SLS: Settlement

The SLS check requires that the settlement of a foundation must be within tolerable or acceptable limits. This section only examines the settlement of an isolated shallow foundation. For typical shallow foundations in cohesionless (non-plastic) soil, such as sand and gravel, settlement will be a more critical design consideration than bearing capacity, especially when the foundation width is greater than 1.5 m (e.g. Jeyapalan and Boehm 1986; Tan and Duncan 1991; Berardi and Lancellotta 1994). For completeness and comparison purposes, the methods to calculate the settlement of foundations in cohesionless soil and their performance will also be discussed in this chapter, although the focus of this book is placed on foundation capacity. The settlement of cohesionless soil occurs primarily from the compression of the soil skeleton because of the rearrangement of soil particles into denser arrangements. As a consequence, a very loose sand or gravel will settle more than the soil in a dense or very dense state. As discussed in Day (2006), there are many other causes of settlement of structures, such as limestone cavities or sinkholes, underground mines and tunnels, subsidence owing to extraction of oil or groundwater and decomposition of organic matter and landfills.

A major difference between cohesive and cohesionless soil is that the settlement of cohesionless soil is usually not time dependent (i.e. without longterm settlement from consolidation) because sand is less compressible than clay. More than twenty methods have been proposed for settlement calculation, and some commonly used methods are summarized in Table 4.6. More details can be found in Akbas (2007) and Day (2006). Generally, these methods can be categorized into three groups:

• 1. Plate load test (PLT) is widely used to determine the settlement of a footing based on an empirical equation that relates the depth of penetration of the plate to the footing settlement (Terzaghi and Peck 1967). PLT can also be used to determine the modulus of subgrade reaction (K_v) with a plot of the stress (q) exerted by the plate versus the penetration of the plate (6). Using this plot, K_v = q,75_v, where q_v and 5_V are the q and 5 values at the yield point where the penetration rapidly increases. Assuming the modulus of elasticity increases linearly with depth, the footing settlement can be computed using the modulus of subgrade reaction (NAVFAC DM-7.1 1982).
• 2. Direct (empirical) methods based on in situ test results, such as the blow count (N_SPT) of a standard penetration test or the cone tip resistance (q_c) of a cone penetration test (CPT), eliminating the intermediate estimation of soil parameters. Terzaghi and Peck (1948) first proposed the SPT-based method that was used widely throughout North America. It involves using a chart that relates N_SPT to the bearing pressure for one-inch settlement, as a function of footing width (B) and depth (D) and groundwater level (D_w). Various modifications have been suggested to improve the Terzaghi and Peck (1948) method (e.g. Gibbs and Holtz 1957; Alpan 1964; Meyerhof 1965; Peck and Bazaraa 1969; Peck et al. 1974). The modifications include (1) correcting N_SPT to take the effect of overburdened pressure into account (e.g. Gibbs and Holtz 1957; Peck et al. 1974), (2) reducing the magnitude of calculated settlement by one-third (Meyerhof 1965) and (3) changing the value of the correction for groundwater (Meyerhof 1965). In addition to SPT and CPT, Briaud and Jordan (1983) presented a shallow foundation design on the basis of pressuremeter tests (PMT), in which both the bearing capacity and settlement calculations were outlined in the form of step-by-step procedures.

Method	Reference	Equation	Note
PLT	Terzaghi and Peck (1967)		• Dp = depth of penetration of the plate, B, = smallest dimension of the plate and В = smallest dimension of the footing. • The pressure exerted by the plate for pp must be the same as exerted on the sand by the footing. • This method can significantly underestimate the settlement, and the test is time-consuming and expensive to perform. Hence it is used less frequently than the other methods.
	NAVFAC DM-7.2 (1982)		• q = vertical footing pressure; Kv = modulus of subgrade reaction estimated from the pressure-penetration curve measured in PLT. • Interpolation is required for shallow foundations having a width В = 6-1 2 m. • For the groundwater table at the footing base, 0.5KV should be used. • For continuous footing, the settlement calculated from the equations should be multiplied by a factor of 2. • This method may underestimate the settlement in cases of large footing when soil deformation properties vary significantly with depth.
Direct	Terzaghi and Peck (1948)		• Cd = 1 for D/B = 0 and 0.75 for D/B > 1, linear interpolation used between these values for 0 < D/B < 1; Cw = 1 for Dw > 2B and 2 for Dw = 0; B0 = 305 mm; S0 = reference settlement = 305 mm; and pa = atmospheric pressure =101 kPa. • For В < 1.22 m, the settlement is equal to the value at В = 1.22 m.

Method	Reference	Equation	Note
	Gibbs and Holtz (1957)		• N, = NSPT corrected for overburden pressure.
	Alpan (1964)		• a0 used to the correction of NSPT for overburden pressure and water table.
	Meyerhof (1965)		• For В < 1.22 m, the settlement is equal to the value at В = 1.22 m.
	Peck and Bazaraa (1969)		• N„ = 4NSPT/(l+2ov0') for ov0' <71.8 kPa and N„ = 4NSPT/ (3.25+O.5av0') for av0' >71.8 kPa; cv0' = effective vertical overburden pressure; К = correction factor for water table; Cd = 1 - 0.4(y'D/q); and y' = effective unit weight of soil.
	Peck et al. (1974)		• N, = CnNspt, where CN = correction factor for overburden pressure = 0.77log[20/(cv07pa)]. Cw = 0.5 + 0.5[DW/(D + B)].

Indirect	D'Appolonia et al. (1970)		• M = E/(l - o2), where о = Poisson’s ratio; E/pa = 196 + 7.9NSPT for normally consolidated sand and E/pa = 416 + I0.9NSPT for preloaded sand. • U0 and U, = empirical factors depending on foundation dimensions, embedment and layer thickness.
	Parry (1971)		• E/pa = 50NSPT. Cd and Ct = empirical factors depending on foundation embedment and depth to the incompressible layer. • Cw = 1 + [DW/(D + 0.25B)] for permanent excavations below the water table and Cw = 1 + {[DW(2B + D - Dw)]/ [2B(D + 0.75B)]}.
	Schultze and Sherif (1973)		• E/pa = 1 6.8(NSPT)087B05( 1 + 0.4D/B).This methods based on a statistical study of settlement measurements from forty-eigth buildings.
	Berardi and Lancellotta (1991)		• E/pa = KE[(cv0' + Д0¥О')/ра]О 5, KE = 100 + 900Dr, where D,. = (N|/60)os < 1 and N, = [2/(1 + cv07pa)]NSPT. and Acrv0' = increase in vertical effective overburden pressure. • Once the settlement is calculated, KE is corrected as KE.COrr = 0.1 91 KE(SC/B)"0625, and then the settlement is calculated with KE = KEcorr until convergence is achieved.

(Continued)

Method	Reference	Equation	Note
	Schmertmann et al. (1978)		• C, = depth factor = 1 - O.5(0vO'/q); C2 = secondary creep factor = 1 + 0.2log(t/0.1); C3 = shape factor = 1.03 - 0.03(L/B) > 0.73; n = number of soil layers; l2i = strain influence factor l2 at midpoint of soil layer i; t = time since the application of load in years; H; = thickness of soil layer i; E, = modulus of soil layer i, estimated from CPT qc values with empirical correlations, where E/qc = 2.5 for normally consolidated silica sand (age < 100 years), 3.5 for normally consolidated silica sand (age > 3,000 years) and six for overconsolidated sand. • For square and circular footings: l2 = 0.1 + (zf/B)(2lzp - 0.2) for zf = 0 to B/2 and l2 = 0.67l2p(2 - zf/B) for zf = B/2 to 2B. • For continuous footings: l2 = 0.2 + (z,/B)(l2p. 0.2) for zf = 0 to В and l2 = 0.33lzp(4 - zf/B) for zf = В to 4B. • For rectangular footings (1 < L/B < 10): l2 = lzs + 0.1 1 (l2C . I2S)(L/B - 1), l2C = l2 for a continuous footing and l2s = l2 for a square footing. • lzp = peak strain influence factor = 0.5 + 0.1 (q/0vO')°5 and if = depth from bottom of footing to midpoint of layer.

	Burland and Burbidge (1985)		• This method is based on the statistical analysis of settlement data for shallow foundations on Scohesionless soil. • lc = compressibility index = 1.7l/(N60)14 for normally consolidated soil and 0.57/(N60)14 for overconsolidated soil. • Ci = depth of influence correction factor = (H/Z;)(2 - Н/ zj <1, where z, = depth of influence = 1.4B0(B/B0)07S. • Cs = shape factor = {[ 1,25(L/B)]/[(L/B) + 0.25]}2 • The difficulty in using the method is to determine the preconsolidation stress op in cohesionless soil.
	Anagnostopoulos et al. (1991)		• This method is obtained from a multiple regression analysis for the database of Burland and Burbidge (1985).

Note: the terms shaded are the methods that will be evaluated in Section 4.6.

3. Indirect (semi-empirical) methods based on elasticity theory where soil parameters (e.g. soil modulus) are estimated using empirical correlations. Since the 1970s, methods based on the theory of elasticity were developed where the soil modulus is determined either using empirical correlations with N_SPT (e.g. D'Appolonia et al. 1970; Parry 1971; Schultze and Sherif 1973; Oweis 1979; Burland and Burbidge 1985; Anagnostopoulos et al. 1991; Berardi and Lancellotta 1991) or empirical correlations with q_c (e.g. Schmertmann 1970; Schmertmann etal. 1978).

Note that direct methods were established typically using a limited number of load tests, and hence these methods could be site or soil specific. When these methods are applied to scenarios outside the scope of the calibration database, their performances are unknown. For indirect methods, Bowles (1997) highlighted two problems: (1) estimations of elasticity modulus and preconsolidation stress based on empirical correlations in which the uncertainty is generally higher than the soil strength parameters, as shown by the statistics in Phoon and Kulhawy (1999) and (2) determination of a stress profile in the underlying soil because of footing pressure based on the theory of elasticity where one of the most common methods is the Boussinesq’s equation (Bowles 1997). More recently, alternate data-driven methods (e.g. neural network) have been applied for settlement calculation (e.g. Shahin et al. 2002, 2005; Rezania and Javadi 2007).

In addition to the Category 1 and 2 methods introduced in Sections 4.3 and 4.4, one notable development is the use of advanced and mechanically consistent numerical methods to model the behaviour of offshore shallow foundations (e.g. steel mudmats, concrete or steel buckets, concrete gravity base foundations and skirted foundations) under various loading scenarios (e.g. simple vertical and concentric loading and more complex loading, such as six-degree-of-freedom loading). These numerical methods include small- strain finite element (SSFE) analyses (Potts and Zdravkovic 1999, 2001), SSFE with a press-replace method (e.g. Tehrani et al. 2016; Lim et al. 2018), remeshing and interpolation technique with small strain approach (Hu and Randolph 1998a, b) and large deformation finite element (LDFE) analysis (e.g. Zhou and Randolph 2006; Wang et al. 2010; Chatterjee et al. 2014), which are classified as Category 3 methods. In his Rankine lecture, Potts (2003) stated that the development of numerical analysis and its application have provided geotechnical engineers with an extremely powerful tool; however, the use of such analysis is still not widespread. Part of the reason for this is a lack of education and of guidance, especially from codes of practice, as to the appropriate use of such methods of analysis. The development ofthe next generation of Eurocode 7 Part 1 (EN 1997-l:202x) was described in one of the series of papers on the theme “Tomorrow’s Geotechnical Toolbox” (Franzen et al. 2019). One of the key changes from the previous version of EN 1997-1 - elaboration on the use of numerical methods within

Eurocode 7 - was discussed in detail by Lees (2019). The proposed clauses cover geotechnical design and limit state verification using advanced numerical methods. If they are adopted in the final version of EN 1997-l:202x, it will be the first geotechnical design code with a set of rules specifically intended for design using advanced numerical methods.

Nowadays, it can be clearly observed that numerical analysis has become increasingly indispensable, particularly in offshore shallow foundations. Generally, model tests with particle image velocimetry (PIV) (White et al. 2003) has provided a valuable tool for investigating soil flow mechanisms under various loading or displacement conditions, but they could be insufficient for quantification purposes, as the input parameters cannot be varied systematically. Numerical methods have provided a powerful tool for parametric analyses to quantify the effects of input parameters. The combination of model test and numerical tool significantly enhances our knowledge and understanding of soil-foundation interaction behaviour that allows for the development and verification of simplified but reasonable geotechnical design models. Such progress can be found in offshore spudcan foundations that will be presented in Chapter 5.