Figure 1

Figure 2
![Stiffness parameters of standard drained triaxial test results: (1) for the MC model, (2) for the HS model, (3) for the HSS model [66]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKH73ILKSZ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T041345Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIDd8oPR8wWjKXVIO3k42LuX1OJVmUFvcFoigskBmjdJmAiEAkNoyg3IlgsXrRF1fybmFsTLhL9hLjRhmN72fz3%2Fc40QqxAUIiP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDPS%2BYmUXCmYo%2F9X87CqYBUf5uGGpMrDKw63iSbr9MZeZ3xAC6HNs3cufs1M%2BMduSQT4R4OL2VuyPoqpuQPOfH1RNMY9vlAGPs3C0rvn69PHdq0LFzsBpaPBXwWnGjLqp5jD0yDThbnbIantll%2B7Wi2JQC6cHKTxEwEkSfU%2BEW%2BPm1JG1hyLOKTTvBfktQzLAZ73X%2F3mNUO4LPgs94yByNZfjAuEAZ1UlS80nqBIOtyBcpjCqOH08WfHSXo7ze%2B1k%2F52zJFEWVfRNrb02j68nzy7tYEgmJoJkaVSQ1e66Jdb%2BoeLlJbwMBU60yY0aqqybGlbIt5xHm0cGC0VTgdbFrjbe5s4gbtGe94e9KHGc%2BmIDCUnRMKI2TEylFpLVA1ZOeiG4B75i9d21bNhZoYIv3cI50T7Bv9b%2BN30HZm7U2oJqsx3yRgJHwSJ6OhSGvLYvdfMI7Hf%2B2UE1Q%2FKI2tBMu%2FJ8YMl6uZDrY7kL%2BwAH0%2FfDs5vNHc8ipiEXgMMAeDAppNuc39pxatIIUZRaCPDlcQNNGZ1KnVp1MoahyFUrZ4nr1I8h8FBBS%2BL3AEN2%2F68TLIvNeNqsQ%2B15Z5wkpuhZeKYiF%2BnA%2Fy8D8VHPPm9W0VIbLPOkrC3oPxht2jyfcu0iEii1z0MdOHI1%2BjIt3o8gZu%2BP7GjWtbK24gxy%2BA2BZP0D77G0sgLZUNU2SqEIuZWes3j%2BkwMA49zcyLudWZCU397n5ENuKuRfP4XZcmixl4mH%2BhKk4lyIQ0p3M7GSJANcU3M3u2YGHmHxn%2FQ1cyExePasgtQJAsXaSdV9ixb5wA85f0OsWbQrT6oxr4DLseh9PASkiaS9nRwqVkaXovtA8uY6o9CxA5yxIL0%2F7qA2lTI9A9ZbEfSZWn9wwZJcAbuEcej4qYJ%2BcB8w6ajezAY6sQH7vZ5wN%2F%2F02LX86gkr8s3zv6EN%2FyF4rWbYHnRIIXW5XTT%2BdPhYo49k%2FCjLSXvxQ2xhVxgXYjo4LdNO2vhIUMdnNOLYl249ciWBJe1mvM6UwGlCiJJLh15o9R%2BUl%2FQxl0TnwReb%2BE9uSAZxUsT%2Bt6TqbxIjMqEmL7J2TO53zRcuhUdQaRM4S%2FQdTLJm4%2FXP%2FzmMa6AKefqaq9PGR46iky2n%2FYDga5qfXU6kNrnU4NMP%2B9A%3D&X-Amz-Signature=f3a1a737090f4c010ab3789c77a0b4ceb4c9ad7cd56d3dcf9e979c265b71b700&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3
![Characteristic stiffness-strain behavior in logarithmic scale (after Atkinson and Sallfors [36] and Mair[76]) (Atkinson, 2000)[77].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKH73ILKSZ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T041345Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIDd8oPR8wWjKXVIO3k42LuX1OJVmUFvcFoigskBmjdJmAiEAkNoyg3IlgsXrRF1fybmFsTLhL9hLjRhmN72fz3%2Fc40QqxAUIiP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDPS%2BYmUXCmYo%2F9X87CqYBUf5uGGpMrDKw63iSbr9MZeZ3xAC6HNs3cufs1M%2BMduSQT4R4OL2VuyPoqpuQPOfH1RNMY9vlAGPs3C0rvn69PHdq0LFzsBpaPBXwWnGjLqp5jD0yDThbnbIantll%2B7Wi2JQC6cHKTxEwEkSfU%2BEW%2BPm1JG1hyLOKTTvBfktQzLAZ73X%2F3mNUO4LPgs94yByNZfjAuEAZ1UlS80nqBIOtyBcpjCqOH08WfHSXo7ze%2B1k%2F52zJFEWVfRNrb02j68nzy7tYEgmJoJkaVSQ1e66Jdb%2BoeLlJbwMBU60yY0aqqybGlbIt5xHm0cGC0VTgdbFrjbe5s4gbtGe94e9KHGc%2BmIDCUnRMKI2TEylFpLVA1ZOeiG4B75i9d21bNhZoYIv3cI50T7Bv9b%2BN30HZm7U2oJqsx3yRgJHwSJ6OhSGvLYvdfMI7Hf%2B2UE1Q%2FKI2tBMu%2FJ8YMl6uZDrY7kL%2BwAH0%2FfDs5vNHc8ipiEXgMMAeDAppNuc39pxatIIUZRaCPDlcQNNGZ1KnVp1MoahyFUrZ4nr1I8h8FBBS%2BL3AEN2%2F68TLIvNeNqsQ%2B15Z5wkpuhZeKYiF%2BnA%2Fy8D8VHPPm9W0VIbLPOkrC3oPxht2jyfcu0iEii1z0MdOHI1%2BjIt3o8gZu%2BP7GjWtbK24gxy%2BA2BZP0D77G0sgLZUNU2SqEIuZWes3j%2BkwMA49zcyLudWZCU397n5ENuKuRfP4XZcmixl4mH%2BhKk4lyIQ0p3M7GSJANcU3M3u2YGHmHxn%2FQ1cyExePasgtQJAsXaSdV9ixb5wA85f0OsWbQrT6oxr4DLseh9PASkiaS9nRwqVkaXovtA8uY6o9CxA5yxIL0%2F7qA2lTI9A9ZbEfSZWn9wwZJcAbuEcej4qYJ%2BcB8w6ajezAY6sQH7vZ5wN%2F%2F02LX86gkr8s3zv6EN%2FyF4rWbYHnRIIXW5XTT%2BdPhYo49k%2FCjLSXvxQ2xhVxgXYjo4LdNO2vhIUMdnNOLYl249ciWBJe1mvM6UwGlCiJJLh15o9R%2BUl%2FQxl0TnwReb%2BE9uSAZxUsT%2Bt6TqbxIjMqEmL7J2TO53zRcuhUdQaRM4S%2FQdTLJm4%2FXP%2FzmMa6AKefqaq9PGR46iky2n%2FYDga5qfXU6kNrnU4NMP%2B9A%3D&X-Amz-Signature=cc5f64eedced4006baf940181cf18aa8a520b5111498d706448c0bde9cce59f2&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9
![Nodal displacement vectors for the wharf supported piles (m)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_009.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKH73ILKSZ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T041345Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIDd8oPR8wWjKXVIO3k42LuX1OJVmUFvcFoigskBmjdJmAiEAkNoyg3IlgsXrRF1fybmFsTLhL9hLjRhmN72fz3%2Fc40QqxAUIiP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDPS%2BYmUXCmYo%2F9X87CqYBUf5uGGpMrDKw63iSbr9MZeZ3xAC6HNs3cufs1M%2BMduSQT4R4OL2VuyPoqpuQPOfH1RNMY9vlAGPs3C0rvn69PHdq0LFzsBpaPBXwWnGjLqp5jD0yDThbnbIantll%2B7Wi2JQC6cHKTxEwEkSfU%2BEW%2BPm1JG1hyLOKTTvBfktQzLAZ73X%2F3mNUO4LPgs94yByNZfjAuEAZ1UlS80nqBIOtyBcpjCqOH08WfHSXo7ze%2B1k%2F52zJFEWVfRNrb02j68nzy7tYEgmJoJkaVSQ1e66Jdb%2BoeLlJbwMBU60yY0aqqybGlbIt5xHm0cGC0VTgdbFrjbe5s4gbtGe94e9KHGc%2BmIDCUnRMKI2TEylFpLVA1ZOeiG4B75i9d21bNhZoYIv3cI50T7Bv9b%2BN30HZm7U2oJqsx3yRgJHwSJ6OhSGvLYvdfMI7Hf%2B2UE1Q%2FKI2tBMu%2FJ8YMl6uZDrY7kL%2BwAH0%2FfDs5vNHc8ipiEXgMMAeDAppNuc39pxatIIUZRaCPDlcQNNGZ1KnVp1MoahyFUrZ4nr1I8h8FBBS%2BL3AEN2%2F68TLIvNeNqsQ%2B15Z5wkpuhZeKYiF%2BnA%2Fy8D8VHPPm9W0VIbLPOkrC3oPxht2jyfcu0iEii1z0MdOHI1%2BjIt3o8gZu%2BP7GjWtbK24gxy%2BA2BZP0D77G0sgLZUNU2SqEIuZWes3j%2BkwMA49zcyLudWZCU397n5ENuKuRfP4XZcmixl4mH%2BhKk4lyIQ0p3M7GSJANcU3M3u2YGHmHxn%2FQ1cyExePasgtQJAsXaSdV9ixb5wA85f0OsWbQrT6oxr4DLseh9PASkiaS9nRwqVkaXovtA8uY6o9CxA5yxIL0%2F7qA2lTI9A9ZbEfSZWn9wwZJcAbuEcej4qYJ%2BcB8w6ajezAY6sQH7vZ5wN%2F%2F02LX86gkr8s3zv6EN%2FyF4rWbYHnRIIXW5XTT%2BdPhYo49k%2FCjLSXvxQ2xhVxgXYjo4LdNO2vhIUMdnNOLYl249ciWBJe1mvM6UwGlCiJJLh15o9R%2BUl%2FQxl0TnwReb%2BE9uSAZxUsT%2Bt6TqbxIjMqEmL7J2TO53zRcuhUdQaRM4S%2FQdTLJm4%2FXP%2FzmMa6AKefqaq9PGR46iky2n%2FYDga5qfXU6kNrnU4NMP%2B9A%3D&X-Amz-Signature=7e558534a8a6d269f2e54c5b22c6e497046f3081275381ac319a9c23639f03d8&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 10

Figure 11
![Total pore pressure contours (Pa)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_011.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKH73ILKSZ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T041345Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIDd8oPR8wWjKXVIO3k42LuX1OJVmUFvcFoigskBmjdJmAiEAkNoyg3IlgsXrRF1fybmFsTLhL9hLjRhmN72fz3%2Fc40QqxAUIiP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDPS%2BYmUXCmYo%2F9X87CqYBUf5uGGpMrDKw63iSbr9MZeZ3xAC6HNs3cufs1M%2BMduSQT4R4OL2VuyPoqpuQPOfH1RNMY9vlAGPs3C0rvn69PHdq0LFzsBpaPBXwWnGjLqp5jD0yDThbnbIantll%2B7Wi2JQC6cHKTxEwEkSfU%2BEW%2BPm1JG1hyLOKTTvBfktQzLAZ73X%2F3mNUO4LPgs94yByNZfjAuEAZ1UlS80nqBIOtyBcpjCqOH08WfHSXo7ze%2B1k%2F52zJFEWVfRNrb02j68nzy7tYEgmJoJkaVSQ1e66Jdb%2BoeLlJbwMBU60yY0aqqybGlbIt5xHm0cGC0VTgdbFrjbe5s4gbtGe94e9KHGc%2BmIDCUnRMKI2TEylFpLVA1ZOeiG4B75i9d21bNhZoYIv3cI50T7Bv9b%2BN30HZm7U2oJqsx3yRgJHwSJ6OhSGvLYvdfMI7Hf%2B2UE1Q%2FKI2tBMu%2FJ8YMl6uZDrY7kL%2BwAH0%2FfDs5vNHc8ipiEXgMMAeDAppNuc39pxatIIUZRaCPDlcQNNGZ1KnVp1MoahyFUrZ4nr1I8h8FBBS%2BL3AEN2%2F68TLIvNeNqsQ%2B15Z5wkpuhZeKYiF%2BnA%2Fy8D8VHPPm9W0VIbLPOkrC3oPxht2jyfcu0iEii1z0MdOHI1%2BjIt3o8gZu%2BP7GjWtbK24gxy%2BA2BZP0D77G0sgLZUNU2SqEIuZWes3j%2BkwMA49zcyLudWZCU397n5ENuKuRfP4XZcmixl4mH%2BhKk4lyIQ0p3M7GSJANcU3M3u2YGHmHxn%2FQ1cyExePasgtQJAsXaSdV9ixb5wA85f0OsWbQrT6oxr4DLseh9PASkiaS9nRwqVkaXovtA8uY6o9CxA5yxIL0%2F7qA2lTI9A9ZbEfSZWn9wwZJcAbuEcej4qYJ%2BcB8w6ajezAY6sQH7vZ5wN%2F%2F02LX86gkr8s3zv6EN%2FyF4rWbYHnRIIXW5XTT%2BdPhYo49k%2FCjLSXvxQ2xhVxgXYjo4LdNO2vhIUMdnNOLYl249ciWBJe1mvM6UwGlCiJJLh15o9R%2BUl%2FQxl0TnwReb%2BE9uSAZxUsT%2Bt6TqbxIjMqEmL7J2TO53zRcuhUdQaRM4S%2FQdTLJm4%2FXP%2FzmMa6AKefqaq9PGR46iky2n%2FYDga5qfXU6kNrnU4NMP%2B9A%3D&X-Amz-Signature=09608dd3384bb4d018f1706c0b328def4ae1a3eb17938ec1a3c7f683ca46f902&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 12

Soil parameters used for HS model
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 | |
| kN/m2 | 4.826 × 104 | 1.310 × 104 | 1.786 × 104 | |
| kN/m2 | 1.810 × 104 | 4.914 × 104 | 6.696 × 104 | |
| Pref | kN/m2 | 100 | 100 | 100 |
| M | - | 0.5 | 0.5 | 0.5 |
| - | 0.3982 | 0.4524 | 0.2929 | |
| Rf | - | 0.9 | 0.9 | 0.9 |
Additional input parameters of HSS model_
| Parameters | Unit | Dense sand | Loose sand | Rockӿll |
|---|---|---|---|---|
| γ0.7 | - | 4.918 × 10–4 | 3.629 × 10–4 | 4.246 × 10–4 |
| kN/m2 | 1.051 × 105 | 9.108 × 104 | 1.038 × 105 |
Lateral and vertical displacement time histories at the top and at the toe of the rock dike_
| Model | Lateral and vertical displacements at the rock dike top | Lateral and vertical displacements at the rock dike toe |
|---|---|---|
| MC | ||
| HS | ||
| HSS |
Soil parameters used for the MC model_
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| φ | ° | 37 | 33.2 | 45 |
| ψ | ° | 21 | 7 | 0 |
| C | kN/m2 | 0.5 | 0.5 | 15 |
| ν | - | 0.3 | 0.3 | 0.2 |
| E | kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 |
Pile and deck properties_
| Parameters | Unit | Pile | Deck |
|---|---|---|---|
| EA | kN/m | 162.75 × 104 | 17.85 × 106 |
| EI | kN.m2/m | 70.49 × 103 | 96.724 × 103 |
| w | kN/m/m | 0.633 | 6.9436 |
| ν | - | 0.2 | 0.2 |