several reasons could result in the difference, especially the fixity of the structure, construction process, and the depth of the model. Keywords. Centrifuge Modeling, Braced Excavation, Underground Structures. 1. Introduction The overall increase of the world s population has led to a rise in the number of individuals moving into the cities. It is estimated that in the next twenty-five years, over two billion people will move into cities [1]. Cities around the world are already condensed tightly in terms of space for buildings and utilities. This trend in population growth presents an enormous engineering concern as to how to solve the issue of overpopulation and lack of residential and industrial space. Over the years, underground structures have been constructed to solve the problem of overpopulation by providing additional space to accommodate utility lines, transportation tunnels, and sub-level floors in mid- to high-rise buildings in dense urban areas. Underground structures can be categorized into two types: shallow and deep. Applications of shallow underground structures can range from parking lots, subway stations, and even shopping malls. During the construction of shallow underground structures, the soil needs to be excavated to a certain depth in order to fit the needs of the structure. During and after excavation, temporary walls are installed, so that side walls remain stable. These walls form a retaining structure and provide lateral stability of the soil against the wall. 1 Corresponding Author. Assistant Professor, Department of Civil and Environmental Engineering, University of New Hampshire, Durham, NH, USA, majid.ghayoomi@unh.edu.

2 Braced excavations are commonly implemented to build shallow foundations or cutand-cover tunnels safely. A braced excavation is a soil retaining system involving sheet pile walls and external bracing struts, as shown in Figure 1. Internal beams (struts) connecting the two walls increase the resistance of the bracing system against the lateral earth pressure. Given the lateral earth pressure behind the walls, the internal strut loads can be determined using simple static equilibrium analysis. Then, the appropriate section profile and joint connection for the strut members will be selected. However, estimating accurate horizontal pressure distribution has been a major challenge in geotechnical engineering practice, ranging from simple practical approach to more sophisticated numerical solutions. In recent years, several studies focused on measuring the lateral earth pressure acting on the wall under both static and dynamic loads [3,4,5]. In this study, a shallow braced excavation system is scaled and physically modeled using the geotechnical centrifuge facility at the University of New Hampshire (UNH). The measured strut loads are compared with the predicted values based on the current practical lateral pressure distribution. Figure 1: Struts in Between Temporary Wall [2] 2. State-of-the-Practice in Estimating the Strut Loads The major step in the design of a braced excavation system is to determine the lateral pressure distribution on the walls from the soil. It depends on soil properties, the depth of the wall, and the flexibility of the braced excavation system. Terzaghi et al. [6] reported several case studies measuring the lateral pressure on the retaining walls. Then, they summarized those findings and categorized them based on the depth and the type of material. For example, the following pressure distribution was recommended for shallow braced excavations with the depth 8 to 19 m in sand, as shown in Figure 2. However, they indicated different distribution pattern at a very shallow depth depending on the site characteristics. In current state-of-the-practice, a uniform distribution, so-called Peck s method [6], is applied for sandy material, where the pressure value is estimated using Equation 1. σ a =.65γHK a (1) where γ is the unit weight of the soil, H is the excavation depth, and K a is the active coefficient of earth pressure. Once the stresses against the walls are found, static moment equilibrium equations are applied to find the loads on each individual strut.

3 Percent Finer by Weight Figure 2: Pressure Distribution Envelope for Sand with Braced Excavations [6] 3. Experimental Procedures 3.1. Tested Material F-75 Ottawa sand, a fine grain, uniformly graded, Ottawa sand was used for this study. The grain size distribution of this sand is shown in Figure 3. A summary of the soil properties used during the course of the project is presented in Table Grain Size (mm).1 Figure 3: Sieve Analysis for Ottawa Sand Table 1. Ottawa Sand Properties Soil Property Friction Angle 35 Unit Weight kn m 3 Specific gravity 2.65 C c 1.71 C u 1.1 e max, e min.8,.49 g ρ max cm 3 ρ min g cm 3

4 3.2 The Geotechnical Centrifuge Geotechnical centrifuges have been used to recreate the prototype stress-strain relationship in a reduced-scaled soil-structure system under high gravitational field. The geotechnical centrifuge at the University of New Hampshire is a 5 g-ton centrifuge with a 1-m radius aluminum alloy arm. The centrifuge has a pay-load capacity of 1 kg and a centrifugal acceleration capacity of 175 g. The facility has been involved in numerous research projects over the years and includes several geotechnical modeling containers and a 1-D in-flight servo-hydraulic shaker [7]. 3.3 Model Structure and Prototype System A.1-m depth, aluminum-made, model structure with two internal struts in depth was constructed. A.5 inch diameter aluminum bar and.375 inch thickness aluminum plate was used for the struts and the walls, respectively. This was due to constructability of the pieces and the available section profiles. In addition, the material thicknesses were selected to avoid excessive deflection and bending, both in the wall and the struts. The struts were then completely constraints and screwed into the designated holes on the wall, representing fixed connections. The struts were evenly spaced in depth, expected to result in similar loads. The bracing system contains two sets of struts in width (i.e. a total of 4 struts in the model). A schematic and a picture of the model structure is shown in Figure 4a and b, respectively. (a) (b) Figure 4: Model structure: (a) schematic view; (b) picture. 3.4 Specimen Preparation and Testing Method As seen in Figure 5, the braced excavation model was constructed in a laminar container with dimensions of mm long, mm wide, and 254 mm height. The sand was dry pluviated with a relative density of about 4% inside the container. Flexible plastic sheets were used to separate the soil model from the container to avoid sand penetration inside the laminar rings. At the target depth, the model structure was placed and the pluviation was continued to the soil surface. Then, the container was placed on the centrifuge platform, and the centrifuge was spun up to reach 5-g at the middle of the bracing walls with the stops at 1g, 2g, 3g, and 4g. These will replicate the prototype systems with excavation heights of 1, 2, 3, 4, and 5m, under 1g, 2g, 3g, 4g, and 5g,

5 respectively. The internal strut load was measured using a load cell machined in the strut. The load cell that is being used in the experimental model is a LCMFL series load cell that can measure up to 2N of force. Because it is a miniature load cell, it is small enough to be threaded into the internal strut. It is stainless steel and can measure in either tension or compression. In addition, the vertical deformation of the soil layer and structural model was controlled using two LVDTs. The measured data in-flight was transferred to the data acquisition system (DAQ) and the data on the DAQ was accessed wirelessly using a PC computer in the lab. A schematic of the system is shown in Figure 5. LVDT 1 LVDT Load Cell Figure 5: Experimental Setup with Braced Excavation, Load Cell, and LVDT 4. Results and Discussion Since excessive settlement during centrifugation can cause a change in relative density, it was essential to check the settlement of the sand layer and the model structure. As seen in Figure 5, LVDT1 measures the settlement of the sand while LVDT shows the settlement of the braced excavation structure. The settlement of the sand (slightly greatest of the two) was used for the calculation of the changes in relative density. On average, the sand would settle approximately.35 centimeter total while the braced excavation settle approximately.3 centimeter at 5g. This would lead to at most 1.7% change in the initial relative density of 4%. Considering the specimen preparation density variation and experimental uncertainties, this change is negligible. Figure 6 shows the settlement increasing slightly as the g-level increases while the relative density barely changes during the spin up of the centrifuge. In addition, the figure also shows how both soil and structure have approximately similar settlement trends.

6 Load kn Settlement (cm) Relative Density (%) Figure 6: Settlement and relative density variations in spin up Three specimens were tested with various load cell locations in addition to two repeated tests, a total of 5 tests. The location of the load cell in each test is explained in Table 2. For each test, the centrifuge was spun up to 5-g but was stabilized at increments of 1-g, representing different prototype excavation heights. Then, the measured load was converted to the prototype scale using the standard scaling laws. The following load values presented herein are in prototype scale. The load cell values during the spin up to 5-g in the centrifuge is shown in Figure 7. The strut load increases in greater excavation depth while the location of the strut wouldn t affect the load. Considering the equal spacing of the struts, these values confirm the assumption of Peck s uniform lateral pressure distribution g-level Settlement LVDT 1 Settlement LVDT Relative Density Table 2: Load cell placement Test Load Cell Placement 1 Top Strut 2 Opposite Top Strut 3 Bottom Strut 4 Top Strut - Repeat 5 Bottom Strut - Repeat g-level Figure 7: Strut loads during centrifuge spin up (prototype scale) Test 1 Test 2 Test 3 Test 4 Test 5 In order to check the consistency of the data and possible adverse effects of centrifugation the strut loads during spin up and spin down were compared. The variation of strut loads for the two of the five tests with lowest and highest differences in spin up and down are compared in Figure 8. Accordingly, the effect of releasing the confining pressure on the strut load during spin down could be observed. Even though test 4 had the greatest gap, the difference between the loads in spin up and down is still acceptable.

7 Experimental Strut Load (kn) Load (kn) Load (kn) (a) Test g-level g-level (b) Figure 8: Strut load comparisons in spin up and down for a) Test 1; b) Test 4 The experimentally measured strut loads in prototype scale were, then, compared with the empirically estimated loads based on Peck s stress distribution (from Equation 1), shown in Figure 9. The measured values are much higher than the predicted values. This can be attributed to the following reasons. In Peck s formula K a-coefficient was used representing an active condition, while the structural model in the centrifuge is a completely rigid model with almost zero wall movement. Consequently, assuming K (at rest) condition seems to be more rational. Thus, the empirical prediction was updated based on K pressure distribution and compared with the experimental values, as shown in Figure 1. As a result, the gap between the two data sets was reduced significantly, closer to 1:1 line : Strut Load based on K a (kn) Test 1 Test 2 Test 3 Test 4 Test 5 Test 1 down Test 2 down Test 3 down Test 4 down Test 5 down Figure 9: Comparison of measured and K a-based empirically estimated strut loads Test Historically, Peck s equation was developed based on several case studies on different sites [6]. In addition, it was mentioned that the pressure distribution could be very different in very shallow depth affecting the constant coefficient (.65) to either a higher or lower value depending on the site. Thus, they recommended this method for depths greater than 8 m. With a careful attention to Figure 1, one can see that that the data points might curve back toward the 1:1 line in higher loads, which would be

8 Experimental Strut Load (kn) simulating the higher excavation depth. Unfortunately, models with larger excavation depth were not tested because of the limited depth of the container and capacity of the centrifuge. However, currently, authors are performing more tests by changing other variables for better understanding of the response, and the results would be presented in future publications. The other reason causing this difference could be the very rigid connection between the struts and the wall, different from the field applications. In addition, different construction processes in the field and the centrifuge model could have led to this dissimilarity in the strut loads : Strut Load based on K (kn) Test 1 up Test 2 up Test 3 up Test 4 up Test 5 up Test 1 down Test 2 down Test 3 down Test 4 down Test 5 down Figure 1: Comparison of measured and K -based empirically estimated strut loads 5. Conclusion: A set of scaled centrifuge physical models were used to measure the strut loads in a shallow braced excavation system. The measured loads were compared with empirically estimated values using Peck s simplified pressure distribution method. The empirical approach underestimated the measured values. This was attributed to the shallow depth of the braced excavation, fixity of the model, construction process, and variation of pressure distribution for different depths. References [1] Sterling, R., Admiraal, H., Bobylev, N., Parker, H., Godard, J., Rogers, C. D. F., Hanamura, T. Sustainability issues for underground spaces in urban areas. Urban Design and Planning, 165(DP4), (21), [2] Dutch Foundation. Dutch Foundation. Retrieved 13 Mar. 213, from [3] Anderson, D. G., Martin, G.R., Lam, I., and Wang, J.N., Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments, NCHRP, Report 611, (28), [4] Nakamura, S., Reexamination of Mononobe-Okabe Theory of Gravity Retaining Walls Using Centrifuge Model Tests, Soils and Foundations, 46 (2), (26), [5] Sitar, N., Mikola, R.G., and Candia, G., Seismically Induced Lateral Earth Pressure on Retaining Structures and Basement Walls, Geotechnical Special Publication No. 226, ASCE, (212), [6] Terzaghi, K., Peck, R.B., and Mesri, G., Soil Mechanics in Engineering Practice, J. Wiley and Sons, (1996). [7] Ghayoomi, M. and Wadsworth, S., Renovation and Reoperation of a Geotechnical Centrifuge at the University of New Hampshire, 8 th ICPMG, Perth, Australia, (214), 5pages.